Implementation of P434

README.md

@@ -5,14 +5,48 @@ SIKE based on field p503 (Round2).
 
 ## Speed
 
+### P503
+
+```
+> go test -run=. -bench=. -benchmem
+goos: linux
+goarch: amd64
+pkg: github.com/henrydcase/go-sike-p503/p503
+BenchmarkKeygen-4            100      10448291 ns/op           0 B/op          0 allocs/op
+BenchmarkEncaps-4            100      17250470 ns/op        1344 B/op          3 allocs/op
+BenchmarkDecaps-4            100      18755075 ns/op        1358 B/op          3 allocs/op
+PASS
+ok      github.com/henrydcase/go-sike-p503/p503 12.676s
+```
+
+### P434
 ```
-> go test -run=. -bench=. -benchmem  
+> go test -run=. -bench=. -benchmem
 goos: linux
 goarch: amd64
-pkg: github.com/henrydcase/go-sike-p503
-BenchmarkKeygen-4            100      12235566 ns/op           0 B/op          0 allocs/op
-BenchmarkEncaps-4            100      20430183 ns/op           0 B/op          0 allocs/op
-BenchmarkDecaps-4             50      23946060 ns/op           2 B/op          0 allocs/op
+pkg: github.com/henrydcase/go-sike-p503/p434
+BenchmarkKeygen-4            200       7298860 ns/op           0 B/op          0 allocs/op
+BenchmarkEncaps-4            100      12008715 ns/op        1344 B/op          3 allocs/op
+BenchmarkDecaps-4            100      12950648 ns/op        1358 B/op          3 allocs/op
 PASS
-ok      github.com/henrydcase/go-sike-p503  13.725s
+ok      github.com/henrydcase/go-sike-p503/p434 9.880s
+```
+
+
+### p434 vs p503
+```
+benchmark             old ns/op     new ns/op     delta
+BenchmarkKeygen-4     10552847      7471517       -29.20%
+BenchmarkEncaps-4     17375489      11897130      -31.53%
+BenchmarkDecaps-4     18927683      12991795      -31.36%
+
+benchmark             old allocs     new allocs     delta
+BenchmarkKeygen-4     0              0              +0.00%
+BenchmarkEncaps-4     3              3              +0.00%
+BenchmarkDecaps-4     3              3              +0.00%
+
+benchmark             old bytes     new bytes     delta
+BenchmarkKeygen-4     0             0             +0.00%
+BenchmarkEncaps-4     1344          1344          +0.00%
+BenchmarkDecaps-4     1358          1358          +0.00%
 ```

p434/arith.go

@@ -0,0 +1,138 @@
+package sike
+
+// Set dest = x^((p-3)/4).  If x is square, this is 1/sqrt(x).
+// Uses variation of sliding-window algorithm from with window size
+// of 5 and least to most significant bit sliding (left-to-right)
+// See HAC 14.85 for general description.
+//
+// Allowed to overlap x with dest.
+// All values in Montgomery domains
+// Set dest = x^(2^k), for k >= 1, by repeated squarings.
+func p34(dest, x *Fp) {
+	var lookup [16]Fp
+
+	// This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy)
+	// multiplications.
+	powStrategy := []uint8{3, 10, 7, 5, 6, 5, 3, 8, 4, 7, 5, 6, 4, 5, 9, 6, 3, 11, 5, 5, 2, 8, 4, 7, 7, 8, 5, 6, 4, 8, 5, 2, 10, 6, 5, 4, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1}
+	mulStrategy := []uint8{2, 15, 9, 8, 14, 12, 2, 8, 5, 15, 8, 15, 6, 6, 3, 2, 0, 10, 9, 13, 1, 12, 3, 7, 1, 10, 8, 11, 2, 15, 14, 1, 11, 12, 14, 3, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0}
+	initialMul := uint8(8)
+
+	// Precompute lookup table of odd multiples of x for window
+	// size k=5.
+	var xx Fp
+	fpMulRdc(&xx, x, x)
+	lookup[0] = *x
+	for i := 1; i < 16; i++ {
+		fpMulRdc(&lookup[i], &lookup[i-1], &xx)
+	}
+
+	// Now lookup = {x, x^3, x^5, ... }
+	// so that lookup[i] = x^{2*i + 1}
+	// so that lookup[k/2] = x^k, for odd k
+	*dest = lookup[initialMul]
+	for i := uint8(0); i < uint8(len(powStrategy)); i++ {
+		fpMulRdc(dest, dest, dest)
+		for j := uint8(1); j < powStrategy[i]; j++ {
+			fpMulRdc(dest, dest, dest)
+		}
+		fpMulRdc(dest, dest, &lookup[mulStrategy[i]])
+	}
+}
+
+func add(dest, lhs, rhs *Fp2) {
+	fpAddRdc(&dest.A, &lhs.A, &rhs.A)
+	fpAddRdc(&dest.B, &lhs.B, &rhs.B)
+}
+
+func sub(dest, lhs, rhs *Fp2) {
+	fpSubRdc(&dest.A, &lhs.A, &rhs.A)
+	fpSubRdc(&dest.B, &lhs.B, &rhs.B)
+}
+
+func mul(dest, lhs, rhs *Fp2) {
+	// Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b).
+	a := &lhs.A
+	b := &lhs.B
+	c := &rhs.A
+	d := &rhs.B
+
+	// We want to compute
+	//
+	// (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i
+	//
+	// Use Karatsuba's trick: note that
+	//
+	// (b - a)*(c - d) = (b*c + a*d) - a*c - b*d
+	//
+	// so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d.
+
+	var ac, bd FpX2
+	fpMul(&ac, a, c) // = a*c*R*R
+	fpMul(&bd, b, d) // = b*d*R*R
+
+	var b_minus_a, c_minus_d Fp
+	fpSubRdc(&b_minus_a, b, a) // = (b-a)*R
+	fpSubRdc(&c_minus_d, c, d) // = (c-d)*R
+
+	var ad_plus_bc FpX2
+	fpMul(&ad_plus_bc, &b_minus_a, &c_minus_d) // = (b-a)*(c-d)*R*R
+	fp2Add(&ad_plus_bc, &ad_plus_bc, &ac)      // = ((b-a)*(c-d) + a*c)*R*R
+	fp2Add(&ad_plus_bc, &ad_plus_bc, &bd)      // = ((b-a)*(c-d) + a*c + b*d)*R*R
+
+	fpMontRdc(&dest.B, &ad_plus_bc) // = (a*d + b*c)*R mod p
+
+	var ac_minus_bd FpX2
+	fp2Sub(&ac_minus_bd, &ac, &bd)   // = (a*c - b*d)*R*R
+	fpMontRdc(&dest.A, &ac_minus_bd) // = (a*c - b*d)*R mod p
+}
+
+func inv(dest, x *Fp2) {
+	var e1, e2 FpX2
+	var f1, f2 Fp
+
+	fpMul(&e1, &x.A, &x.A) // = a*a*R*R
+	fpMul(&e2, &x.B, &x.B) // = b*b*R*R
+	fp2Add(&e1, &e1, &e2)  // = (a^2 + b^2)*R*R
+	fpMontRdc(&f1, &e1)    // = (a^2 + b^2)*R mod p
+	// Now f1 = a^2 + b^2
+
+	fpMulRdc(&f2, &f1, &f1)
+	p34(&f2, &f2)
+	fpMulRdc(&f2, &f2, &f2)
+	fpMulRdc(&f2, &f2, &f1)
+
+	fpMul(&e1, &x.A, &f2)
+	fpMontRdc(&dest.A, &e1)
+
+	fpSubRdc(&f1, &Fp{}, &x.B)
+	fpMul(&e1, &f1, &f2)
+	fpMontRdc(&dest.B, &e1)
+}
+
+func sqr(dest, x *Fp2) {
+	var a2, aPlusB, aMinusB Fp
+	var a2MinB2, ab2 FpX2
+
+	a := &x.A
+	b := &x.B
+
+	// (a + bi)*(a + bi) = (a^2 - b^2) + 2abi.
+	fpAddRdc(&a2, a, a)                // = a*R + a*R = 2*a*R
+	fpAddRdc(&aPlusB, a, b)            // = a*R + b*R = (a+b)*R
+	fpSubRdc(&aMinusB, a, b)           // = a*R - b*R = (a-b)*R
+	fpMul(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R
+	fpMul(&ab2, &a2, b)                // = 2*a*b*R*R
+	fpMontRdc(&dest.A, &a2MinB2)       // = (a^2 - b^2)*R mod p
+	fpMontRdc(&dest.B, &ab2)           // = 2*a*b*R mod p
+}
+
+// In case choice == 1, performs following swap in constant time:
+// 	xPx <-> xQx
+//	xPz <-> xQz
+// Otherwise returns xPx, xPz, xQx, xQz unchanged
+func condSwap(xPx, xPz, xQx, xQz *Fp2, choice uint8) {
+	fpSwapCond(&xPx.A, &xQx.A, choice)
+	fpSwapCond(&xPx.B, &xQx.B, choice)
+	fpSwapCond(&xPz.A, &xQz.A, choice)
+	fpSwapCond(&xPz.B, &xQz.B, choice)
+}

p434/consts.go

@@ -0,0 +1,183 @@
+package sike
+
+const (
+	// Number of uint64 limbs used to store field element
+	FP_WORDS = 7
+)
+
+// Used internally by this package
+// -------------------------------
+
+var p = Fp{
+	0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF,
+	0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x2341F27177344,
+}
+
+// 2*p434
+var pX2 = Fp{
+	0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF,
+	0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x4683E4E2EE688,
+}
+
+// p434 + 1
+var p1 = Fp{
+	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000,
+	0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344,
+}
+
+// R^2=(2^512)^2 mod p
+var pR2 = Fp{
+	0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B,
+	0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A,
+}
+
+// 1/2 * R mod p
+var half = Fp2{
+	A: Fp{
+		0x0000000000003A16, 0x0000000000000000, 0x0000000000000000, 0x5C87FA027E000000,
+		0x6C00D27DAACFD66A, 0x74992A2A2FBBA086, 0x0000767753DE976D},
+}
+
+// 1*R mod p
+var one = Fp2{
+	A: Fp{
+		0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000,
+		0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA},
+}
+
+// 6*R mod p
+var six = Fp2{
+	A: Fp{
+		0x000000000002B90A, 0x0000000000000000, 0x0000000000000000, 0x5ADCCB2822000000,
+		0x187D24F39F0CAFB4, 0x9D353A4D394145A0, 0x00012559A0403298},
+}
+
+var Params SidhParams
+
+func init() {
+	Params = SidhParams{
+		// SIDH public key byte size.
+		PublicKeySize: 330,
+		// SIDH shared secret byte size.
+		SharedSecretSize: 110,
+		InitCurve: ProjectiveCurveParameters{
+			A: six,
+			C: one,
+		},
+		A: DomainParams{
+			// The x-coordinate of PA
+			Affine_P: Fp2{
+				A: Fp{
+					0x05ADF455C5C345BF, 0x91935C5CC767AC2B, 0xAFE4E879951F0257, 0x70E792DC89FA27B1,
+					0xF797F526BB48C8CD, 0x2181DB6131AF621F, 0x00000A1C08B1ECC4,
+				},
+				B: Fp{
+					0x74840EB87CDA7788, 0x2971AA0ECF9F9D0B, 0xCB5732BDF41715D5, 0x8CD8E51F7AACFFAA,
+					0xA7F424730D7E419F, 0xD671EB919A179E8C, 0x0000FFA26C5A924A,
+				},
+			},
+			// The x-coordinate of QA
+			Affine_Q: Fp2{
+				A: Fp{
+					0xFEC6E64588B7273B, 0xD2A626D74CBBF1C6, 0xF8F58F07A78098C7, 0xE23941F470841B03,
+					0x1B63EDA2045538DD, 0x735CFEB0FFD49215, 0x0001C4CB77542876,
+				},
+				B: Fp{
+					0xADB0F733C17FFDD6, 0x6AFFBD037DA0A050, 0x680EC43DB144E02F, 0x1E2E5D5FF524E374,
+					0xE2DDA115260E2995, 0xA6E4B552E2EDE508, 0x00018ECCDDF4B53E,
+				},
+			},
+			// The x-coordinate of RA = PA-QA
+			Affine_R: Fp2{
+				A: Fp{
+					0x01BA4DB518CD6C7D, 0x2CB0251FE3CC0611, 0x259B0C6949A9121B, 0x60E17AC16D2F82AD,
+					0x3AA41F1CE175D92D, 0x413FBE6A9B9BC4F3, 0x00022A81D8D55643,
+				},
+				B: Fp{
+					0xB8ADBC70FC82E54A, 0xEF9CDDB0D5FADDED, 0x5820C734C80096A0, 0x7799994BAA96E0E4,
+					0x044961599E379AF8, 0xDB2B94FBF09F27E2, 0x0000B87FC716C0C6,
+				},
+			},
+			// Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1
+			SecretBitLen: 216,
+			// SecretBitLen in bytes.
+			SecretByteLen: 28,
+			// 2-torsion group computation strategy
+			IsogenyStrategy: []uint32{
+				0x30, 0x1C, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
+				0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04,
+				0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
+				0x02, 0x01, 0x01, 0x0D, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02,
+				0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x04,
+				0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,
+				0x15, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
+				0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01,
+				0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03,
+				0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04,
+				0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01},
+		},
+		B: DomainParams{
+			// The x-coordinate of PB
+			Affine_P: Fp2{
+				A: Fp{
+					0x6E5497556EDD48A3, 0x2A61B501546F1C05, 0xEB919446D049887D, 0x5864A4A69D450C4F,
+					0xB883F276A6490D2B, 0x22CC287022D5F5B9, 0x0001BED4772E551F,
+				},
+				B: Fp{
+					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
+					0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
+				},
+			},
+			// The x-coordinate of QB
+			Affine_Q: Fp2{
+				A: Fp{
+					0xFAE2A3F93D8B6B8E, 0x494871F51700FE1C, 0xEF1A94228413C27C, 0x498FF4A4AF60BD62,
+					0xB00AD2A708267E8A, 0xF4328294E017837F, 0x000034080181D8AE,
+				},
+				B: Fp{
+					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
+					0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
+				},
+			},
+			// The x-coordinate of RB = PB - QB
+			Affine_R: Fp2{
+				A: Fp{
+					0x283B34FAFEFDC8E4, 0x9208F44977C3E647, 0x7DEAE962816F4E9A, 0x68A2BA8AA262EC9D,
+					0x8176F112EA43F45B, 0x02106D022634F504, 0x00007E8A50F02E37,
+				},
+				B: Fp{
+					0xB378B7C1DA22CCB1, 0x6D089C99AD1D9230, 0xEBE15711813E2369, 0x2B35A68239D48A53,
+					0x445F6FD138407C93, 0xBEF93B29A3F6B54B, 0x000173FA910377D3,
+				},
+			},
+			// Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1.
+			SecretBitLen: 217,
+			// SecretBitLen in bytes.
+			SecretByteLen: 28,
+			// 3-torsion group computation strategy
+			IsogenyStrategy: []uint32{
+				0x42, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01,
+				0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01,
+				0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02,
+				0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10,
+				0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
+				0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01,
+				0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
+				0x01, 0x20, 0x10, 0x08, 0x04, 0x03, 0x01, 0x01, 0x01, 0x01,
+				0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
+				0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
+				0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01,
+				0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
+				0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
+				0x02, 0x01, 0x01, 0x02, 0x01, 0x01},
+		},
+		OneFp2:  one,
+		HalfFp2: half,
+		MsgLen:  16,
+		// SIKEp434 provides 128 bit of classical security ([SIKE], 5.1)
+		KemSize: 16,
+		// ceil(434+7/8)
+		Bytelen:        55,
+		CiphertextSize: 16 + 330,
+	}
+}

p434/curve.go

@@ -0,0 +1,386 @@
+package sike
+
+// Stores isogeny 3 curve constants
+type isogeny3 struct {
+	K1 Fp2
+	K2 Fp2
+}
+
+// Stores isogeny 4 curve constants
+type isogeny4 struct {
+	isogeny3
+	K3 Fp2
+}
+
+// Helper function for RightToLeftLadder(). Returns A+2C / 4.
+func calcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) {
+	var tmp Fp2
+
+	// 2C
+	add(&tmp, &cparams.C, &cparams.C)
+	// A+2C
+	add(&ret, &cparams.A, &tmp)
+	// 1/4C
+	add(&tmp, &tmp, &tmp)
+	inv(&tmp, &tmp)
+	// A+2C/4C
+	mul(&ret, &ret, &tmp)
+	return
+}
+
+// Converts values in x.A and x.B to Montgomery domain
+// x.A = x.A * R mod p
+// x.B = x.B * R mod p
+// Performs v = v*R^2*R^(-1) mod p, for both x.A and x.B
+func toMontDomain(x *Fp2) {
+	var aRR FpX2
+
+	// convert to montgomery domain
+	fpMul(&aRR, &x.A, &pR2) // = a*R*R
+	fpMontRdc(&x.A, &aRR)   // = a*R mod p
+	fpMul(&aRR, &x.B, &pR2)
+	fpMontRdc(&x.B, &aRR)
+}
+
+// Converts values in x.A and x.B from Montgomery domain
+// a = x.A mod p
+// b = x.B mod p
+//
+// After returning from the call x is not modified.
+func fromMontDomain(x *Fp2, out *Fp2) {
+	var aR FpX2
+
+	// convert from montgomery domain
+	copy(aR[:], x.A[:])
+	fpMontRdc(&out.A, &aR) // = a mod p in [0, 2p)
+	fpRdcP(&out.A)         // = a mod p in [0, p)
+	for i := range aR {
+		aR[i] = 0
+	}
+	copy(aR[:], x.B[:])
+	fpMontRdc(&out.B, &aR)
+	fpRdcP(&out.B)
+}
+
+// Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result
+// is returned in 'j'. Implementation corresponds to Algorithm 9 from SIKE.
+func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) {
+	var t0, t1 Fp2
+
+	sqr(j, &cparams.A)   // j  = A^2
+	sqr(&t1, &cparams.C) // t1 = C^2
+	add(&t0, &t1, &t1)   // t0 = t1 + t1
+	sub(&t0, j, &t0)     // t0 = j - t0
+	sub(&t0, &t0, &t1)   // t0 = t0 - t1
+	sub(j, &t0, &t1)     // t0 = t0 - t1
+	sqr(&t1, &t1)        // t1 = t1^2
+	mul(j, j, &t1)       // j = j * t1
+	add(&t0, &t0, &t0)   // t0 = t0 + t0
+	add(&t0, &t0, &t0)   // t0 = t0 + t0
+	sqr(&t1, &t0)        // t1 = t0^2
+	mul(&t0, &t0, &t1)   // t0 = t0 * t1
+	add(&t0, &t0, &t0)   // t0 = t0 + t0
+	add(&t0, &t0, &t0)   // t0 = t0 + t0
+	inv(j, j)            // j  = 1/j
+	mul(j, &t0, j)       // j  = t0 * j
+}
+
+// Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function
+// recorvers projective coordinate A of a curve. This is Algorithm 10 from SIKE.
+func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) {
+	var t0, t1 Fp2
+
+	add(&t1, xp, xq)                        // t1 = Xp + Xq
+	mul(&t0, xp, xq)                        // t0 = Xp * Xq
+	mul(&curve.A, xr, &t1)                  // A  = X(q-p) * t1
+	add(&curve.A, &curve.A, &t0)            // A  = A + t0
+	mul(&t0, &t0, xr)                       // t0 = t0 * X(q-p)
+	sub(&curve.A, &curve.A, &Params.OneFp2) // A  = A - 1
+	add(&t0, &t0, &t0)                      // t0 = t0 + t0
+	add(&t1, &t1, xr)                       // t1 = t1 + X(q-p)
+	add(&t0, &t0, &t0)                      // t0 = t0 + t0
+	sqr(&curve.A, &curve.A)                 // A  = A^2
+	inv(&t0, &t0)                           // t0 = 1/t0
+	mul(&curve.A, &curve.A, &t0)            // A  = A * t0
+	sub(&curve.A, &curve.A, &t1)            // A  = A - t1
+}
+
+// Computes equivalence (A:C) ~ (A+2C : A-2C)
+func ToEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv {
+	var coef CurveCoefficientsEquiv
+	var c2 Fp2
+
+	add(&c2, &cparams.C, &cparams.C)
+	// A24p = A+2*C
+	add(&coef.A, &cparams.A, &c2)
+	// A24m = A-2*C
+	sub(&coef.C, &cparams.A, &c2)
+	return coef
+}
+
+// Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C).
+func FromEquiv3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) {
+	add(&cparams.A, &coefEq.A, &coefEq.C)
+	// cparams.A = 2*(A+2C+A-2C) = 4A
+	add(&cparams.A, &cparams.A, &cparams.A)
+	// cparams.C = (A+2C-A+2C) = 4C
+	sub(&cparams.C, &coefEq.A, &coefEq.C)
+	return
+}
+
+// Computes equivalence (A:C) ~ (A+2C : 4C)
+func ToEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv {
+	var coefEq CurveCoefficientsEquiv
+
+	add(&coefEq.C, &cparams.C, &cparams.C)
+	// A24p = A+2C
+	add(&coefEq.A, &cparams.A, &coefEq.C)
+	// C24 = 4*C
+	add(&coefEq.C, &coefEq.C, &coefEq.C)
+	return coefEq
+}
+
+// Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C).
+func FromEquiv4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) {
+	// cparams.C = (4C)*1/2=2C
+	mul(&cparams.C, &coefEq.C, &Params.HalfFp2)
+	// cparams.A = A+2C - 2C = A
+	sub(&cparams.A, &coefEq.A, &cparams.C)
+	// cparams.C = 2C * 1/2 = C
+	mul(&cparams.C, &cparams.C, &Params.HalfFp2)
+	return
+}
+
+// Combined coordinate doubling and differential addition. Takes projective points
+// P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E.
+// Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE
+func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) {
+	var t0, t1, t2 Fp2
+	xQmP, zQmP := &QmP.X, &QmP.Z
+	xPaQ, zPaQ := &PaQ.X, &PaQ.Z
+	x2P, z2P := &dblP.X, &dblP.Z
+	xP, zP := &P.X, &P.Z
+	xQ, zQ := &Q.X, &Q.Z
+
+	add(&t0, xP, zP)      // t0   = Xp+Zp
+	sub(&t1, xP, zP)      // t1   = Xp-Zp
+	sqr(x2P, &t0)         // 2P.X = t0^2
+	sub(&t2, xQ, zQ)      // t2   = Xq-Zq
+	add(xPaQ, xQ, zQ)     // Xp+q = Xq+Zq
+	mul(&t0, &t0, &t2)    // t0   = t0 * t2
+	mul(z2P, &t1, &t1)    // 2P.Z = t1 * t1
+	mul(&t1, &t1, xPaQ)   // t1   = t1 * Xp+q
+	sub(&t2, x2P, z2P)    // t2   = 2P.X - 2P.Z
+	mul(x2P, x2P, z2P)    // 2P.X = 2P.X * 2P.Z
+	mul(xPaQ, a24, &t2)   // Xp+q = A24 * t2
+	sub(zPaQ, &t0, &t1)   // Zp+q = t0 - t1
+	add(z2P, xPaQ, z2P)   // 2P.Z = Xp+q + 2P.Z
+	add(xPaQ, &t0, &t1)   // Xp+q = t0 + t1
+	mul(z2P, z2P, &t2)    // 2P.Z = 2P.Z * t2
+	sqr(zPaQ, zPaQ)       // Zp+q = Zp+q ^ 2
+	sqr(xPaQ, xPaQ)       // Xp+q = Xp+q ^ 2
+	mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q
+	mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q
+	return
+}
+
+// Given the curve parameters, xP = x(P), computes xP = x([2^k]P)
+// Safe to overlap xP, x2P.
+func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) {
+	var t0, t1 Fp2
+
+	x, z := &xP.X, &xP.Z
+	for i := uint32(0); i < k; i++ {
+		sub(&t0, x, z)           // t0  = Xp - Zp
+		add(&t1, x, z)           // t1  = Xp + Zp
+		sqr(&t0, &t0)            // t0  = t0 ^ 2
+		sqr(&t1, &t1)            // t1  = t1 ^ 2
+		mul(z, &params.C, &t0)   // Z2p = C24 * t0
+		mul(x, z, &t1)           // X2p = Z2p * t1
+		sub(&t1, &t1, &t0)       // t1  = t1 - t0
+		mul(&t0, &params.A, &t1) // t0  = A24+ * t1
+		add(z, z, &t0)           // Z2p = Z2p + t0
+		mul(z, z, &t1)           // Zp  = Z2p * t1
+	}
+}
+
+// Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P).
+//
+// Safe to overlap xP, xR.
+func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) {
+	var t0, t1, t2, t3, t4, t5, t6 Fp2
+
+	x, z := &xP.X, &xP.Z
+	for i := uint32(0); i < k; i++ {
+		sub(&t0, x, z)           // t0  = Xp - Zp
+		sqr(&t2, &t0)            // t2  = t0^2
+		add(&t1, x, z)           // t1  = Xp + Zp
+		sqr(&t3, &t1)            // t3  = t1^2
+		add(&t4, &t1, &t0)       // t4  = t1 + t0
+		sub(&t0, &t1, &t0)       // t0  = t1 - t0
+		sqr(&t1, &t4)            // t1  = t4^2
+		sub(&t1, &t1, &t3)       // t1  = t1 - t3
+		sub(&t1, &t1, &t2)       // t1  = t1 - t2
+		mul(&t5, &t3, &params.A) // t5  = t3 * A24+
+		mul(&t3, &t3, &t5)       // t3  = t5 * t3
+		mul(&t6, &t2, &params.C) // t6  = t2 * A24-
+		mul(&t2, &t2, &t6)       // t2  = t2 * t6
+		sub(&t3, &t2, &t3)       // t3  = t2 - t3
+		sub(&t2, &t5, &t6)       // t2  = t5 - t6
+		mul(&t1, &t2, &t1)       // t1  = t2 * t1
+		add(&t2, &t3, &t1)       // t2  = t3 + t1
+		sqr(&t2, &t2)            // t2  = t2^2
+		mul(x, &t2, &t4)         // X3p = t2 * t4
+		sub(&t1, &t3, &t1)       // t1  = t3 - t1
+		sqr(&t1, &t1)            // t1  = t1^2
+		mul(z, &t1, &t0)         // Z3p = t1 * t0
+	}
+}
+
+// Set (y1, y2, y3)  = (1/x1, 1/x2, 1/x3).
+//
+// All xi, yi must be distinct.
+func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) {
+	var x1x2, t Fp2
+
+	mul(&x1x2, x1, x2) // x1*x2
+	mul(&t, &x1x2, x3) // 1/(x1*x2*x3)
+	inv(&t, &t)
+	mul(y1, &t, x2) // 1/x1
+	mul(y1, y1, x3)
+	mul(y2, &t, x1) // 1/x2
+	mul(y2, y2, x3)
+	mul(y3, &t, &x1x2) // 1/x3
+}
+
+// ScalarMul3Pt is a right-to-left point multiplication that given the
+// x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P.
+// nbits must be smaller or equal to len(scalar).
+func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint {
+	var R0, R2, R1 ProjectivePoint
+	aPlus2Over4 := calcAplus2Over4(cparams)
+	R1 = *P
+	R2 = *PmQ
+	R0 = *Q
+
+	// Iterate over the bits of the scalar, bottom to top
+	prevBit := uint8(0)
+	for i := uint(0); i < nbits; i++ {
+		bit := (scalar[i>>3] >> (i & 7) & 1)
+		swap := prevBit ^ bit
+		prevBit = bit
+		condSwap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap)
+		R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4)
+	}
+	condSwap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit)
+	return R1
+}
+
+// Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the
+// three-isogeny phi : E_(A:C) -> E_(A:C)/<P_3> = E_(A':C').
+//
+// Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C
+// Output: * Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/<P3>
+//         * isogeny phi with constants in F_p^2
+func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv {
+	var t0, t1, t2, t3, t4 Fp2
+	var coefEq CurveCoefficientsEquiv
+	var K1, K2 = &phi.K1, &phi.K2
+
+	sub(K1, &p.X, &p.Z)            // K1 = XP3 - ZP3
+	sqr(&t0, K1)                   // t0 = K1^2
+	add(K2, &p.X, &p.Z)            // K2 = XP3 + ZP3
+	sqr(&t1, K2)                   // t1 = K2^2
+	add(&t2, &t0, &t1)             // t2 = t0 + t1
+	add(&t3, K1, K2)               // t3 = K1 + K2
+	sqr(&t3, &t3)                  // t3 = t3^2
+	sub(&t3, &t3, &t2)             // t3 = t3 - t2
+	add(&t2, &t1, &t3)             // t2 = t1 + t3
+	add(&t3, &t3, &t0)             // t3 = t3 + t0
+	add(&t4, &t3, &t0)             // t4 = t3 + t0
+	add(&t4, &t4, &t4)             // t4 = t4 + t4
+	add(&t4, &t1, &t4)             // t4 = t1 + t4
+	mul(&coefEq.C, &t2, &t4)       // A24m = t2 * t4
+	add(&t4, &t1, &t2)             // t4 = t1 + t2
+	add(&t4, &t4, &t4)             // t4 = t4 + t4
+	add(&t4, &t0, &t4)             // t4 = t0 + t4
+	mul(&t4, &t3, &t4)             // t4 = t3 * t4
+	sub(&t0, &t4, &coefEq.C)       // t0 = t4 - A24m
+	add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0
+	return coefEq
+}
+
+// Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate
+// of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C').
+//
+// The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve
+// parameters are returned by the GenerateCurve function used to construct phi.
+func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) ProjectivePoint {
+	var t0, t1, t2 Fp2
+	var q ProjectivePoint
+	var K1, K2 = &phi.K1, &phi.K2
+	var px, pz = &p.X, &p.Z
+
+	add(&t0, px, pz)   // t0 = XQ + ZQ
+	sub(&t1, px, pz)   // t1 = XQ - ZQ
+	mul(&t0, K1, &t0)  // t2 = K1 * t0
+	mul(&t1, K2, &t1)  // t1 = K2 * t1
+	add(&t2, &t0, &t1) // t2 = t0 + t1
+	sub(&t0, &t1, &t0) // t0 = t1 - t0
+	sqr(&t2, &t2)      // t2 = t2 ^ 2
+	sqr(&t0, &t0)      // t0 = t0 ^ 2
+	mul(&q.X, px, &t2) // XQ'= XQ * t2
+	mul(&q.Z, pz, &t0) // ZQ'= ZQ * t0
+	return q
+}
+
+// Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the
+// four-isogeny phi : E_(A:C) -> E_(A:C)/<P_4> = E_(A':C').
+//
+// Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C
+// Output: * Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/<P4>
+//         * isogeny phi with constants in F_p^2
+func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv {
+	var coefEq CurveCoefficientsEquiv
+	var xp4, zp4 = &p.X, &p.Z
+	var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3
+
+	sub(K2, xp4, zp4)
+	add(K3, xp4, zp4)
+	sqr(K1, zp4)
+	add(K1, K1, K1)
+	sqr(&coefEq.C, K1)
+	add(K1, K1, K1)
+	sqr(&coefEq.A, xp4)
+	add(&coefEq.A, &coefEq.A, &coefEq.A)
+	sqr(&coefEq.A, &coefEq.A)
+	return coefEq
+}
+
+// Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate
+// of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C').
+//
+// Input: isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C
+// Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0
+func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) ProjectivePoint {
+	var t0, t1 Fp2
+	var q = *p
+	var xq, zq = &q.X, &q.Z
+	var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3
+
+	add(&t0, xq, zq)
+	sub(&t1, xq, zq)
+	mul(xq, &t0, K2)
+	mul(zq, &t1, K3)
+	mul(&t0, &t0, &t1)
+	mul(&t0, &t0, K1)
+	add(&t1, xq, zq)
+	sub(zq, xq, zq)
+	sqr(&t1, &t1)
+	sqr(zq, zq)
+	add(xq, &t0, &t1)
+	sub(&t0, zq, &t0)
+	mul(xq, xq, &t1)
+	mul(zq, zq, &t0)
+	return q
+}

p434/etc/PQCkemKAT_374.rsp

@@ -0,0 +1,702 @@
+# SIKEp434
+
+count = 0
+seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1
+pk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
+sk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
+ct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
+ss = 35F7F8FF388714DEDC41F139078CEDC9
+
+count = 1
+seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F
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+
+count = 7
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+
+count = 8
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+
+count = 9
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+count = 10
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+ct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
+ss = B49ABAAE30A790FECE54A3F113FD575B
+
+count = 11
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+ct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
+ss = A663DA396F96655AED1602ACFB1C83B3
+
+count = 12
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+
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+pk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
+sk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
+ct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
+ss = A5D8459E0B0C063FF5696743360F4186
+
+count = 24
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+ct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
+ss = D5D19932C9F4580ECB0EAAE0504526AC
+
+count = 25
+seed = AD1424E804F306C7FF513DA4C1E8D445AFCA7BC942FAC5C0B335733AAF70693712ECBDE26EA726EE0F9FD9D52A83B1A4
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+ct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
+ss = F777EF5840DD876797535F8122B2DFBA
+
+count = 26
+seed = 7C33CA0E987226C8524DD56C811FA4D1CCF9995B1E4E4DD5B1481974E88CFABFBF6787775C2611CEFB27ED4403EA9B46
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+ct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
+ss = B2F713B6EE25BD7E567BEBCC5997F6A4
+
+count = 27
+seed = 54770EA1252EA2857D6635151194F5F520ADEA8A41E409FF498D40C271359858FE2B084D5B96BEE087B8E8F4DD4E00C5
+pk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
+sk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
+ct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
+ss = B5004ADF0D36CFB07BD259921AF706CC
+
+count = 28
+seed = CD6CFE94E9C0A1CC4FFDCD2D7876504BE5F50F1D1CA5CF93482943465B268276056F2781F4DE805C138976CA72621387
+pk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
+sk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
+ct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
+ss = 4F8AE0D0BC2AA3FF8717C6C7A876924B
+
+count = 29
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+
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+
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+ss = 4CF1CCA95A4F53EDEAEAF084D0D6A0FB
+
+count = 34
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+ct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
+ss = AE968D6A27804749820215D949802EF1
+
+count = 35
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+ss = 106D77DECF74C78D230AE3A4C60E9209
+
+count = 36
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+
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+
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+ss = B58E59F4A05558B84AE4851836CC49B2
+
+count = 39
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+ss = 2F93D724C4655F62C3BC06277EFE84CB
+
+count = 40
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+count = 53
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+
+count = 56
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+ss = A345B90C57E48D5257A155B917500E62
+
+count = 57
+seed = 4142237070C216BCBE245A39BD9220533C97651D84832B26727855AD994A0760C52B9319AD404693E4248B8C5FF324B3
+pk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+ct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
+ss = 48F4CAAAC964251E2A039063C206E99B
+
+count = 58
+seed = BD334D7B7EB14E00E68863F2E5551A095F8AF10681C28353FD19B9A7E70B8BFE266840860609008A567ABC66316C77CE
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+ss = A5611782265E1932DF3B7E736F40BA3A
+
+count = 59
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+ct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
+ss = BBA5BD08A7BD6DB8620A1C1149B00D03
+
+count = 60
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+ct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
+ss = E72DEB6A7678A71CC4986737F98204E5
+
+count = 61
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+ct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
+ss = 14E0D35F4EEF91D784C700B5C9E99296
+
+count = 62
+seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5
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+sk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
+ct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
+ss = 3588D259EA898E25FE7883554B9B4A77
+
+count = 63
+seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC
+pk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
+sk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
+ct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
+ss = 5CA9F51BE147CEAD8A910A5AACBE78CF
+
+count = 64
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+pk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+ss = 5E0D47D983AD86F377EC2B28DF453778
+
+count = 65
+seed = 905074033D7B75DEB2D06A2F29144EB377B452534C5710632989F02D45312D156557E96D4486020826DB200153BC4A8B
+pk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+ct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
+ss = 3F4B8410B799D38F26202CAC1B52A37C
+
+count = 66
+seed = A3E2E511AFA7BB560446BDADF67D2EE2E16FFC7BAEAE7EFB8C5455068BBD4E91BF9BE9D98B280072FABA7712C75B26D4
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+ct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
+ss = 19949A812632BA36C87F77EE12C9529B
+
+count = 67
+seed = 074AB1A37BA5A0403D8F68D26FB787BC2C90F5EF88F2A6D286C3E6B168ABD85D393D8225618608B8EEB301D26AF53BC0
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+ct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
+ss = 5D20C1D82577713863D76ED5A40C184D
+
+count = 68
+seed = CC0C86CC0ABF86FA21899BE1953913C00E7C46E6B5F730C4E88B3C034012763981D7F14459D3081638080378348856EA
+pk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
+sk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
+ct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
+ss = 3774A74D416427DF3F63B8AE681FDCB5
+
+count = 69
+seed = 6D5A7CC326ECF3983C4E7683F45263A37F692F3BCD2D920E1FD9584350119E74F9A3F905F70D3E20318C1413DE2A0DEA
+pk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
+sk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
+ct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
+ss = 202E3D6D3132D36F93EF6BD8BA489C3D
+
+count = 70
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+ss = 9B5515A30B0C0C147AE152BDFB20599D
+
+count = 71
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+ct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
+ss = E8F99D5CFDF7D84DCFB663A77856D6B3
+
+count = 72
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+ss = 58FF3C071363D83AA6B6B330A6E48D5F
+
+count = 73
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+ct = 45B85520B276EEECB71AECADCB02674CD14D2D35108207C8053807291BE2443BC5BF59566F582007BFBC418987C6685C4587E7AB984F00905136A595DEC7B9A70BF8A34D84D924D1C14B5FC4706C0DE7A1B886A8A6F9E100F8BFD1924F581F0250CFF6CA33139F8DFA9ED2BAEF01BA369656EDBBDADF489860DD6AF421DC7C2DE8C94B5B35F2AAB071496EB4C30B091830B40FB599C9E6494C776299D2696DB123B21024023D518CF99CD614D4F44DD730263AA9D9245F1A7793C75E4B7FF3E71F96D85A02EE2CAD361A3873A2E0A40F1C1E9043A03DD9D475946301E88930E226CAAAFE8D84FE49DC70A6EC9839ACEC4CD315417F05C2807404F98A0E6B4ED1F6B707C0B9035ECB2E0965AA15C1CEC22C010213B5252C33586DBC66EEC7EBB83B849EC9A46D2C48E52F78C24B0E3F9D00D380D4C0AF1ACBCD7F7582AF5F76EBC58FDB75271840EE07017D0D7275AAB4062C0C8FA446ABA19191
+ss = A4E753CE52D682D4BD468D9BD872A6D8
+
+count = 74
+seed = DEB963F8B1D8FBDF499D564BA8D2D47915BB402DA02F17031B37B4039A842AFB9B7E48F37200605992BD2429427A7A4E
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+sk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
+ct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
+ss = D229BBB3CA9080B96B26D87F2FBFCC26
+
+count = 75
+seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13
+pk = 642C64398DEDD29CFF26006A5C989C9114FE2CF5D2E5DB45A1DB66A42C13DBD08EFD116CDC3092271A78BF5D80197921ECE35537A3770109AC49BFDC73254DEC64BEFD4D326002293FE8C5177E3CA648E8ACF9D3A3A1B576EE40187A68CAD01DF11E337455860377318097B861002B3E1A7E06D7BC8A11BBEA50419EF432DF8946A62DAB52D04C01FCD01EAB2CCF798D0E3B4625CB8A06F853A0B3716243606B6C871ED800B13DDFC1196E65C2065E7EA3E70B450D82551A52F2F848CEF9DC41F9BBAF2C5A9345C3EF4E915B43FE4C8E4883D403D420AC4F19ADC7008C944732181E48C3650AFAC2A6BD47815CD0891FCBCC5ADCA9BC0CD788998F947D11880CADFE1FD458DE4218C5837D07DEB0E989C1E001A9F281283F8273BB0CDB912F54066F13A3A73E65691BE0CFFE719C0C556BD2BA770484278E91B9E4FA76BE271DB91A7939CF48CC54ED01
+sk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
+ct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
+ss = C96B986298CC6BFDA4253200192D1573
+
+count = 76
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+count = 82
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+sk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
+ct = ADA6439834C7BCAC8F61B4DBAFFD4EBC116196FDE0BEEC1F216D52AADAB44E967692B0CC5D6593B3A02A501F3415679A3D1C4D128DB500169EDA624EA81F0B9B31B320D135ED13BCE80B4320EB66DCFBF76D7C45C3506151A256475B4105B17B276AB35DBA3E6BD5FC8B54BF98005FFD6C4CA4C714914D29708DE71C948B235C6C66613CF86B8D6666283E78584D8FC7A1A332A82E2C17DCD09B65255BC7412D1ACCB36D01A539FE37FAA72432674A2B62AC63FFBCE68DD364F5F25CDFAA3B842966EB09992BB096241BB7924D180F11535709CB2BBC7EE4B8C98301ACF3E0AF53D3B8CA222C703279EB719FF3580E1033041B5474EA9D6753A0237BBE446E75FFF86F62F0FD7594B43D3E0CCA22889D669301CB1AE3593669DC516480F11192B23F6644E1AA106AC98B976AF3743A9FFD3C52402725061F87F9D14D01800E08BBC7AD3DB8B7AC312F0204D0A5BFD970CD7D90A6E388798D92FD
+ss = F83EC12EBE74AD7A567E22537E605B62
+
+count = 83
+seed = 16BEF67F7AC3A755C59C816478B75FCC16CE5844DB537791ACCD1EBD49D2824B105FD2E970F728C8F0CF16E439A9AE2F
+pk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
+sk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
+ct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
+ss = DA75F7C38E010985947EF930BA6B83E7
+
+count = 84
+seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8
+pk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
+sk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
+ct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
+ss = 389E75A62D289C99CD55DEE471EFD8FE
+
+count = 85
+seed = FBC38D7614D7718E931EDB850D2C6F0C5EEA9EE889B3E25BD69AC255D5B91E885D93E808E66BF9C88C655DC594DA5792
+pk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+ct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
+ss = 57651B54AEAEEEA98B87A7D60BE38C90
+
+count = 86
+seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35
+pk = 9900D987D9DE09CDF27B12E7743BFDC905E61AFF645EAF02C67D3778935C42F5EF223B6057EF4224158BCB1C989105D70145D594425600C996218C12C222ABDA46A3F9BB51D172A3558F6EBFB4B92E5F63BFA44D12B1FC6B065850EDFA5997E43F7B7B4A92333D704B19A48527029369A58624E88CD0C12BF76ADC19324696FD8C6E632A37A8F0ECDAACB7DE805C80C5FB7368A3CD40F2F86D42BE61CD660609DF5BFB37017E47F082C907E4CF21650D351711B5D3C8156D077D1CADE204D0118377BF582E3116295482744C3D325AA48356DAB735AB91E98D2569015BB69791A80437956724D843E39F5C4ACB573581941CBE2D1F813D181A75DD33949189F2EE1BDE52BD9013D135DC6965D211924E1AB601979A4B1E9BB82D52F0E3EB6EE349F5088E6D797D7F53211C6531FAF94E68CE1CC8FCA2ED9D2F3C3AF387FCE8A7D4EE6CB2424568E1AD01
+sk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
+ct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
+ss = F6082FA9C2DF2BBAB518B4DE9F489231
+
+count = 87
+seed = AC139B78FD16CA0F26D6D7F9E15345C888D857B1910CF38D883339B37EAD2DCAC30F7CF10176F23FF34B4488EB79437C
+pk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
+sk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
+ct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
+ss = 35C62EBA540CB14180433A41CADE8988
+
+count = 88
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+count = 94
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+pk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
+sk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
+ct = 6DB5EBD78172494CE2632DC81F94CF776DDD3474FF190EC6AA62D0545795FAA588446F814322DCB94D6F67985D003F33C32188E55876015C851687E3B39465BE6E02509626AB4F5E87EE6A6E0BC3EBB20A98FD1C467A7BFFD343650EE27DF889B541E3A324431017A0E27D74A001FF79284A3A8760768AB96ED6F5725EE6D9B05C34C5D85BF8071E78A9B5BBFCEC1425560F9220A4C5D9221D63B6BE969B2310F2AB023500D969B696ED1BAB48782E3F2FA1746AE18D5F5DB3FD64FC551203900246A1E9F513F49C15DFFCFD41C1363085090AA9403A7EF820F1F401BD745E61C07829BEE835592CE1FE04C53FEF4206F8CB176D0D268F47E7B73F9798438F943DD7ECA2BF69FFC88AD764E77AA3EF29C32B00153A06AB5113183985585C9F8354D6E46A2874C50266202EDE0D13BD2A730E37D6814C5BBEA973A530083AAE5B0E4184DA86E7984396016A8FA6DFB656BAFC94D71078977EF9A0
+ss = 6D17E0011D13654679310C7137BEFF80
+
+count = 95
+seed = 121D90E70AF6204445D0DEB28AC0C108262719E9FD3476ACA74BBFDE89FAF04D8D5F89A624E8A75DB80431F0D10AD28F
+pk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
+sk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
+ct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
+ss = 8C41BCA14516014306BE132DC6EFDDDA
+
+count = 96
+seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420
+pk = FCA24F4391DD603BC837E1943024C8AC4694356C42C324BAABC61EC0A32ABA45130FAC2CC13991F65F0D78B3106F42007799D14618DF015886196C948804F388A365A5E0240489AD6D93778C9868C3CA68125459C1FB8D170D679722340BE2906D8BA011AD7DC8E452A00CA2F800FBC219F2FFE71A45B05D30291C8608411D0AF98FBA4F441D5A319E9A8208EA689671D962FA0DAFC03F889D807346E393D14ED787ED5C0034FBB2D1F7BC30B5D108D87AC2B3132693EDB656894CD08B51252EAD45F07ADCD4E0365B5AA9600D2DB0C77C1715E375839EE1DCF9BA0052A0166229B30C97661250A4D65117E047A0E6A3626BDECD94ED27FBC3FE661ED669EC5B980FD42A9CD23A95912E2D7AE8C5B60B563101B0B66CCE2AC11575C0F8A20612D106B01A582200EB9FBA2D4C8B6929A519477ED91DB66279BEA619B34F9018B01093CCD7CD48A5261700
+sk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
+ct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
+ss = A6DB9C606E364AECDF4AC552B41757DE
+
+count = 97
+seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4
+pk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
+sk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
+ct = 0DC86F3AFB7047767E12D21BCE9308FBED0CF6E673632F078313E67B07B58DBAA60011BD321566F2C8990996B662C5D12F1CCF5304B400E1FA7E496BC63DCAD33C3A660173DA466FB2879979453C89D81A672A4708954C1662337050C4A62382CDC4A02CA52CE361C66ED9A8FD0075E908B062AC2F12905819905C08CCD223B0651663A43C980CDB6568010A85D25FC9F4921199670AE34C89A2A926A65D4376350935BF0162FB035CB6A64DE199B88BC2E49D1B425CF0F27AF6968E6DD5BD51E4D6A494EEC29A066736462738721733AF9999FCE2E64D4078783A015F45F74AF20550081A01D81669D3EC84335E80BB367DF9298E084E16EEA5E444BB0554403D900D2DC320F9DF999E57E36122BC2E14950111D146D2C3BB78481DBA632EB346468862E44F3D6C433B8097BFF0D295258243502309B8A5DC0E75F487E9789675966B8DFEA8D513D300EA74CC7C9787D4A7AAD9401FC1D8D9C6
+ss = F68927D6306B93CC1F822E2CBB5C43B3
+
+count = 98
+seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12
+pk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
+sk = AA6DD1E5799CDF7AF9C4FC632B3EB9D5068EB2D3B95AB779EE1275C14C5AF22568E19CE77BC30BF50CD537005F5E6BEF94BC0012EA7D7558EF4EFB72C137EFE6B14562E0C5F3BE819D7D5809C332F5E5007D3B7992B92719CE077CBD4DCA38FBCC4C0190AB60D8016AE2B4DDDF9ABCB58A3763B3A45947EABDB9A04271F94A0D17B364B854157F3D155D85F7F7C8A171BE9B2373AC90F3C34C001E961ED2CC130ED884486760EAE9156FE69FC0959C9FDA964D212DD304EEBB18AAE58B5D253997794B675AE8BBFD98777E7634696E0E01E005113DEABDB23404FE8D7CBD180C6B0FC0DFB6A995FF3FD2F962DA1FCEFB1080B373E0702FA46D602B7C0F838D6FEA0F6FE948E44201AAA0854135B694547C688C6A1A80809334E321CF47B8FBA421877EB562588E4717B5D1835F6B81A539F8173A300BFF53264A092D110E00B4C4058028EC647DA3C8BAF90520ACD123A20D027E2952A1A45AA892948C84E3092985F8A49293DB7FB98869704A6E8E6827B7C6F20301
+ct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
+ss = ABB141C9189DD1D2F5BCD86C02037C36
+
+count = 99
+seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B
+pk = 867436C365BC16B95C51E7F0141842F0BCF468592D95294141E6051F329F36DAB2F22FC2C76ED5B66CDCA197D111D7BD9E78EBF1D52E02770B91B6BE2D4BA7D895906D72F7DDB7667C41691EDE3B153BADE39B7873F4772264249EDDEE0FB5A78C7AC439CE9668E231C568C44B004292F96CD47AA8EFE07746AD6E40075D976BFB75BFC481D94C210FDDE78D3371156DBE081064F6274DDFF1F9BE05BDA76886345AAC5F005C307D9A2F2C3DCB6E16EF29530BED4D583DE8507AADC01F7C364DBCF11A1EE94588BC6EC6AE9C23835080ACDB0DCCB33B73A400AB9101111649F226657F153C58C2067A963173A955124AA33334E85F1380830E859EF99EEE2994F4CF9AB19EE0F8D426FA774D4F36A17668870051C1445B987A0034B16F76329FE7E3927E39FEF157C082212046512AADEA51EC22BA069B4684A939937613FC581E9B7596EBA0088B8000
+sk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
+ct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
+ss = DA40C7AB4E2ED76E4A3BDB509B806E5C
+

p434/fp.go

@@ -0,0 +1,192 @@
+package sike
+
+import (
+	"math/bits"
+)
+
+// Fp implementation
+
+// Compute z = x + y (mod 2*p).
+func fpAddRdc(z, x, y *Fp) {
+	var carry uint64
+
+	// z=x+y % p503
+	for i := 0; i < FP_WORDS; i++ {
+		z[i], carry = bits.Add64(x[i], y[i], carry)
+	}
+
+	// z = z - pX2
+	carry = 0
+	for i := 0; i < FP_WORDS; i++ {
+		z[i], carry = bits.Sub64(z[i], pX2[i], carry)
+	}
+
+	// if z<0 add pX2 back
+	mask := uint64(0 - carry)
+	carry = 0
+	for i := 0; i < FP_WORDS; i++ {
+		z[i], carry = bits.Add64(z[i], pX2[i]&mask, carry)
+	}
+}
+
+// Compute z = x - y (mod 2*p).
+func fpSubRdc(z, x, y *Fp) {
+	var borrow uint64
+
+	// z = z - pX2
+	for i := 0; i < FP_WORDS; i++ {
+		z[i], borrow = bits.Sub64(x[i], y[i], borrow)
+	}
+
+	// if z<0 add pX2 back
+	mask := uint64(0 - borrow)
+	borrow = 0
+	for i := 0; i < FP_WORDS; i++ {
+		z[i], borrow = bits.Add64(z[i], pX2[i]&mask, borrow)
+	}
+}
+
+// Reduce a field element in [0, 2*p) to one in [0,p).
+func fpRdcP(x *Fp) {
+	var borrow, mask uint64
+	for i := 0; i < FP_WORDS; i++ {
+		x[i], borrow = bits.Sub64(x[i], p[i], borrow)
+	}
+
+	// Sets all bits if borrow = 1
+	mask = 0 - borrow
+	borrow = 0
+	for i := 0; i < FP_WORDS; i++ {
+		x[i], borrow = bits.Add64(x[i], p[i]&mask, borrow)
+	}
+}
+
+// Implementation doesn't actually depend on a prime field.
+func fpSwapCond(x, y *Fp, mask uint8) {
+	if mask != 0 {
+		var tmp Fp
+		copy(tmp[:], y[:])
+		copy(y[:], x[:])
+		copy(x[:], tmp[:])
+	}
+}
+
+// Compute z = x * y.
+func fpMul(z *FpX2, x, y *Fp) {
+	var carry, t, u, v uint64
+	var hi, lo uint64
+
+	for i := uint64(0); i < FP_WORDS; i++ {
+		for j := uint64(0); j <= i; j++ {
+			hi, lo = bits.Mul64(x[j], y[i-j])
+			v, carry = bits.Add64(lo, v, 0)
+			u, carry = bits.Add64(hi, u, carry)
+			t += carry
+		}
+		z[i] = v
+		v = u
+		u = t
+		t = 0
+	}
+
+	for i := FP_WORDS; i < (2*FP_WORDS)-1; i++ {
+		for j := i - FP_WORDS + 1; j < FP_WORDS; j++ {
+			hi, lo = bits.Mul64(x[j], y[i-j])
+			v, carry = bits.Add64(lo, v, 0)
+			u, carry = bits.Add64(hi, u, carry)
+			t += carry
+		}
+		z[i] = v
+		v = u
+		u = t
+		t = 0
+	}
+	z[2*FP_WORDS-1] = v
+}
+
+// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p)
+// with R=2^512. Destroys the input value.
+func fpMontRdc(z *Fp, x *FpX2) {
+	var carry, t, u, v uint64
+	var hi, lo uint64
+	var count int
+
+	count = 3 // number of 0 digits in the least significat part of p503 + 1
+
+	for i := 0; i < FP_WORDS; i++ {
+		for j := 0; j < i; j++ {
+			if j < (i - count + 1) {
+				hi, lo = bits.Mul64(z[j], p1[i-j])
+				v, carry = bits.Add64(lo, v, 0)
+				u, carry = bits.Add64(hi, u, carry)
+				t += carry
+			}
+		}
+		v, carry = bits.Add64(v, x[i], 0)
+		u, carry = bits.Add64(u, 0, carry)
+		t += carry
+
+		z[i] = v
+		v = u
+		u = t
+		t = 0
+	}
+
+	for i := FP_WORDS; i < 2*FP_WORDS-1; i++ {
+		if count > 0 {
+			count--
+		}
+		for j := i - FP_WORDS + 1; j < FP_WORDS; j++ {
+			if j < (FP_WORDS - count) {
+				hi, lo = bits.Mul64(z[j], p1[i-j])
+				v, carry = bits.Add64(lo, v, 0)
+				u, carry = bits.Add64(hi, u, carry)
+				t += carry
+			}
+		}
+		v, carry = bits.Add64(v, x[i], 0)
+		u, carry = bits.Add64(u, 0, carry)
+
+		t += carry
+		z[i-FP_WORDS] = v
+		v = u
+		u = t
+		t = 0
+	}
+	v, carry = bits.Add64(v, x[2*FP_WORDS-1], 0)
+	z[FP_WORDS-1] = v
+}
+
+// Compute z = x + y, without reducing mod p.
+func fp2Add(z, x, y *FpX2) {
+	var carry uint64
+	for i := 0; i < 2*FP_WORDS; i++ {
+		z[i], carry = bits.Add64(x[i], y[i], carry)
+	}
+}
+
+// Compute z = x - y, without reducing mod p.
+func fp2Sub(z, x, y *FpX2) {
+	var borrow, mask uint64
+	for i := 0; i < 2*FP_WORDS; i++ {
+		z[i], borrow = bits.Sub64(x[i], y[i], borrow)
+	}
+
+	// Sets all bits if borrow = 1
+	mask = 0 - borrow
+	borrow = 0
+	for i := FP_WORDS; i < 2*FP_WORDS; i++ {
+		z[i], borrow = bits.Add64(z[i], p[i-FP_WORDS]&mask, borrow)
+	}
+}
+
+// Montgomery multiplication. Input values must be already
+// in Montgomery domain.
+func fpMulRdc(dest, lhs, rhs *Fp) {
+	a := lhs // = a*R
+	b := rhs // = b*R
+
+	var ab FpX2
+	fpMul(&ab, a, b)     // = a*b*R*R
+	fpMontRdc(dest, &ab) // = a*b*R mod p
+}

p434/sike.go

@@ -0,0 +1,710 @@
+package sike
+
+import (
+	"crypto/subtle"
+	"errors"
+	"github.com/henrydcase/nobs/hash/shake"
+	"io"
+)
+
+const (
+	// n can is max 256-bit (see 1.4 of [SIKE])
+	MaxMsgLen           = 32
+	MaxSharedSecretSize = 188
+	MaxSecretByteLenA   = 47
+)
+
+func cpick(pick int, out, in1, in2 []byte) {
+	var which = byte((int8(pick << 7)) >> 7)
+	for i, _ := range out {
+		out[i] = (in1[i] & which) | (in2[i] & ^which)
+	}
+}
+
+type KEM struct {
+	allocated   bool
+	rng         io.Reader
+	msg         []byte
+	secretBytes []byte
+}
+
+// Zeroize Fp2
+func zeroize(fp *Fp2) {
+	// Zeroizing in 2 seperated loops tells compiler to
+	// use fast runtime.memclr()
+	for i := range fp.A {
+		fp.A[i] = 0
+	}
+	for i := range fp.B {
+		fp.B[i] = 0
+	}
+}
+
+// Convert the input to wire format.
+//
+// The output byte slice must be at least 2*bytelen(p) bytes long.
+func convFp2ToBytes(output []byte, fp2 *Fp2) {
+	if len(output) < Params.SharedSecretSize {
+		panic("output byte slice too short")
+	}
+	var a Fp2
+	fromMontDomain(fp2, &a)
+
+	// convert to bytes in little endian form
+	for i := 0; i < Params.Bytelen; i++ {
+		// set i = j*8 + k
+		tmp := i / 8
+		k := uint64(i % 8)
+		output[i] = byte(a.A[tmp] >> (8 * k))
+		output[i+Params.Bytelen] = byte(a.B[tmp] >> (8 * k))
+	}
+}
+
+// Read 2*bytelen(p) bytes into the given ExtensionFieldElement.
+//
+// It is an error to call this function if the input byte slice is less than 2*bytelen(p) bytes long.
+func convBytesToFp2(fp2 *Fp2, input []byte) {
+	if len(input) < Params.SharedSecretSize {
+		panic("input byte slice too short")
+	}
+
+	for i := 0; i < Params.Bytelen; i++ {
+		j := i / 8
+		k := uint64(i % 8)
+		fp2.A[j] |= uint64(input[i]) << (8 * k)
+		fp2.B[j] |= uint64(input[i+Params.Bytelen]) << (8 * k)
+	}
+	toMontDomain(fp2)
+}
+
+// -----------------------------------------------------------------------------
+// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is
+//
+
+// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
+// for public key generation.
+func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint, pub *PublicKey) {
+	var points = make([]ProjectivePoint, 0, 8)
+	var indices = make([]int, 0, 8)
+	var i, sIdx int
+	var phi isogeny4
+
+	cparam := ToEquiv4(curve)
+	strat := pub.params.A.IsogenyStrategy
+	stratSz := len(strat)
+
+	for j := 1; j <= stratSz; j++ {
+		for i <= stratSz-j {
+			points = append(points, *xR)
+			indices = append(indices, i)
+
+			k := strat[sIdx]
+			sIdx++
+			Pow2k(xR, &cparam, 2*k)
+			i += int(k)
+		}
+
+		cparam = phi.GenerateCurve(xR)
+		for k := 0; k < len(points); k++ {
+			points[k] = phi.EvaluatePoint(&points[k])
+		}
+
+		*phiP = phi.EvaluatePoint(phiP)
+		*phiQ = phi.EvaluatePoint(phiQ)
+		*phiR = phi.EvaluatePoint(phiR)
+
+		// pop xR from points
+		*xR, points = points[len(points)-1], points[:len(points)-1]
+		i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
+	}
+}
+
+// Traverses isogeny tree in order to compute xR needed
+// for public key generation.
+func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint, pub *PublicKey) {
+	var points = make([]ProjectivePoint, 0, 8)
+	var indices = make([]int, 0, 8)
+	var i, sIdx int
+	var phi isogeny4
+
+	cparam := ToEquiv4(curve)
+	strat := pub.params.A.IsogenyStrategy
+	stratSz := len(strat)
+
+	for j := 1; j <= stratSz; j++ {
+		for i <= stratSz-j {
+			points = append(points, *xR)
+			indices = append(indices, i)
+
+			k := strat[sIdx]
+			sIdx++
+			Pow2k(xR, &cparam, 2*k)
+			i += int(k)
+		}
+
+		cparam = phi.GenerateCurve(xR)
+		for k := 0; k < len(points); k++ {
+			points[k] = phi.EvaluatePoint(&points[k])
+		}
+
+		// pop xR from points
+		*xR, points = points[len(points)-1], points[:len(points)-1]
+		i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
+	}
+}
+
+// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
+// for public key generation.
+func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint, pub *PublicKey) {
+	var points = make([]ProjectivePoint, 0, 8)
+	var indices = make([]int, 0, 8)
+	var i, sIdx int
+	var phi isogeny3
+
+	cparam := ToEquiv3(curve)
+	strat := pub.params.B.IsogenyStrategy
+	stratSz := len(strat)
+
+	for j := 1; j <= stratSz; j++ {
+		for i <= stratSz-j {
+			points = append(points, *xR)
+			indices = append(indices, i)
+
+			k := strat[sIdx]
+			sIdx++
+			Pow3k(xR, &cparam, k)
+			i += int(k)
+		}
+
+		cparam = phi.GenerateCurve(xR)
+		for k := 0; k < len(points); k++ {
+			points[k] = phi.EvaluatePoint(&points[k])
+		}
+
+		*phiP = phi.EvaluatePoint(phiP)
+		*phiQ = phi.EvaluatePoint(phiQ)
+		*phiR = phi.EvaluatePoint(phiR)
+
+		// pop xR from points
+		*xR, points = points[len(points)-1], points[:len(points)-1]
+		i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
+	}
+}
+
+// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
+// for public key generation.
+func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint, pub *PublicKey) {
+	var points = make([]ProjectivePoint, 0, 8)
+	var indices = make([]int, 0, 8)
+	var i, sIdx int
+	var phi isogeny3
+
+	cparam := ToEquiv3(curve)
+	strat := pub.params.B.IsogenyStrategy
+	stratSz := len(strat)
+
+	for j := 1; j <= stratSz; j++ {
+		for i <= stratSz-j {
+			points = append(points, *xR)
+			indices = append(indices, i)
+
+			k := strat[sIdx]
+			sIdx++
+			Pow3k(xR, &cparam, k)
+			i += int(k)
+		}
+
+		cparam = phi.GenerateCurve(xR)
+		for k := 0; k < len(points); k++ {
+			points[k] = phi.EvaluatePoint(&points[k])
+		}
+
+		// pop xR from points
+		*xR, points = points[len(points)-1], points[:len(points)-1]
+		i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
+	}
+}
+
+// Generate a public key in the 2-torsion group
+func publicKeyGenA(pub *PublicKey, prv *PrivateKey) {
+	var xPA, xQA, xRA ProjectivePoint
+	var xPB, xQB, xRB, xK ProjectivePoint
+	var invZP, invZQ, invZR Fp2
+	var phi isogeny4
+
+	// Load points for A
+	xPA = ProjectivePoint{X: prv.params.A.Affine_P, Z: prv.params.OneFp2}
+	xQA = ProjectivePoint{X: prv.params.A.Affine_Q, Z: prv.params.OneFp2}
+	xRA = ProjectivePoint{X: prv.params.A.Affine_R, Z: prv.params.OneFp2}
+
+	// Load points for B
+	xRB = ProjectivePoint{X: prv.params.B.Affine_R, Z: prv.params.OneFp2}
+	xQB = ProjectivePoint{X: prv.params.B.Affine_Q, Z: prv.params.OneFp2}
+	xPB = ProjectivePoint{X: prv.params.B.Affine_P, Z: prv.params.OneFp2}
+
+	// Find isogeny kernel
+	xK = ScalarMul3Pt(&pub.params.InitCurve, &xPA, &xQA, &xRA, prv.params.A.SecretBitLen, prv.Scalar)
+	traverseTreePublicKeyA(&pub.params.InitCurve, &xK, &xPB, &xQB, &xRB, pub)
+
+	// Secret isogeny
+	phi.GenerateCurve(&xK)
+	xPA = phi.EvaluatePoint(&xPB)
+	xQA = phi.EvaluatePoint(&xQB)
+	xRA = phi.EvaluatePoint(&xRB)
+	Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR)
+
+	mul(&pub.affine_xP, &xPA.X, &invZP)
+	mul(&pub.affine_xQ, &xQA.X, &invZQ)
+	mul(&pub.affine_xQmP, &xRA.X, &invZR)
+}
+
+// Generate a public key in the 3-torsion group
+func publicKeyGenB(pub *PublicKey, prv *PrivateKey) {
+	var xPB, xQB, xRB, xK ProjectivePoint
+	var xPA, xQA, xRA ProjectivePoint
+	var invZP, invZQ, invZR Fp2
+	var phi isogeny3
+
+	// Load points for A
+	xPA = ProjectivePoint{X: prv.params.A.Affine_P, Z: prv.params.OneFp2}
+	xQA = ProjectivePoint{X: prv.params.A.Affine_Q, Z: prv.params.OneFp2}
+	xRA = ProjectivePoint{X: prv.params.A.Affine_R, Z: prv.params.OneFp2}
+
+	// Load points for B
+	xRB = ProjectivePoint{X: prv.params.B.Affine_R, Z: prv.params.OneFp2}
+	xQB = ProjectivePoint{X: prv.params.B.Affine_Q, Z: prv.params.OneFp2}
+	xPB = ProjectivePoint{X: prv.params.B.Affine_P, Z: prv.params.OneFp2}
+
+	xK = ScalarMul3Pt(&pub.params.InitCurve, &xPB, &xQB, &xRB, prv.params.B.SecretBitLen, prv.Scalar)
+	traverseTreePublicKeyB(&pub.params.InitCurve, &xK, &xPA, &xQA, &xRA, pub)
+
+	phi.GenerateCurve(&xK)
+	xPB = phi.EvaluatePoint(&xPA)
+	xQB = phi.EvaluatePoint(&xQA)
+	xRB = phi.EvaluatePoint(&xRA)
+	Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR)
+
+	mul(&pub.affine_xP, &xPB.X, &invZP)
+	mul(&pub.affine_xQ, &xQB.X, &invZQ)
+	mul(&pub.affine_xQmP, &xRB.X, &invZR)
+}
+
+// -----------------------------------------------------------------------------
+// Key agreement functions
+//
+
+// Establishing shared keys in in 2-torsion group
+func deriveSecretA(ss []byte, prv *PrivateKey, pub *PublicKey) {
+	var xP, xQ, xQmP ProjectivePoint
+	var xK ProjectivePoint
+	var phi isogeny4
+	var jInv Fp2
+
+	// Recover curve coefficients
+	cparam := pub.params.InitCurve
+	RecoverCoordinateA(&cparam, &pub.affine_xP, &pub.affine_xQ, &pub.affine_xQmP)
+
+	// Find kernel of the morphism
+	xP = ProjectivePoint{X: pub.affine_xP, Z: pub.params.OneFp2}
+	xQ = ProjectivePoint{X: pub.affine_xQ, Z: pub.params.OneFp2}
+	xQmP = ProjectivePoint{X: pub.affine_xQmP, Z: pub.params.OneFp2}
+	xK = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, pub.params.A.SecretBitLen, prv.Scalar)
+
+	// Traverse isogeny tree
+	traverseTreeSharedKeyA(&cparam, &xK, pub)
+
+	// Calculate j-invariant on isogeneus curve
+	c := phi.GenerateCurve(&xK)
+	FromEquiv4(&cparam, &c)
+	Jinvariant(&cparam, &jInv)
+	convFp2ToBytes(ss, &jInv)
+}
+
+// Establishing shared keys in in 3-torsion group
+func deriveSecretB(ss []byte, prv *PrivateKey, pub *PublicKey) {
+	var xP, xQ, xQmP ProjectivePoint
+	var xK ProjectivePoint
+	var phi isogeny3
+	var jInv Fp2
+
+	// Recover curve coefficients
+	cparam := pub.params.InitCurve
+	RecoverCoordinateA(&cparam, &pub.affine_xP, &pub.affine_xQ, &pub.affine_xQmP)
+
+	// Find kernel of the morphism
+	xP = ProjectivePoint{X: pub.affine_xP, Z: pub.params.OneFp2}
+	xQ = ProjectivePoint{X: pub.affine_xQ, Z: pub.params.OneFp2}
+	xQmP = ProjectivePoint{X: pub.affine_xQmP, Z: pub.params.OneFp2}
+	xK = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, pub.params.B.SecretBitLen, prv.Scalar)
+
+	// Traverse isogeny tree
+	traverseTreeSharedKeyB(&cparam, &xK, pub)
+
+	// Calculate j-invariant on isogeneus curve
+	c := phi.GenerateCurve(&xK)
+	FromEquiv3(&cparam, &c)
+	Jinvariant(&cparam, &jInv)
+	convFp2ToBytes(ss, &jInv)
+}
+
+func generateCiphertext(ctext []byte, skA *PrivateKey, pkA, pkB *PublicKey, ptext []byte) error {
+	var n [MaxMsgLen]byte
+	var j [MaxSharedSecretSize]byte
+	var ptextLen = len(ptext)
+
+	if pkB.keyVariant != KeyVariant_SIKE {
+		return errors.New("wrong key type")
+	}
+
+	err := DeriveSecret(j[:], skA, pkB)
+	if err != nil {
+		return err
+	}
+
+	f := shake.NewShake256()
+	f.Write(j[:Params.SharedSecretSize])
+	f.Read(n[:ptextLen])
+	for i, _ := range ptext {
+		n[i] ^= ptext[i]
+	}
+
+	pkA.Export(ctext)
+	copy(ctext[pkA.Size():], n[:ptextLen])
+	return nil
+}
+
+// NewPrivateKey initializes private key.
+// Usage of this function guarantees that the object is correctly initialized.
+func NewPrivateKey(v KeyVariant) *PrivateKey {
+	prv := &PrivateKey{key: key{params: &Params, keyVariant: v}}
+	if (v & KeyVariant_SIDH_A) == KeyVariant_SIDH_A {
+		prv.Scalar = make([]byte, prv.params.A.SecretByteLen)
+	} else {
+		prv.Scalar = make([]byte, prv.params.B.SecretByteLen)
+	}
+	if v == KeyVariant_SIKE {
+		prv.S = make([]byte, prv.params.MsgLen)
+	}
+	return prv
+}
+
+// NewPublicKey initializes public key.
+// Usage of this function guarantees that the object is correctly initialized.
+func NewPublicKey(v KeyVariant) *PublicKey {
+	return &PublicKey{key: key{params: &Params, keyVariant: v}}
+}
+
+// Import clears content of the public key currently stored in the structure
+// and imports key stored in the byte string. Returns error in case byte string
+// size is wrong. Doesn't perform any validation.
+func (pub *PublicKey) Import(input []byte) error {
+	if len(input) != pub.Size() {
+		return errors.New("sidh: input to short")
+	}
+
+	ssSz := pub.params.SharedSecretSize
+	convBytesToFp2(&pub.affine_xP, input[0:ssSz])
+	convBytesToFp2(&pub.affine_xQ, input[ssSz:2*ssSz])
+	convBytesToFp2(&pub.affine_xQmP, input[2*ssSz:3*ssSz])
+	return nil
+}
+
+// Exports currently stored key. In case structure hasn't been filled with key data
+// returned byte string is filled with zeros.
+func (pub *PublicKey) Export(out []byte) {
+	ssSz := pub.params.SharedSecretSize
+	convFp2ToBytes(out[0:ssSz], &pub.affine_xP)
+	convFp2ToBytes(out[ssSz:2*ssSz], &pub.affine_xQ)
+	convFp2ToBytes(out[2*ssSz:3*ssSz], &pub.affine_xQmP)
+}
+
+// Size returns size of the public key in bytes
+func (pub *PublicKey) Size() int {
+	return pub.params.PublicKeySize
+}
+
+// Exports currently stored key. In case structure hasn't been filled with key data
+// returned byte string is filled with zeros.
+func (prv *PrivateKey) Export(out []byte) {
+	copy(out, prv.S)
+	copy(out[len(prv.S):], prv.Scalar)
+}
+
+// Size returns size of the private key in bytes
+func (prv *PrivateKey) Size() int {
+	tmp := len(prv.Scalar)
+	if prv.keyVariant == KeyVariant_SIKE {
+		tmp += int(prv.params.MsgLen)
+	}
+	return tmp
+}
+
+// Import clears content of the private key currently stored in the structure
+// and imports key from octet string. In case of SIKE, the random value 'S'
+// must be prepended to the value of actual private key (see SIKE spec for details).
+// Function doesn't import public key value to PrivateKey object.
+func (prv *PrivateKey) Import(input []byte) error {
+	if len(input) != prv.Size() {
+		return errors.New("sidh: input to short")
+	}
+	copy(prv.S, input[:len(prv.S)])
+	copy(prv.Scalar, input[len(prv.S):])
+	return nil
+}
+
+// Generates random private key for SIDH or SIKE. Generated value is
+// formed as little-endian integer from key-space <2^(e2-1)..2^e2 - 1>
+// for KeyVariant_A or <2^(s-1)..2^s - 1>, where s = floor(log_2(3^e3)),
+// for KeyVariant_B.
+//
+// Returns error in case user provided RNG fails.
+func (prv *PrivateKey) Generate(rand io.Reader) error {
+	var err error
+	var dp *DomainParams
+
+	if (prv.keyVariant & KeyVariant_SIDH_A) == KeyVariant_SIDH_A {
+		dp = &prv.params.A
+	} else {
+		dp = &prv.params.B
+	}
+
+	if prv.keyVariant == KeyVariant_SIKE && err == nil {
+		_, err = io.ReadFull(rand, prv.S)
+	}
+
+	// Private key generation takes advantage of the fact that keyspace for secret
+	// key is (0, 2^x - 1), for some possitivite value of 'x' (see SIKE, 1.3.8).
+	// It means that all bytes in the secret key, but the last one, can take any
+	// value between <0x00,0xFF>. Similarily for the last byte, but generation
+	// needs to chop off some bits, to make sure generated value is an element of
+	// a key-space.
+	_, err = io.ReadFull(rand, prv.Scalar)
+	if err != nil {
+		return err
+	}
+	prv.Scalar[len(prv.Scalar)-1] &= (1 << (dp.SecretBitLen % 8)) - 1
+	// Make sure scalar is SecretBitLen long. SIKE spec says that key
+	// space starts from 0, but I'm not confortable with having low
+	// value scalars used for private keys. It is still secrure as per
+	// table 5.1 in [SIKE].
+	prv.Scalar[len(prv.Scalar)-1] |= 1 << ((dp.SecretBitLen % 8) - 1)
+	return err
+}
+
+// Generates public key.
+//
+// Constant time.
+func (prv *PrivateKey) GeneratePublicKey(pub *PublicKey) {
+	if (prv.keyVariant & KeyVariant_SIDH_A) == KeyVariant_SIDH_A {
+		publicKeyGenA(pub, prv)
+	} else {
+		publicKeyGenB(pub, prv)
+	}
+}
+
+// Computes a shared secret which is a j-invariant. Function requires that pub has
+// different KeyVariant than prv. Length of returned output is 2*ceil(log_2 P)/8),
+// where P is a prime defining finite field.
+//
+// It's important to notice that each keypair must not be used more than once
+// to calculate shared secret.
+//
+// Function may return error. This happens only in case provided input is invalid.
+// Constant time for properly initialized private and public key.
+func DeriveSecret(ss []byte, prv *PrivateKey, pub *PublicKey) error {
+	if (pub == nil) || (prv == nil) {
+		return errors.New("sidh: invalid arguments")
+	}
+
+	if (pub.keyVariant == prv.keyVariant) || (pub.params.Id != prv.params.Id) {
+		return errors.New("sidh: public and private are incompatbile")
+	}
+
+	if (prv.keyVariant & KeyVariant_SIDH_A) == KeyVariant_SIDH_A {
+		deriveSecretA(ss, prv, pub)
+	} else {
+		deriveSecretB(ss, prv, pub)
+	}
+	return nil
+}
+
+// Uses SIKE public key to encrypt plaintext. Requires cryptographically secure PRNG
+// Returns ciphertext in case encryption succeeds. Returns error in case PRNG fails
+// or wrongly formated input was provided.
+func encrypt(ctext []byte, rng io.Reader, pub *PublicKey, ptext []byte) error {
+	var ptextLen = len(ptext)
+	// c1 must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3)
+	if ptextLen != pub.params.KemSize {
+		return errors.New("Unsupported message length")
+	}
+
+	skA := NewPrivateKey(KeyVariant_SIDH_A)
+	pkA := NewPublicKey(KeyVariant_SIDH_A)
+	err := skA.Generate(rng)
+	if err != nil {
+		return err
+	}
+
+	skA.GeneratePublicKey(pkA)
+	return generateCiphertext(ctext, skA, pkA, pub, ptext)
+}
+
+// Uses SIKE private key to decrypt ciphertext. Returns plaintext in case
+// decryption succeeds or error in case unexptected input was provided.
+// Constant time
+func decrypt(n []byte, prv *PrivateKey, ctext []byte) (int, error) {
+	var c1_len int
+	var j [MaxSharedSecretSize]byte
+	var pk_len = prv.params.PublicKeySize
+
+	if prv.keyVariant != KeyVariant_SIKE {
+		return 0, errors.New("wrong key type")
+	}
+
+	// ctext is a concatenation of (ciphertext = pubkey_A || c1)
+	// it must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3)
+	c1_len = len(ctext) - pk_len
+	if c1_len != prv.params.KemSize {
+		return 0, errors.New("wrong size of cipher text")
+	}
+
+	c0 := NewPublicKey(KeyVariant_SIDH_A)
+	err := c0.Import(ctext[:pk_len])
+	if err != nil {
+		return 0, err
+	}
+	err = DeriveSecret(j[:], prv, c0)
+	if err != nil {
+		return 0, err
+	}
+
+	s := shake.NewShake256()
+	s.Write(j[:Params.SharedSecretSize])
+	s.Read(n[:c1_len])
+	for i, _ := range n[:c1_len] {
+		n[i] ^= ctext[pk_len+i]
+	}
+	return c1_len, nil
+}
+
+// KEM API
+func (kem *KEM) Allocate(rng io.Reader) {
+	kem.allocated = true
+	kem.rng = rng
+	kem.msg = make([]byte, Params.MsgLen)
+	kem.secretBytes = make([]byte, Params.A.SecretByteLen)
+}
+
+func (kem *KEM) Reset() {
+	for i, _ := range kem.msg {
+		kem.msg[i] = 0
+	}
+
+	for i, _ := range kem.secretBytes {
+		kem.secretBytes[i] = 0
+	}
+}
+
+func (kem *KEM) CiphertextSize() int {
+	return Params.CiphertextSize
+}
+
+func (kem *KEM) SharedSecretSize() int {
+	return Params.KemSize
+}
+
+// Encapsulation receives the public key and generates SIKE ciphertext and shared secret.
+// The generated ciphertext is used for authentication.
+// The rng must be cryptographically secure PRNG.
+// Error is returned in case PRNG fails or wrongly formated input was provided.
+func (kem *KEM) Encapsulate(ciphertext, secret []byte, pub *PublicKey) error {
+	var buf [3 * MaxSharedSecretSize]byte
+	var skA = PrivateKey{
+		key: key{
+			params:     &Params,
+			keyVariant: KeyVariant_SIDH_A},
+		Scalar: kem.secretBytes}
+
+	if !kem.allocated {
+		panic("KEM unallocated")
+	}
+
+	// Generate ephemeral value
+	_, err := io.ReadFull(kem.rng, kem.msg[:])
+	if err != nil {
+		return err
+	}
+
+	pub.Export(buf[:])
+	g := shake.NewShake256()
+	g.Write(kem.msg)
+	g.Write(buf[:3*Params.SharedSecretSize])
+	g.Read(skA.Scalar)
+
+	// Ensure bitlength is not bigger then to 2^e2-1
+	skA.Scalar[len(skA.Scalar)-1] &= (1 << (pub.params.A.SecretBitLen % 8)) - 1
+	pkA := NewPublicKey(KeyVariant_SIDH_A)
+	skA.GeneratePublicKey(pkA)
+	err = generateCiphertext(ciphertext, &skA, pkA, pub, kem.msg[:])
+	if err != nil {
+		return err
+	}
+
+	// K = H(msg||(c0||c1))
+	h := shake.NewShake256()
+	h.Write(kem.msg)
+	h.Write(ciphertext)
+	h.Read(secret)
+	return nil
+}
+
+// Decapsulate given the keypair and ciphertext as inputs, Decapsulate outputs a shared
+// secret if plaintext verifies correctly, otherwise function outputs random value.
+// Decapsulation may fail in case input is wrongly formated.
+// Constant time for properly initialized input.
+func (kem *KEM) Decapsulate(secret []byte, prv *PrivateKey, pub *PublicKey, ctext []byte) error {
+	var m [MaxMsgLen]byte
+	var r [MaxSecretByteLenA]byte
+	var pkBytes [3 * MaxSharedSecretSize]byte
+	var skA = PrivateKey{
+		key: key{
+			params:     &Params,
+			keyVariant: KeyVariant_SIDH_A},
+		Scalar: kem.secretBytes}
+	var pkA = NewPublicKey(KeyVariant_SIDH_A)
+
+	c1_len, err := decrypt(m[:], prv, ctext)
+	if err != nil {
+		return err
+	}
+
+	// r' = G(m'||pub)
+	//var key = make([]byte, pub.Size()+2*Params.MsgLen)
+	pub.Export(pkBytes[:])
+	g := shake.NewShake256()
+	g.Write(m[:c1_len])
+	g.Write(pkBytes[:3*pub.params.SharedSecretSize])
+	g.Read(r[:pub.params.A.SecretByteLen])
+	// Ensure bitlength is not bigger than 2^e2-1
+	r[pub.params.A.SecretByteLen-1] &= (1 << (pub.params.A.SecretBitLen % 8)) - 1
+
+	// Never fails
+	skA.Import(r[:pub.params.A.SecretByteLen])
+	skA.GeneratePublicKey(pkA)
+	pkA.Export(pkBytes[:])
+
+	// S is chosen at random when generating a key and unknown to other party. It
+	// may seem weird, but it's correct. It is important that S is unpredictable
+	// to other party. Without this check, it is possible to recover a secret, by
+	// providing series of invalid ciphertexts. It is also important that isn case
+	//
+	// See more details in "On the security of supersingular isogeny cryptosystems"
+	// (S. Galbraith, et al., 2016, ePrint #859).
+	mask := subtle.ConstantTimeCompare(pkBytes[:pub.params.PublicKeySize], ctext[:pub.params.PublicKeySize])
+	cpick(mask, m[:c1_len], m[:c1_len], prv.S)
+	h := shake.NewShake256()
+	h.Write(m[:c1_len])
+	h.Write(ctext)
+	h.Read(secret)
+	return nil
+}

p434/sike_test.go

@@ -0,0 +1,753 @@
+package sike
+
+import (
+	"bufio"
+	"bytes"
+	"crypto/rand"
+	"encoding/hex"
+	"io"
+	"math/big"
+	"os"
+	"strings"
+	"testing"
+)
+
+var tdata = struct {
+	name     string
+	katFile  string
+	PrA_sidh string
+	PkA_sidh string
+	PrB_sidh string
+	PkB_sidh string
+	PkB_sike string
+	PrB_sike string
+}{
+	name:     "SIKEp434",
+	katFile:  "etc/PQCkemKAT_374.rsp",
+	PrA_sidh: "3A727E04EA9B7E2A766A6F846489E7E7B915263BCEED308BB10FC900",
+	PkA_sidh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
+	PrB_sidh: "E37BFE55B43B32448F375903D8D226EC94ADBFEA1D2B3536EB987001",
+	PkB_sidh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
+	PrB_sike: "4B622DE1350119C45A9F2E2EF3DC5DF56A27FCDFCDDAF58CD69B903752D68C200934E160B234E49EDE247601",
+	PkB_sike: "1BD0A2E81307B6F96461317DDF535ACC0E59C742627BAE60D27605E10FAF722D22A73E184CB572A12E79DCD58C6B54FB01442114CBE9010B6CAEC25D04C16C5E42540C1524C545B8C67614ED4183C9FA5BD0BE45A7F89FBC770EE8E7E5E391C7EE6F35F74C29E6D9E35B1663DA01E48E9DEB2347512D366FDE505161677055E3EF23054D276E817E2C57025DA1C10D2461F68617F2D11256EEE4E2D7DBDF6C8E34F3A0FD00C625428CB41857002159DAB94267ABE42D630C6AAA91AF837C7A6740754EA6634C45454C51B0BB4D44C3CCCCE4B32C00901CF69C008D013348379B2F9837F428A01B6173584691F2A6F3A3C4CF487D20D261B36C8CDB1BC158E2A5162A9DA4F7A97AA0879B9897E2B6891B672201F9AEFBF799C27B2587120AC586A511360926FB7DA8EBF5CB5272F396AE06608422BE9792E2CE9BEF21BF55B7EFF8DC7EC8C99910D3F800",
+}
+
+/* -------------------------------------------------------------------------
+   Helpers
+   -------------------------------------------------------------------------*/
+// Fail if err !=nil. Display msg as an error message
+func checkErr(t testing.TB, err error, msg string) {
+	t.Helper()
+	if err != nil {
+		t.Error(msg)
+	}
+}
+
+// Utility used for running same test with all registered prime fields
+type MultiIdTestingFunc func(testing.TB)
+
+// Converts string to private key
+func convToPrv(s string, v KeyVariant) *PrivateKey {
+	key := NewPrivateKey(v)
+	hex, e := hex.DecodeString(s)
+	if e != nil {
+		panic("non-hex number provided")
+	}
+	e = key.Import(hex)
+	if e != nil {
+		panic("Can't import private key")
+	}
+	return key
+}
+
+// Converts string to public key
+func convToPub(s string, v KeyVariant) *PublicKey {
+	key := NewPublicKey(v)
+	hex, e := hex.DecodeString(s)
+	if e != nil {
+		panic("non-hex number provided")
+	}
+	e = key.Import(hex)
+	if e != nil {
+		panic("Can't import public key")
+	}
+	return key
+}
+
+/* -------------------------------------------------------------------------
+   Unit tests
+   -------------------------------------------------------------------------*/
+func TestKeygen(t *testing.T) {
+	var keyExp, keyGot [55 * 2 * 3]byte
+	alicePrivate := convToPrv(tdata.PrA_sidh, KeyVariant_SIDH_A)
+	bobPrivate := convToPrv(tdata.PrB_sidh, KeyVariant_SIDH_B)
+	expPubA := convToPub(tdata.PkA_sidh, KeyVariant_SIDH_A)
+	expPubB := convToPub(tdata.PkB_sidh, KeyVariant_SIDH_B)
+
+	pubA := NewPublicKey(KeyVariant_SIDH_A)
+	alicePrivate.GeneratePublicKey(pubA)
+	pubB := NewPublicKey(KeyVariant_SIDH_B)
+	bobPrivate.GeneratePublicKey(pubB)
+
+	pubA.Export(keyExp[:])
+	expPubA.Export(keyGot[:])
+	if !bytes.Equal(keyExp[:], keyGot[:]) {
+		t.Fatalf("unexpected value of public key A [\nGot: %X\nExp: %X]\n",
+			keyExp, keyGot)
+	}
+
+	for i, _ := range keyExp {
+		keyExp[i] = 0
+		keyGot[i] = 0
+	}
+
+	pubB.Export(keyExp[:])
+	expPubB.Export(keyGot[:])
+	if !bytes.Equal(keyExp[:], keyGot[:]) {
+		t.Fatalf("unexpected value of public key B [\nGot: %X\nExp: %X]\n",
+			keyGot, keyExp)
+	}
+}
+
+func TestImportExport(t *testing.T) {
+	var err error
+	var aBytes, bBytes [110 * 3]byte
+
+	a := NewPublicKey(KeyVariant_SIDH_A)
+	b := NewPublicKey(KeyVariant_SIDH_B)
+
+	// Import keys
+	aHex, err := hex.DecodeString(tdata.PkA_sidh)
+	checkErr(t, err, "invalid hex-number provided")
+
+	err = a.Import(aHex)
+	checkErr(t, err, "import failed")
+
+	bHex, err := hex.DecodeString(tdata.PkB_sike)
+	checkErr(t, err, "invalid hex-number provided")
+
+	err = b.Import(bHex)
+	checkErr(t, err, "import failed")
+
+	a.Export(aBytes[:])
+	b.Export(bBytes[:])
+
+	// Export and check if same
+	if !bytes.Equal(bBytes[:], bHex) || !bytes.Equal(aBytes[:], aHex) {
+		t.Fatalf("export/import failed")
+	}
+
+	if (len(bBytes) != b.Size()) || (len(aBytes) != a.Size()) {
+		t.Fatalf("wrong size of exported keys")
+	}
+}
+
+func testPrivateKeyBelowMax(t testing.TB) {
+	for variant, keySz := range map[KeyVariant]*DomainParams{
+		KeyVariant_SIDH_A: &Params.A,
+		KeyVariant_SIDH_B: &Params.B} {
+
+		func(v KeyVariant, dp *DomainParams) {
+			var blen = int(dp.SecretByteLen)
+			var prv = NewPrivateKey(v)
+			var secretBytes = make([]byte, prv.Size())
+
+			// Calculate either (2^e2 - 1) or (2^s - 1); where s=ceil(log_2(3^e3)))
+			maxSecertVal := big.NewInt(int64(dp.SecretBitLen))
+			maxSecertVal.Exp(big.NewInt(int64(2)), maxSecertVal, nil)
+			maxSecertVal.Sub(maxSecertVal, big.NewInt(1))
+
+			// Do same test 1000 times
+			for i := 0; i < 1000; i++ {
+				err := prv.Generate(rand.Reader)
+				checkErr(t, err, "Private key generation")
+
+				// Convert to big-endian, as that's what expected by (*Int)SetBytes()
+				prv.Export(secretBytes)
+				for i := 0; i < int(blen/2); i++ {
+					tmp := secretBytes[i] ^ secretBytes[blen-i-1]
+					secretBytes[i] = tmp ^ secretBytes[i]
+					secretBytes[blen-i-1] = tmp ^ secretBytes[blen-i-1]
+				}
+				prvBig := new(big.Int).SetBytes(secretBytes)
+				// Check if generated key is bigger then acceptable
+				if prvBig.Cmp(maxSecertVal) == 1 {
+					t.Error("Generated private key is wrong")
+				}
+			}
+		}(variant, keySz)
+	}
+}
+
+func testKeyAgreement(t *testing.T, pkA, prA, pkB, prB string) {
+	var e error
+	var s1, s2 [110 * 3]byte
+
+	// KeyPairs
+	alicePublic := convToPub(pkA, KeyVariant_SIDH_A)
+	bobPublic := convToPub(pkB, KeyVariant_SIDH_B)
+	alicePrivate := convToPrv(prA, KeyVariant_SIDH_A)
+	bobPrivate := convToPrv(prB, KeyVariant_SIDH_B)
+
+	// Do actual test
+	e = DeriveSecret(s1[:], bobPrivate, alicePublic)
+	checkErr(t, e, "derivation s1")
+	e = DeriveSecret(s2[:], alicePrivate, bobPublic)
+	checkErr(t, e, "derivation s1")
+
+	if !bytes.Equal(s1[:], s2[:]) {
+		t.Fatalf("two shared keys: %d, %d do not match", s1, s2)
+	}
+
+	// Negative case
+	dec, e := hex.DecodeString(tdata.PkA_sidh)
+	if e != nil {
+		t.FailNow()
+	}
+	dec[0] = ^dec[0]
+	e = alicePublic.Import(dec)
+	if e != nil {
+		t.FailNow()
+	}
+
+	e = DeriveSecret(s1[:], bobPrivate, alicePublic)
+	checkErr(t, e, "derivation of s1 failed")
+	e = DeriveSecret(s2[:], alicePrivate, bobPublic)
+	checkErr(t, e, "derivation of s2 failed")
+
+	if bytes.Equal(s1[:], s2[:]) {
+		t.Fatalf("The two shared keys: %d, %d match", s1, s2)
+	}
+}
+
+func TestDerivationRoundTrip(t *testing.T) {
+	var err error
+	var s1, s2 [110 * 3]byte
+
+	pubA := NewPublicKey(KeyVariant_SIDH_A)
+	prvA := NewPrivateKey(KeyVariant_SIDH_A)
+	pubB := NewPublicKey(KeyVariant_SIDH_B)
+	prvB := NewPrivateKey(KeyVariant_SIDH_B)
+
+	// Generate private keys
+	err = prvA.Generate(rand.Reader)
+	checkErr(t, err, "key generation failed")
+	err = prvB.Generate(rand.Reader)
+	checkErr(t, err, "key generation failed")
+
+	// Generate public keys
+	prvA.GeneratePublicKey(pubA)
+	prvB.GeneratePublicKey(pubB)
+
+	// Derive shared secret
+	err = DeriveSecret(s1[:], prvB, pubA)
+	checkErr(t, err, "")
+
+	err = DeriveSecret(s2[:], prvA, pubB)
+	checkErr(t, err, "")
+
+	if !bytes.Equal(s1[:], s2[:]) {
+		t.Fatalf("Two shared keys: \n%X, \n%X do not match", s1, s2)
+	}
+}
+
+// encrypt, decrypt, check if input/output plaintext is the same
+func TestPKERoundTrip(t *testing.T) {
+	// Message to be encrypted
+	var msg = make([]byte, Params.MsgLen)
+	var ct = make([]byte, kem.CiphertextSize())
+	for i, _ := range msg {
+		msg[i] = byte(i)
+	}
+
+	// Import keys
+	pkB := NewPublicKey(KeyVariant_SIKE)
+	skB := NewPrivateKey(KeyVariant_SIKE)
+	pk_hex, err := hex.DecodeString(tdata.PkB_sike)
+	if err != nil {
+		t.Fatal(err)
+	}
+	sk_hex, err := hex.DecodeString(tdata.PrB_sike)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if pkB.Import(pk_hex) != nil || skB.Import(sk_hex) != nil {
+		t.Error("Import")
+	}
+
+	err = encrypt(ct, rand.Reader, pkB, msg[:])
+	if err != nil {
+		t.Fatal(err)
+	}
+	var pt [40]byte
+	pt_len, err := decrypt(pt[:], skB, ct)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !bytes.Equal(pt[:pt_len], msg[:]) {
+		t.Errorf("Decryption failed \n got : %X\n exp : %X", pt, msg)
+	}
+}
+
+// Generate key and check if can encrypt
+func TestPKEKeyGeneration(t *testing.T) {
+	// Message to be encrypted
+	var msg = make([]byte, Params.MsgLen)
+	var ct = make([]byte, kem.CiphertextSize())
+	var err error
+	for i, _ := range msg {
+		msg[i] = byte(i)
+	}
+
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	err = sk.Generate(rand.Reader)
+	checkErr(t, err, "PEK key generation")
+	pk := NewPublicKey(KeyVariant_SIKE)
+	sk.GeneratePublicKey(pk)
+
+	// Try to encrypt
+	err = encrypt(ct, rand.Reader, pk, msg[:])
+	checkErr(t, err, "PEK encryption")
+	var pt [40]byte
+	pt_len, err := decrypt(pt[:], sk, ct)
+	checkErr(t, err, "PEK key decryption")
+
+	if !bytes.Equal(pt[:pt_len], msg[:]) {
+		t.Fatalf("Decryption failed \n got : %X\n exp : %X", pt, msg)
+	}
+}
+
+func TestNegativePKE(t *testing.T) {
+	var msg [40]byte
+	var err error
+	var ct = make([]byte, kem.CiphertextSize())
+
+	// Generate key
+	pk := NewPublicKey(KeyVariant_SIKE)
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	err = sk.Generate(rand.Reader)
+	checkErr(t, err, "key generation")
+
+	sk.GeneratePublicKey(pk)
+
+	// bytelen(msg) - 1
+	err = encrypt(ct, rand.Reader, pk, msg[:Params.KemSize+8-1])
+	if err == nil {
+		t.Fatal("Error hasn't been returned")
+	}
+	for _, v := range ct {
+		if v != 0 {
+			t.Fatal("Returned ciphertext must be not changed")
+		}
+	}
+
+	// KemSize - 1
+	var pt [40]byte
+	pt_len, err := decrypt(pt[:], sk, msg[:Params.KemSize+8-1])
+	if err == nil {
+		t.Fatal("Error hasn't been returned")
+	}
+	if pt_len != 0 {
+		t.Fatal("Ciphertext must be nil")
+	}
+}
+
+func testKEMRoundTrip(t *testing.T, pkB, skB []byte) {
+	ct := make([]byte, kem.CiphertextSize())
+	ss_e := make([]byte, kem.SharedSecretSize())
+	ss_d := make([]byte, kem.SharedSecretSize())
+	// Import keys
+	pk := NewPublicKey(KeyVariant_SIKE)
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	if pk.Import(pkB) != nil || sk.Import(skB) != nil {
+		t.Error("Import failed")
+	}
+
+	checkErr(t, kem.Encapsulate(ct, ss_e, pk),
+		"error: Encapsulation during round-trip")
+	checkErr(t, kem.Decapsulate(ss_d, sk, pk, ct),
+		"error: Decapsulation during round-trip")
+
+	if !bytes.Equal(ss_e, ss_d) {
+		t.Error("Shared secrets from decapsulation and encapsulation differ")
+	}
+}
+
+func TestKEMRoundTrip(t *testing.T) {
+	pk, err := hex.DecodeString(tdata.PkB_sike)
+	checkErr(t, err, "public key B not a number")
+	sk, err := hex.DecodeString(tdata.PrB_sike)
+	checkErr(t, err, "private key B not a number")
+	testKEMRoundTrip(t, pk, sk)
+}
+
+func TestKEMKeyGeneration(t *testing.T) {
+	ct := make([]byte, kem.CiphertextSize())
+	ss_e := make([]byte, kem.SharedSecretSize())
+	ss_d := make([]byte, kem.SharedSecretSize())
+
+	// Generate key
+	pk := NewPublicKey(KeyVariant_SIKE)
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	checkErr(t, sk.Generate(rand.Reader), "error: key generation")
+	sk.GeneratePublicKey(pk)
+
+	// calculated shared secret
+	checkErr(t, kem.Encapsulate(ct, ss_e, pk),
+		"encapsulation failed")
+	checkErr(t, kem.Decapsulate(ss_d, sk, pk, ct),
+		"decapsulation failed")
+
+	if !bytes.Equal(ss_e, ss_d) {
+		t.Fatalf("KEM failed \n encapsulated: %X\n decapsulated: %X", ss_d, ss_e)
+	}
+}
+
+func TestNegativeKEM(t *testing.T) {
+	ct := make([]byte, kem.CiphertextSize())
+	ss_e := make([]byte, kem.SharedSecretSize())
+	ss_d := make([]byte, kem.SharedSecretSize())
+
+	pk := NewPublicKey(KeyVariant_SIKE)
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	checkErr(t, sk.Generate(rand.Reader), "error: key generation")
+	sk.GeneratePublicKey(pk)
+
+	checkErr(t, kem.Encapsulate(ct, ss_e, pk),
+		"pre-requisite for a test failed")
+
+	ct[0] = ct[0] - 1
+	checkErr(t, kem.Decapsulate(ss_d, sk, pk, ct),
+		"decapsulation returns error when invalid ciphertext provided")
+
+	if bytes.Equal(ss_e[:], ss_d) {
+		// no idea how this could ever happen, but it would be very bad
+		t.Error("critical error")
+	}
+
+	// Try encapsulating with SIDH key
+	pkSidh := NewPublicKey(KeyVariant_SIDH_B)
+	prSidh := NewPrivateKey(KeyVariant_SIDH_B)
+	err := kem.Encapsulate(ct, ss_e, pkSidh)
+	if err == nil {
+		t.Error("encapsulation accepts SIDH public key")
+	}
+	// Try decapsulating with SIDH key
+	err = kem.Decapsulate(ss_e, prSidh, pk, ct)
+	if err == nil {
+		t.Error("decapsulation accepts SIDH private key key")
+	}
+}
+
+// In case invalid ciphertext is provided, SIKE's decapsulation must
+// return same (but unpredictable) result for a given key.
+func TestNegativeKEMSameWrongResult(t *testing.T) {
+	ct := make([]byte, kem.CiphertextSize())
+	ss_e := make([]byte, kem.SharedSecretSize())
+	ss_d1 := make([]byte, kem.SharedSecretSize())
+	ss_d2 := make([]byte, kem.SharedSecretSize())
+
+	sk := NewPrivateKey(KeyVariant_SIKE)
+	pk := NewPublicKey(KeyVariant_SIKE)
+
+	// generate keys
+	checkErr(t, sk.Generate(rand.Reader), "error: key generation")
+	sk.GeneratePublicKey(pk)
+
+	checkErr(t, kem.Encapsulate(ct, ss_e, pk),
+		"pre-requisite for a test failed")
+
+	// make ciphertext wrong
+	ct[0] = ct[0] - 1
+	checkErr(t, kem.Decapsulate(ss_d1, sk, pk, ct),
+		"pre-requisite for a test failed")
+
+	// second decapsulation must be done with same, but imported private key
+	var expSk = make([]byte, sk.Size())
+	sk.Export(expSk)
+
+	// creat new private key
+	sk = NewPrivateKey(KeyVariant_SIKE)
+	checkErr(t, sk.Import(expSk),
+		"import failed")
+
+	// try decapsulating again. ss2 must be same as ss1 and different than
+	// original plaintext
+	checkErr(t, kem.Decapsulate(ss_d2, sk, pk, ct),
+		"pre-requisite for a test failed")
+
+	if !bytes.Equal(ss_d1, ss_d2) {
+		t.Error("decapsulation is insecure")
+	}
+
+	if bytes.Equal(ss_e, ss_d1) || bytes.Equal(ss_e, ss_d2) {
+		// this test requires that decapsulation returns wrong result
+		t.Errorf("test implementation error")
+	}
+}
+
+func testKeygen(t *testing.T, pk, sk []byte) {
+	var pubKeyBytes [110 * 3]byte
+	// Import provided private key
+	var prvKey = NewPrivateKey(KeyVariant_SIKE)
+	if prvKey.Import(sk) != nil {
+		panic("sike test: can't load KAT")
+	}
+
+	// Generate public key
+	pubKey := NewPublicKey(KeyVariant_SIKE)
+	prvKey.GeneratePublicKey(pubKey)
+	pubKey.Export(pubKeyBytes[:])
+	if !bytes.Equal(pubKeyBytes[:], pk) {
+		t.Fatalf("KAT keygen form private failed\nExp: %X\nGot: %X\n", pubKeyBytes[:], pk)
+	}
+}
+
+func TestKeyAgreement(t *testing.T) {
+	testKeyAgreement(t, tdata.PkA_sidh, tdata.PrA_sidh, tdata.PkB_sidh, tdata.PrB_sidh)
+}
+
+// Same values as in sike_test.cc
+func TestDecapsulation(t *testing.T) {
+
+	var sk = [28 + 16]byte{
+		0x04, 0x5E, 0x01, 0x42, 0xB8, 0x2F, 0xE1, 0x9A, 0x38, 0x25,
+		0x92, 0xE7, 0xDC, 0xBA, 0xF7, 0x1B, 0xB1, 0xFD, 0x34, 0x42,
+		0xDB, 0x02, 0xBC, 0x9D, 0x4C, 0xD0, 0x72, 0x34, 0x4D, 0xBD,
+		0x06, 0xDF, 0x1C, 0x7D, 0x0A, 0x88, 0xB2, 0x50, 0xC4, 0xF6,
+		0xAE, 0xE8, 0x25, 0x01,
+	}
+
+	var pk = [330]byte{
+		0x6D, 0x8D, 0xF5, 0x7B, 0xCD, 0x47, 0xCA, 0xCB, 0x7A, 0x38,
+		0xB7, 0xA6, 0x90, 0xB7, 0x37, 0x03, 0xD4, 0x6F, 0x27, 0x73,
+		0x74, 0x17, 0x5A, 0xA4, 0x0D, 0xC6, 0x81, 0xAD, 0xDB, 0xF7,
+		0x18, 0xB2, 0x3C, 0x30, 0xCF, 0xAA, 0x08, 0x11, 0x91, 0xCC,
+		0x27, 0x4E, 0xF1, 0xA6, 0xB7, 0xDA, 0xD2, 0xCF, 0x99, 0x7F,
+		0xF7, 0xE1, 0xD0, 0xCE, 0x00, 0xD2, 0x4B, 0xA4, 0x33, 0xB4,
+		0x87, 0x01, 0x3F, 0x02, 0xF7, 0xF9, 0xDE, 0xC3, 0x60, 0x62,
+		0xDA, 0x3F, 0x74, 0xA9, 0x44, 0xBE, 0x19, 0xD5, 0x03, 0x2A,
+		0x79, 0x8C, 0xA7, 0xFF, 0xEA, 0xB3, 0xBB, 0xB5, 0xD4, 0x1D,
+		0x8F, 0x92, 0xCE, 0x62, 0x6E, 0x99, 0x24, 0xD7, 0x57, 0xFA,
+		0xCD, 0xB6, 0xE2, 0x8E, 0xFD, 0x22, 0x0E, 0x31, 0x21, 0x01,
+		0x8D, 0x79, 0xF8, 0x3E, 0x27, 0xEC, 0x43, 0x40, 0xDB, 0x82,
+		0xE5, 0xEB, 0x6C, 0x97, 0x66, 0x29, 0x15, 0x68, 0xB7, 0x4D,
+		0x84, 0xD1, 0x8A, 0x0B, 0x12, 0x36, 0x2C, 0x0C, 0x0A, 0x6E,
+		0x4E, 0xDE, 0xA5, 0x8A, 0xDE, 0x77, 0xDD, 0x70, 0x49, 0x73,
+		0xAC, 0x27, 0x6D, 0x8D, 0x25, 0x9A, 0xE4, 0x25, 0xE8, 0x95,
+		0x8F, 0xFE, 0x90, 0x3B, 0x00, 0x69, 0x20, 0xE8, 0x7C, 0xA5,
+		0xF5, 0x79, 0xC0, 0x61, 0x51, 0x91, 0x35, 0x25, 0x3F, 0x17,
+		0x2F, 0x70, 0x73, 0xF0, 0x89, 0xB5, 0xC8, 0x25, 0xB8, 0xE5,
+		0x7E, 0x34, 0xDD, 0x11, 0xE5, 0xD6, 0xC3, 0xD5, 0x29, 0x89,
+		0xC6, 0x2C, 0x99, 0x53, 0x1D, 0x2C, 0x77, 0xB0, 0xB6, 0xA1,
+		0xBD, 0x79, 0xFB, 0x4A, 0xC2, 0x48, 0x4C, 0x62, 0x51, 0x00,
+		0xE3, 0x91, 0x2A, 0xCB, 0x84, 0x03, 0x5D, 0x2D, 0xC8, 0x33,
+		0xE9, 0x14, 0xBF, 0x74, 0x21, 0xBC, 0xF4, 0x76, 0xE5, 0x42,
+		0xB8, 0xBD, 0xE2, 0xE7, 0x20, 0x95, 0x54, 0xF2, 0xED, 0xC0,
+		0x79, 0x38, 0x1E, 0xD2, 0xEA, 0x1A, 0x63, 0x85, 0xE7, 0x3A,
+		0xDA, 0xAD, 0xAB, 0x1B, 0x1E, 0x19, 0x9E, 0x73, 0xD0, 0x10,
+		0x2E, 0x38, 0xAC, 0x8B, 0x00, 0x6A, 0x30, 0x2C, 0x3D, 0x70,
+		0x8E, 0x39, 0x6D, 0xC0, 0x12, 0x61, 0x7D, 0x2A, 0x0A, 0x04,
+		0x95, 0x8E, 0x09, 0x3C, 0x7B, 0xEC, 0x2E, 0xBC, 0xE8, 0xE8,
+		0xE8, 0x37, 0x29, 0xC4, 0x7E, 0x76, 0x48, 0xB9, 0x3B, 0x72,
+		0xE5, 0x99, 0x9B, 0xF9, 0xE3, 0x99, 0x72, 0x3F, 0x35, 0x29,
+		0x85, 0xE0, 0xC8, 0xBF, 0xB1, 0x6B, 0xB1, 0x6E, 0x72, 0x00,
+	}
+
+	var ct = [330 + 16]byte{
+		0x7C, 0xAB, 0x4E, 0x65, 0x2E, 0xBA, 0xD2, 0xBD, 0x8B, 0x66,
+		0xCA, 0x2B, 0xA8, 0xF9, 0xEF, 0xE2, 0xFD, 0x2E, 0xCA, 0x83,
+		0xE9, 0xCF, 0x50, 0x63, 0x7B, 0x5C, 0x3D, 0xA5, 0xE7, 0xF5,
+		0x9F, 0x73, 0xAC, 0xC8, 0xE4, 0x85, 0xFC, 0x05, 0xCD, 0xED,
+		0x03, 0x25, 0x02, 0xA4, 0xF5, 0x57, 0x4A, 0x76, 0x3C, 0xDE,
+		0x76, 0x52, 0xD0, 0x1B, 0x01, 0xA3, 0xD3, 0xB1, 0x8E, 0xC6,
+		0xE1, 0x54, 0x3F, 0x9B, 0xA9, 0xB6, 0x9B, 0x1A, 0xED, 0x62,
+		0xB5, 0x7A, 0x58, 0xFB, 0xAC, 0xF2, 0xBD, 0xE6, 0x95, 0x0B,
+		0xED, 0x3A, 0x5D, 0x34, 0xB0, 0x54, 0x2D, 0xEF, 0xA9, 0xA7,
+		0xA3, 0xA8, 0xD2, 0xA1, 0x8B, 0x96, 0xFA, 0x8F, 0xDD, 0x2E,
+		0xE4, 0x93, 0x82, 0x97, 0x19, 0x72, 0xC7, 0x7E, 0x50, 0x00,
+		0x8A, 0xE0, 0x0C, 0x5A, 0x94, 0xB2, 0xE1, 0xC3, 0xA5, 0x4D,
+		0x92, 0x97, 0xA2, 0x59, 0x97, 0xBC, 0xB9, 0x7F, 0x27, 0x92,
+		0xA7, 0x7F, 0x5A, 0x7B, 0x8D, 0x24, 0xFF, 0x9A, 0x99, 0xDB,
+		0xDB, 0xE1, 0x5B, 0xD2, 0x10, 0x34, 0x2D, 0x45, 0xA5, 0xE5,
+		0x99, 0x7F, 0xFE, 0x02, 0xCC, 0x57, 0x7A, 0x3A, 0xAB, 0xB3,
+		0x27, 0xE1, 0x55, 0x70, 0x01, 0x3D, 0xC8, 0xAB, 0x90, 0xC6,
+		0x8F, 0x63, 0x8B, 0x30, 0x6F, 0xA1, 0xDC, 0x91, 0xE5, 0x25,
+		0xDF, 0x9A, 0x68, 0x05, 0xC2, 0xD4, 0x13, 0x64, 0xAA, 0xEF,
+		0x21, 0x63, 0x5E, 0xFF, 0x41, 0xFD, 0xF3, 0x92, 0x76, 0xA6,
+		0x09, 0x90, 0xBD, 0x65, 0x56, 0xC9, 0x6D, 0x41, 0xA7, 0x9E,
+		0xC7, 0x15, 0xBF, 0xE1, 0x2D, 0xB0, 0x96, 0x26, 0x21, 0x01,
+		0x60, 0x54, 0x71, 0x56, 0xD9, 0xA2, 0x9B, 0xD2, 0x21, 0x9C,
+		0xD9, 0x0F, 0xF8, 0x5F, 0xC4, 0xF4, 0xF6, 0x8E, 0xCA, 0x87,
+		0x7B, 0x7A, 0xDE, 0x28, 0x05, 0x3F, 0x3F, 0xE7, 0xDA, 0x3B,
+		0x56, 0x64, 0xE0, 0x8D, 0xEB, 0x4A, 0x54, 0x88, 0x05, 0x4C,
+		0x5E, 0x99, 0x45, 0x8C, 0x65, 0x8A, 0x6E, 0x2D, 0x53, 0x1C,
+		0x9B, 0x44, 0xA7, 0xEF, 0x01, 0xF8, 0x31, 0x4D, 0x31, 0xE3,
+		0x75, 0x7B, 0x5F, 0x79, 0x5F, 0xE7, 0x47, 0x4C, 0x08, 0x86,
+		0x84, 0xC8, 0x84, 0x48, 0x89, 0x89, 0x5F, 0x7F, 0x92, 0x68,
+		0x2E, 0x9F, 0xBA, 0x46, 0x6D, 0x34, 0x93, 0x86, 0xE4, 0xEA,
+		0xE6, 0x1F, 0xF8, 0xE1, 0x94, 0xFF, 0x6E, 0xB6, 0x8D, 0x46,
+		0x64, 0xF0, 0xE3, 0xB7, 0x84, 0x0A, 0x5B, 0xE2, 0xC4, 0x01,
+		0x6E, 0xA5, 0xB8, 0xFA, 0xA5, 0x5A, 0x1C, 0x2D, 0xF6, 0x81,
+		0xC2, 0x44, 0x81, 0x5B, 0x00, 0x17,
+	}
+	var ss_exp = [16]byte{
+		0xCB, 0x9C, 0x6B, 0x0A, 0x64, 0x95, 0x32, 0xA7, 0x35, 0x4E,
+		0xE5, 0x14, 0xC8, 0xB7, 0x82, 0xB6,
+	}
+
+	var prvObj = NewPrivateKey(KeyVariant_SIKE)
+	var pubObj = NewPublicKey(KeyVariant_SIKE)
+
+	if pubObj.Import(pk[:]) != nil || prvObj.Import(sk[:]) != nil {
+		t.Error("Can't import one of the keys")
+	}
+
+	res := make([]byte, kem.SharedSecretSize())
+	checkErr(t, kem.Decapsulate(res, prvObj, pubObj, ct[:]),
+		"error: Decapsulation failed")
+
+	if !bytes.Equal(ss_exp[:], res) {
+		t.Error("Wrong decapsulation result")
+	}
+}
+
+func readAndCheckLine(r *bufio.Reader) []byte {
+	// Read next line from buffer
+	line, isPrefix, err := r.ReadLine()
+	if err != nil || isPrefix {
+		panic("Wrong format of input file")
+	}
+
+	// Function expects that line is in format "KEY = HEX_VALUE". Get
+	// value, which should be a hex string
+	hexst := strings.Split(string(line), "=")[1]
+	hexst = strings.TrimSpace(hexst)
+	// Convert value to byte string
+	ret, err := hex.DecodeString(hexst)
+	if err != nil {
+		panic("Wrong format of input file")
+	}
+	return ret
+}
+
+func TestKAT(t *testing.T) {
+	ssGot := make([]byte, kem.SharedSecretSize())
+	testDecapsulation := func(t *testing.T, pk, sk, ct, ssExpected []byte) {
+		var pubKey = NewPublicKey(KeyVariant_SIKE)
+		var prvKey = NewPrivateKey(KeyVariant_SIKE)
+		if pubKey.Import(pk) != nil || prvKey.Import(sk) != nil {
+			panic("sike test: can't load KAT")
+		}
+
+		err := kem.Decapsulate(ssGot, prvKey, pubKey, ct)
+		if err != nil {
+			panic("sike test: can't perform degcapsulation KAT")
+		}
+
+		if (err != nil) || !bytes.Equal(ssGot, ssExpected) {
+			t.Fatalf("KAT decapsulation failed\n")
+		}
+	}
+	f, err := os.Open(tdata.katFile)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	r := bufio.NewReader(f)
+	for {
+		line, isPrefix, err := r.ReadLine()
+		if err != nil || isPrefix {
+			if err == io.EOF {
+				break
+			} else {
+				t.Fatal(err)
+			}
+		}
+		if len(strings.TrimSpace(string(line))) == 0 || line[0] == '#' {
+			continue
+		}
+
+		// count
+		_ = strings.Split(string(line), "=")[1]
+		// seed
+		_ = readAndCheckLine(r)
+		// pk
+		pk := readAndCheckLine(r)
+		// sk (secret key in test vector is concatenation of
+		// MSG + SECRET_BOB_KEY + PUBLIC_BOB_KEY. We use only MSG+SECRET_BOB_KEY
+		sk := readAndCheckLine(r)
+		sk = sk[:Params.MsgLen+int(Params.B.SecretByteLen)]
+		// ct
+		ct := readAndCheckLine(r)
+		// ss
+		ss := readAndCheckLine(r)
+		testKeygen(t, pk, sk)
+		testDecapsulation(t, pk, sk, ct, ss)
+		testKEMRoundTrip(t, pk, sk)
+	}
+}
+
+/* -------------------------------------------------------------------------
+Benchmarking
+-------------------------------------------------------------------------*/
+
+func BenchmarkKeygen(b *testing.B) {
+	pk := NewPublicKey(KeyVariant_SIKE)
+	prv := NewPrivateKey(KeyVariant_SIKE)
+	prv.Generate(rand.Reader)
+
+	for n := 0; n < b.N; n++ {
+		prv.GeneratePublicKey(pk)
+	}
+}
+
+func BenchmarkEncaps(b *testing.B) {
+	pub := NewPublicKey(KeyVariant_SIKE)
+	prv := NewPrivateKey(KeyVariant_SIKE)
+
+	if prv.Generate(rand.Reader) != nil {
+		b.FailNow()
+	}
+	prv.GeneratePublicKey(pub)
+
+	var ct [16 + 330]byte
+	var ss [16]byte
+
+	for n := 0; n < b.N; n++ {
+		kem.Reset()
+		kem.Encapsulate(ct[:], ss[:], pub)
+	}
+}
+
+func BenchmarkDecaps(b *testing.B) {
+	var ct [16 + 330]byte
+	var ss [16]byte
+
+	pkA := NewPublicKey(KeyVariant_SIKE)
+	prvA := NewPrivateKey(KeyVariant_SIKE)
+	pkB := NewPublicKey(KeyVariant_SIKE)
+	prvB := NewPrivateKey(KeyVariant_SIKE)
+
+	if prvA.Generate(rand.Reader) != nil || prvB.Generate(rand.Reader) != nil {
+		b.FailNow()
+	}
+
+	prvA.GeneratePublicKey(pkA)
+	prvB.GeneratePublicKey(pkB)
+
+	err := kem.Encapsulate(ct[:], ss[:], pkA)
+	if err != nil {
+		b.FailNow()
+	}
+
+	for n := 0; n < b.N; n++ {
+		kem.Decapsulate(ss[:], prvA, pkB, ct[:])
+	}
+}
+
+var kem KEM
+
+func init() {
+	kem.Allocate(rand.Reader)
+}

p434/types.go

@@ -0,0 +1,122 @@
+package sike
+
+// I keep it bool in order to be able to apply logical NOT
+type KeyVariant uint
+
+// Representation of an element of the base field F_p.
+//
+// No particular meaning is assigned to the representation -- it could represent
+// an element in Montgomery form, or not.  Tracking the meaning of the field
+// element is left to higher types.
+type Fp [FP_WORDS]uint64
+
+// Represents an intermediate product of two elements of the base field F_p.
+type FpX2 [2 * FP_WORDS]uint64
+
+// Represents an element of the extended field Fp^2 = Fp(x+i)
+type Fp2 struct {
+	A Fp
+	B Fp
+}
+
+type DomainParams struct {
+	// P, Q and R=P-Q base points
+	Affine_P, Affine_Q, Affine_R Fp2
+	// Size of a compuatation strategy for x-torsion group
+	IsogenyStrategy []uint32
+	// Max size of secret key for x-torsion group
+	SecretBitLen uint
+	// Max size of secret key for x-torsion group
+	SecretByteLen uint
+}
+
+type SidhParams struct {
+	Id uint8
+	// Bytelen of P
+	Bytelen int
+	// The public key size, in bytes.
+	PublicKeySize int
+	// The shared secret size, in bytes.
+	SharedSecretSize int
+	// Defines A,C constant for starting curve Cy^2 = x^3 + Ax^2 + x
+	InitCurve ProjectiveCurveParameters
+	// 2- and 3-torsion group parameter definitions
+	A, B DomainParams
+	// Precomputed 1/2 in the Fp2 in Montgomery domain
+	HalfFp2 Fp2
+	// Precomputed identity element in the Fp2 in Montgomery domain
+	OneFp2 Fp2
+	// Length of SIKE secret message. Must be one of {24,32,40},
+	// depending on size of prime field used (see [SIKE], 1.4 and 5.1)
+	MsgLen int
+	// Length of SIKE ephemeral KEM key (see [SIKE], 1.4 and 5.1)
+	KemSize int
+	// Size of a ciphertext returned by encapsulation in bytes
+	CiphertextSize int
+}
+
+// Stores curve projective parameters equivalent to A/C. Meaning of the
+// values depends on the context. When working with isogenies over
+// subgroup that are powers of:
+// * three then  (A:C) ~ (A+2C:A-2C)
+// * four then   (A:C) ~ (A+2C:  4C)
+// See Appendix A of SIKE for more details
+type CurveCoefficientsEquiv struct {
+	A Fp2
+	C Fp2
+}
+
+// A point on the projective line P^1(F_{p^2}).
+//
+// This represents a point on the Kummer line of a Montgomery curve.  The
+// curve is specified by a ProjectiveCurveParameters struct.
+type ProjectivePoint struct {
+	X Fp2
+	Z Fp2
+}
+
+// Base type for public and private key. Used mainly to carry domain
+// parameters.
+type key struct {
+	// Domain parameters of the algorithm to be used with a key
+	params *SidhParams
+	// Flag indicates wether corresponds to 2-, 3-torsion group or SIKE
+	keyVariant KeyVariant
+}
+
+// Defines operations on private key
+type PrivateKey struct {
+	key
+	// Secret key
+	Scalar []byte
+	// Used only by KEM
+	S []byte
+}
+
+// Defines operations on public key
+type PublicKey struct {
+	key
+	affine_xP   Fp2
+	affine_xQ   Fp2
+	affine_xQmP Fp2
+}
+
+// A point on the projective line P^1(F_{p^2}).
+//
+// This is used to work projectively with the curve coefficients.
+type ProjectiveCurveParameters struct {
+	A Fp2
+	C Fp2
+}
+
+const (
+	// First 2 bits identify SIDH variant third bit indicates
+	// wether key is a SIKE variant (set) or SIDH (not set)
+
+	// 001 - SIDH: corresponds to 2-torsion group
+	KeyVariant_SIDH_A KeyVariant = 1 << 0
+	// 010 - SIDH: corresponds to 3-torsion group
+	KeyVariant_SIDH_B = 1 << 1
+	// 110 - SIKE
+	KeyVariant_SIKE = 1<<2 | KeyVariant_SIDH_B
+)

p503/arith.go

@@ -11,12 +11,11 @@ package sike
 func p34(dest, x *Fp) {
 	var lookup [16]Fp
 
-	// Sliding-window strategy computed with etc/scripts/sliding_window_strat_calc.py
-	//
 	// This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy)
 	// multiplications.
-	powStrategy := []uint8{1, 12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3}
-	mulStrategy := []uint8{0, 12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3}
+	powStrategy := []uint8{12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3}
+	mulStrategy := []uint8{12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3}
+	initialMul := uint8(0)
 
 	// Precompute lookup table of odd multiples of x for window
 	// size k=5.
@@ -30,8 +29,8 @@ func p34(dest, x *Fp) {
 	// Now lookup = {x, x^3, x^5, ... }
 	// so that lookup[i] = x^{2*i + 1}
 	// so that lookup[k/2] = x^k, for odd k
-	*dest = lookup[mulStrategy[0]]
-	for i := uint8(1); i < uint8(len(powStrategy)); i++ {
+	*dest = lookup[initialMul]
+	for i := uint8(0); i < uint8(len(powStrategy)); i++ {
 		fpMulRdc(dest, dest, dest)
 		for j := uint8(1); j < powStrategy[i]; j++ {
 			fpMulRdc(dest, dest, dest)

p503/consts.go

@@ -31,12 +31,6 @@ var pR2 = Fp{
 	0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771,
 }
 
-// p503 + 1 left-shifted by 8, assuming little endianness
-var p1s8 = Fp{
-	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
-	0x085BDA2211E7A0AC, 0x9BF6C87B7E7DAF13, 0x45C6BDDA77A4D01B, 0x4066F541811E1E60,
-}
-
 // 1/2 * R mod p
 var half = Fp2{
 	A: Fp{

p503/sike_test.go

@@ -37,6 +37,7 @@ var tdata = struct {
    -------------------------------------------------------------------------*/
 // Fail if err !=nil. Display msg as an error message
 func checkErr(t testing.TB, err error, msg string) {
+	t.Helper()
 	if err != nil {
 		t.Error(msg)
 	}
@@ -92,7 +93,7 @@ func TestKeygen(t *testing.T) {
 	expPubA.Export(keyGot[:])
 	if !bytes.Equal(keyExp[:], keyGot[:]) {
 		t.Fatalf("unexpected value of public key A [\nGot: %X\nExp: %X]\n",
-			keyExp, keyGot)
+			keyGot, keyExp)
 	}
 
 	for i, _ := range keyExp {
@@ -104,7 +105,7 @@ func TestKeygen(t *testing.T) {
 	expPubB.Export(keyGot[:])
 	if !bytes.Equal(keyExp[:], keyGot[:]) {
 		t.Fatalf("unexpected value of public key B [\nGot: %X\nExp: %X]\n",
-			keyExp, keyGot)
+			keyGot, keyExp)
 	}
 }
 
@@ -642,22 +643,22 @@ func readAndCheckLine(r *bufio.Reader) []byte {
 
 func TestKAT(t *testing.T) {
 	ssGot := make([]byte, kemSikeP503.SharedSecretSize())
-		testDecapsulation := func(t *testing.T, pk, sk, ct, ssExpected []byte) {
-			var pubKey = NewPublicKey(KeyVariant_SIKE)
-			var prvKey = NewPrivateKey(KeyVariant_SIKE)
-			if pubKey.Import(pk) != nil || prvKey.Import(sk) != nil {
-				panic("sike test: can't load KAT")
-			}
+	testDecapsulation := func(t *testing.T, pk, sk, ct, ssExpected []byte) {
+		var pubKey = NewPublicKey(KeyVariant_SIKE)
+		var prvKey = NewPrivateKey(KeyVariant_SIKE)
+		if pubKey.Import(pk) != nil || prvKey.Import(sk) != nil {
+			panic("sike test: can't load KAT")
+		}
 
-			err := kemSikeP503.Decapsulate(ssGot, prvKey, pubKey, ct)
-			if err != nil {
-				panic("sike test: can't perform degcapsulation KAT")
-			}
+		err := kemSikeP503.Decapsulate(ssGot, prvKey, pubKey, ct)
+		if err != nil {
+			panic("sike test: can't perform degcapsulation KAT")
+		}
 
-			if (err != nil) || !bytes.Equal(ssGot, ssExpected) {
-				t.Fatalf("KAT decapsulation failed\n")
-			}
+		if (err != nil) || !bytes.Equal(ssGot, ssExpected) {
+			t.Fatalf("KAT decapsulation failed\n")
 		}
+	}
 	f, err := os.Open(tdata.katFile)
 	if err != nil {
 		t.Fatal(err)

tools/sliding_window_strat_calc.py

@@ -0,0 +1,74 @@
+#!/usr/bin/env python2
+
+# Calculates .... yeah, what does it really calculate? OZAPTF
+# (P-3)/4: Least significant bit is first
+
+# Configuration
+# kWindowSize and kP34 must be specified
+#
+# P434
+kP34 = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+# P503
+#kP34 = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+# P751
+#kP34 = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+kWindowSize = 5
+
+
+table_pow = []
+table_mul = []
+
+i=0
+while i<len(kP34):
+    count_pow2k=0
+    count_mul=0
+
+    # Count zeros, each zero means additional x^2 operation
+    if kP34[i] == 0:
+        while i < len(kP34) and kP34[i] == 0:
+            count_pow2k = count_pow2k + 1
+            i = i + 1
+
+    # Stop if finished
+    if i>=len(kP34):
+        break
+
+    # Calculate length of a {1,0}, so that it starts & ends
+    # with 1 and len() <= kWindowSize
+    if kP34[i] == 1:
+        # max string len is either 5 or len(kP34)
+        if i+kWindowSize>=len(kP34):
+            string_max_len = len(kP34)-i
+        else:
+            string_max_len = kWindowSize
+
+        # look backward for first occurence of 1
+        tmp = i + string_max_len - 1
+        while tmp>=i:
+            if kP34[tmp] == 1:
+                break
+            tmp = tmp - 1
+        e_string_len = tmp - i + 1
+
+        # calculate number from bit-string of size e_string_len
+        tmp = 0
+        num = 0
+        for x in kP34[i:i+e_string_len]:
+            num = num | (x << e_string_len - tmp - 1)
+            tmp = tmp + 1
+        table_mul.append(int(num/2))
+
+        # set new number of pow2k operations
+        count_pow2k = count_pow2k + e_string_len
+
+        # advance i
+        i = i + e_string_len
+
+    else:
+        raise "Wrong number in kP34 at possition " % i
+
+    table_pow.append(count_pow2k)
+
+# skips first values to print exact table used by the algorithm
+print(table_pow)
+print(table_mul)