nobs/dh/sidh/sidh_test.go

package sidh

import (
	"bytes"
	"crypto/rand"
	"encoding/hex"
	"fmt"
	"math/big"
	"testing"

	. "github.com/henrydcase/nobs/dh/sidh/internal/isogeny"
)

/* -------------------------------------------------------------------------
   Test data
   -------------------------------------------------------------------------*/
var tdata = map[uint8]struct {
	name    string
	KatFile string
	PkA     string
	PrA     string
	PkB     string
	PrB     string
}{
	FP_503: {
		name: "P-503",
		PrA:  "B0AD510708F4ABCF3E0D97DC2F2FF112D9D2AAE49D97FFD1E4267F21C6E71C03",
		PrB:  "A885A8B889520A6DBAD9FB33365E5B77FDED629440A16A533F259A510F63A822",
		PkA: "A6BADBA04518A924B20046B59AC197DCDF0EA48014C9E228C4994CCA432F360E" +
			"2D527AFB06CA7C96EE5CEE19BAD53BF9218A3961CAD7EC092BD8D9EBB22A3D51" +
			"33008895A3F1F6A023F91E0FE06A00A622FD6335DAC107F8EC4283DC2632F080" +
			"4E64B390DAD8A2572F1947C67FDF4F8787D140CE2C6B24E752DA9A195040EDFA" +
			"C27333FAE97DBDEB41DA9EEB2DB067AE7DA8C58C0EF57AEFC18A3D6BD0576FF2" +
			"F1CFCAEC50C958331BF631F3D2E769790C7B6DF282B74BBC02998AD10F291D47" +
			"C5A762FF84253D3B3278BDF20C8D4D4AA317BE401B884E26A1F02C7308AADB68" +
			"20EBDB0D339F5A63346F3B40CACED72F544DAF51566C6E807D0E6E1E38514342" +
			"432661DC9564DA07548570E256688CD9E8060D8775F95D501886D958588CACA0" +
			"9F2D2AE1913F996E76AF63E31A179A7A7D2A46EDA03B2BCCF9020A5AA15F9A28" +
			"9340B33F3AE7F97360D45F8AE1B9DD48779A57E8C45B50A02C00349CD1C58C55" +
			"1D68BC2A75EAFED944E8C599C288037181E997471352E24C952B",
		PkB: "244AF1F367C2C33912750A98497CC8214BC195BD52BD76513D32ACE4B75E31F0" +
			"281755C265F5565C74E3C04182B9C244071859C8588CC7F09547CEFF8F7705D2" +
			"60CE87D6BFF914EE7DBE4B9AF051CA420062EEBDF043AF58184495026949B068" +
			"98A47046BFAE8DF3B447746184AF550553BB5D266D6E1967ACA33CAC5F399F90" +
			"360D70867F2C71EF6F94FF915C7DA8BC9549FB7656E691DAEFC93CF56876E482" +
			"CA2F8BE2D6CDCC374C31AD8833CABE997CC92305F38497BEC4DFD1821B004FEC" +
			"E16448F9A24F965EFE409A8939EEA671633D9FFCF961283E59B8834BDF7EDDB3" +
			"05D6275B61DA6692325432A0BAA074FC7C1F51E76208AB193A57520D40A76334" +
			"EE5712BDC3E1EFB6103966F2329EDFF63082C4DFCDF6BE1C5A048630B81871B8" +
			"83B735748A8FD4E2D9530C272163AB18105B10015CA7456202FE1C9B92CEB167" +
			"5EAE1132E582C88E47ED87B363D45F05BEA714D5E9933D7AF4071CBB5D49008F" +
			"3E3DAD7DFF935EE509D5DE561842B678CCEB133D62E270E9AC3E",
	},
	FP_751: {
		name: "P-751",
		// PrA - Alice's Private Key: 2*randint(0,2^371)
		PrA: "C09957CC83045FB4C3726384D784476ACB6FFD92E5B15B3C2D451BA063F1BD4CED8FBCF682A98DD0954D3" +
			"7BCAF730E",
		// PrB - Bob's Private Key: 3*randint(0,3^238)
		PrB: "393E8510E78A16D2DC1AACA9C9D17E7E78DB630881D8599C7040D05BB5557ECAE8165C45D5366ECB37B00" +
			"969740AF201",
		PkA: "74D8EF08CB74EC99BF08B6FBE4FB3D048873B67F018E44988B9D70C564D058401D20E093C7DF0C66F022C" +
			"823E5139D2EA0EE137804B4820E950B046A90B0597759A0B6A197C56270128EA089FA1A2007DDE3430B37" +
			"A3E6350BD47B7F513863741C125FA63DEDAFC475C13DB59E533055B7CBE4B2F32672DF2DF97E03E29617B" +
			"0E9B6A35B58ABB26527A721142701EB147C7050E1D9125DA577B08CD51C8BB50627B8B47FACFC9C7C07DD" +
			"00DD75115DD83719FD5F96115DED23ECAA50B1044C6BF3F27442DA284BA4A272D850F414FB185801BF2EF" +
			"7E628EDB5643E35694B992CF30A2C5120CAF9434F09ACFCA3645B3FFC3A308901FAC7B8955FD5C98576AE" +
			"FD03F5806CB7430F75B3431B75BEC080596ABCA26E637E6E8D4C25175A8C052C9CBE77900A863F83FAB00" +
			"95B32D9C3858EF8A35B9F163D429E71DBA47539EB4791D117FE39DDE94EA7801A42DB12D84DE4740ACF51" +
			"CD7C32BB854569D7D94E11E69D9663CC7ED02E78CF48F4069DF3D3E86198B307095C6B11D46C0DC849F9D" +
			"94C7693209E5B3848AFAA6DA6A8D73362D779CBC43515902ED2BCE3A748C537DE2FCF092FD3E91B790AF5" +
			"4E1092C5E5B89BE5BE23B955A52F769D97277EF69F820109042F28C316AC90AE69EB374C9280300B816E6" +
			"2494B2E01072D1CA96E4B284D2BE1368D6969744B614FACBC8C165864E26E33481D4FDC47B6E523954A25" +
			"C1A096A37CD23FB81AE64FB11BD0A439609F1CE40673B06DD96F698A910E935219D840F3D411EDFB00D98" +
			"065AB9868C32D3DA05FF415",
		PkB: "F6C260C4141E418457CB442E11F0F5558375437576E55D211D19EF83E2839E51D07A82765D8E7B6366FA7" +
			"0B56CDE3AD3B629ACF542A433369496EDA51EDFBE16EFA1B8DEE1CE46B37820ECBD0CD674AACD4F21FABC" +
			"2436651E3AF604356FF3EB2CA87976890E34A56FAEC9A2ACD9559B1BB67B69AC1A521342E1E787DA5D709" +
			"32B0F5842ECA1C99B269DB6C2ED8397F0FC49F114CF8B5AF327A698C0251575CDD1D67732668109A91A3B" +
			"FA5B47D413C7FAB8817FCBEBFE9BDD9C0B1F3B1934A7028A65233E8B58A92E7E9F66B68B2057ECBF7E44A" +
			"0EF6EFCC3C8AA5414E100FA0C24F7545324AD17062FC11377A2A4749DEE27E192460E099DBDA8E840EA11" +
			"AD9D5C83DF065AF77030E7FE18CE24CFC71D356B9B9601811B93676C12CB6B41747133D5259E7A20CC065" +
			"FAB99DF944FDB34ABB9A374F9E9CC8F9C186BD2181DC2771F69C02629C3E4801A7E7C21F6F3CFF7D257E2" +
			"257C88C015F0CC8DC0E7FB3373CF4ED6A786AB329E7F16895CA147AD91F6EAE1DFE38116580DF52381599" +
			"E4246278CB1848FE4A56ABF98652E9E7C2E681551A3D78FA033D932087D8B6567D779A56B726B153033D7" +
			"2231A1B5C16ED7DC4458308D6B64AF6723CC0F52C94E04C58FCA9739E890AA40CC05E22321F10129D2B59" +
			"1F317102034C109A56D711591E5B44C717CFC9C9B9461894767CAFA42D2B394194B03999C2A9EF48868F3" +
			"FB03D1A40F596613AF97F4ED7643A1C2D12692E959C6DEB8E72403ADC0E42204DBCE5056EEF0CC60B0C6E" +
			"83B8B55AC01F6C85644EE49",
	},
}

/* -------------------------------------------------------------------------
   Helpers
   -------------------------------------------------------------------------*/
// Fail if err !=nil. Display msg as an error message
func checkErr(t testing.TB, err error, msg string) {
	if err != nil {
		t.Error(msg)
	}
}

// Utility used for running same test with all registered prime fields
type MultiIdTestingFunc func(testing.TB, uint8)

func Do(f MultiIdTestingFunc, t testing.TB) {
	for id, val := range tdata {
		fmt.Printf("\tTesting: %s\n", val.name)
		f(t, id)
	}
}

// Converts string to private key
func convToPrv(s string, v KeyVariant, id uint8) *PrivateKey {
	key := NewPrivateKey(id, 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, id uint8) *PublicKey {
	key := NewPublicKey(id, 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.TB, id uint8) {
	prvB := NewPrivateKey(id, KeyVariant_SIDH_B)
	err := prvB.Generate(rand.Reader)
	checkErr(t, err, "key generation failed")

	alicePrivate := convToPrv(tdata[id].PrA, KeyVariant_SIDH_A, id)
	bobPrivate := convToPrv(tdata[id].PrB, KeyVariant_SIDH_B, id)
	expPubA := convToPub(tdata[id].PkA, KeyVariant_SIDH_A, id)
	expPubB := convToPub(tdata[id].PkB, KeyVariant_SIDH_B, id)

	pubA := alicePrivate.GeneratePublicKey()
	pubB := bobPrivate.GeneratePublicKey()

	if !bytes.Equal(pubA.Export(), expPubA.Export()) {
		t.Fatalf("unexpected value of public key A")
	}
	if !bytes.Equal(pubB.Export(), expPubB.Export()) {
		t.Fatalf("unexpected value of public key B")
	}
}

func testRoundtrip(t testing.TB, id uint8) {
	var err error

	prvA := NewPrivateKey(id, KeyVariant_SIDH_A)
	prvB := NewPrivateKey(id, 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
	pubA := prvA.GeneratePublicKey()
	pubB := prvB.GeneratePublicKey()

	// Derive shared secret
	s1, err := DeriveSecret(prvB, pubA)
	checkErr(t, err, "")

	s2, err := DeriveSecret(prvA, pubB)
	checkErr(t, err, "")

	if !bytes.Equal(s1[:], s2[:]) {
		t.Fatalf("Tthe two shared keys: \n%X, \n%X do not match", s1, s2)
	}
}

func testKeyAgreement(t testing.TB, id uint8, pkA, prA, pkB, prB string) {
	var e error

	// KeyPairs
	alicePublic := convToPub(pkA, KeyVariant_SIDH_A, id)
	bobPublic := convToPub(pkB, KeyVariant_SIDH_B, id)
	alicePrivate := convToPrv(prA, KeyVariant_SIDH_A, id)
	bobPrivate := convToPrv(prB, KeyVariant_SIDH_B, id)

	// Do actual test
	s1, e := DeriveSecret(bobPrivate, alicePublic)
	checkErr(t, e, "derivation s1")
	s2, e := DeriveSecret(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[id].PkA)
	if e != nil {
		t.FailNow()
	}
	dec[0] = ^dec[0]
	e = alicePublic.Import(dec)
	if e != nil {
		t.FailNow()
	}

	s1, e = DeriveSecret(bobPrivate, alicePublic)
	checkErr(t, e, "derivation of s1 failed")
	s2, e = DeriveSecret(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 testImportExport(t testing.TB, id uint8) {
	var err error
	a := NewPublicKey(id, KeyVariant_SIDH_A)
	b := NewPublicKey(id, KeyVariant_SIDH_B)

	// Import keys
	a_hex, err := hex.DecodeString(tdata[id].PkA)
	checkErr(t, err, "invalid hex-number provided")

	err = a.Import(a_hex)
	checkErr(t, err, "import failed")

	b_hex, err := hex.DecodeString(tdata[id].PkB)
	checkErr(t, err, "invalid hex-number provided")

	err = b.Import(b_hex)
	checkErr(t, err, "import failed")

	// Export and check if same
	if !bytes.Equal(b.Export(), b_hex) || !bytes.Equal(a.Export(), a_hex) {
		t.Fatalf("export/import failed")
	}

	if (len(b.Export()) != b.Size()) || (len(a.Export()) != a.Size()) {
		t.Fatalf("wrong size of exported keys")
	}
}

func testPrivateKeyBelowMax(t testing.TB, id uint8) {
	params := Params(id)
	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(id, v)

			// 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()
				secretBytes := prv.Export()
				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 TestKeyAgreementP751(t *testing.T) {
	for id, val := range tdata {
		fmt.Printf("\tTesting: %s\n", val.name)
		testKeyAgreement(t, id, tdata[id].PkA, tdata[id].PrA, tdata[id].PkB, tdata[id].PrB)
	}
}

func TestKeyAgreementP751_AliceEvenNumber(t *testing.T) {
	// even alice
	prE := "C09957CC83045FB4C3726384D784476ACB6FFD92E5B15B3C2D451BA063F1BD4CED8FBCF682A98DD0954D37BCAF730F"
	pkE := "8A2DE6FD963C475F7829B689C8B8306FC0917A39EBBC35CA171546269A85698FEC0379E2E1A3C567BE1B8EF5639F81F304889737E6CC444DBED4579DB204DC8C7928F5CBB1ECDD682A1B5C48C0DAF34208C06BF201BE4E6063B1BFDC42413B0537F8E76BEE645C1A24118301BAB17EB8D6E0F283BCB16EFB833E4BB3463953C93165A0DDAC55B385059F27FF7228486D0A733812C81C792BE9EC3A16A5DB0EB099EEA76AC0E59612251A3AD19F7CC567DA2AEBD7733171F48E471D17648692355164E27B515D2A47D7BA34B3B48A047BE7C09C4ABEE2FCC9ACA7396C8A8C9E73E29533FC7369094DFA7988778E55E53F309922C6E233F8F9C7936C3D29CEA640406FCA06450AA1978FF39F227BF06B1E072F1763447C6F513B23CDF3B0EC0379070AEE5A02D9AD8E0EB023461D631F4A9643A4C79921334945F6B33DDFC11D9703BD06B047B4DA404AB12EFD2C3A49E5C42D10DA063352748B21DE41C32A5693FE1C0DCAB111F4990CD58BECADB1892EE7A7E99C9DB4DA4E69C96E57138B99038BC9B877ECE75914EFB98DD08B9E4A2DCCB948A8F7D2F26678A9952BA0EFAB1E9CF6E51B557480DEC2BA30DE0FE4AFE30A6B30765EE75EF64F678316D81C72755AD2CFA0B8C7706B07BFA52FBC3DB84EF9E79796C0089305B1E13C78660779E0FF2A13820CE141104F976B1678990F85B2D3D2B89CD5BC4DD52603A5D24D3EFEDA44BAA0F38CDB75A220AF45EAB70F2799875D435CE50FC6315EDD4BB7AA7260AFD7CD0561B69B4FA3A817904322661C3108DA24"
	testKeyAgreement(t, FP_751, pkE, prE, tdata[FP_751].PkB, tdata[FP_751].PrB)
}

/* -------------------------------------------------------------------------
   Wrappers for 'testing' module
   -------------------------------------------------------------------------*/
func TestKeygen(t *testing.T)             { Do(testKeygen, t) }
func TestRoundtrip(t *testing.T)          { Do(testRoundtrip, t) }
func TestImportExport(t *testing.T)       { Do(testImportExport, t) }
func TestPrivateKeyBelowMax(t *testing.T) { Do(testPrivateKeyBelowMax, t) }

/* -------------------------------------------------------------------------
   Benchmarking
   -------------------------------------------------------------------------*/
func BenchmarkSidhKeyAgreementP751(b *testing.B) {
	// KeyPairs
	alicePublic := convToPub(tdata[FP_751].PkA, KeyVariant_SIDH_A, FP_751)
	bobPublic := convToPub(tdata[FP_751].PkB, KeyVariant_SIDH_B, FP_751)
	alicePrivate := convToPrv(tdata[FP_751].PrA, KeyVariant_SIDH_A, FP_751)
	bobPrivate := convToPrv(tdata[FP_751].PrB, KeyVariant_SIDH_B, FP_751)

	for i := 0; i < b.N; i++ {
		// Derive shared secret
		DeriveSecret(bobPrivate, alicePublic)
		DeriveSecret(alicePrivate, bobPublic)
	}
}

func BenchmarkSidhKeyAgreementP503(b *testing.B) {
	// KeyPairs
	alicePublic := convToPub(tdata[FP_503].PkA, KeyVariant_SIDH_A, FP_503)
	bobPublic := convToPub(tdata[FP_503].PkB, KeyVariant_SIDH_B, FP_503)
	alicePrivate := convToPrv(tdata[FP_503].PrA, KeyVariant_SIDH_A, FP_503)
	bobPrivate := convToPrv(tdata[FP_503].PrB, KeyVariant_SIDH_B, FP_503)

	for i := 0; i < b.N; i++ {
		// Derive shared secret
		DeriveSecret(bobPrivate, alicePublic)
		DeriveSecret(alicePrivate, bobPublic)
	}
}

func BenchmarkAliceKeyGenPrvP751(b *testing.B) {
	prv := NewPrivateKey(FP_751, KeyVariant_SIDH_A)
	for n := 0; n < b.N; n++ {
		prv.Generate(rand.Reader)
	}
}

func BenchmarkAliceKeyGenPrvP503(b *testing.B) {
	prv := NewPrivateKey(FP_503, KeyVariant_SIDH_A)
	for n := 0; n < b.N; n++ {
		prv.Generate(rand.Reader)
	}
}

func BenchmarkBobKeyGenPrvP751(b *testing.B) {
	prv := NewPrivateKey(FP_751, KeyVariant_SIDH_B)
	for n := 0; n < b.N; n++ {
		prv.Generate(rand.Reader)
	}
}

func BenchmarkBobKeyGenPrvP503(b *testing.B) {
	prv := NewPrivateKey(FP_503, KeyVariant_SIDH_B)
	for n := 0; n < b.N; n++ {
		prv.Generate(rand.Reader)
	}
}

func BenchmarkAliceKeyGenPubP751(b *testing.B) {
	prv := NewPrivateKey(FP_751, KeyVariant_SIDH_A)
	prv.Generate(rand.Reader)
	for n := 0; n < b.N; n++ {
		prv.GeneratePublicKey()
	}
}

func BenchmarkAliceKeyGenPubP503(b *testing.B) {
	prv := NewPrivateKey(FP_503, KeyVariant_SIDH_A)
	prv.Generate(rand.Reader)
	for n := 0; n < b.N; n++ {
		prv.GeneratePublicKey()
	}
}

func BenchmarkBobKeyGenPubP751(b *testing.B) {
	prv := NewPrivateKey(FP_751, KeyVariant_SIDH_B)
	prv.Generate(rand.Reader)
	for n := 0; n < b.N; n++ {
		prv.GeneratePublicKey()
	}
}

func BenchmarkBobKeyGenPubP503(b *testing.B) {
	prv := NewPrivateKey(FP_503, KeyVariant_SIDH_B)
	prv.Generate(rand.Reader)
	for n := 0; n < b.N; n++ {
		prv.GeneratePublicKey()
	}
}

func BenchmarkSharedSecretAliceP751(b *testing.B) {
	aPr := convToPrv(tdata[FP_751].PrA, KeyVariant_SIDH_A, FP_751)
	bPk := convToPub(tdata[FP_751].PkB, KeyVariant_SIDH_B, FP_751)
	for n := 0; n < b.N; n++ {
		DeriveSecret(aPr, bPk)
	}
}

func BenchmarkSharedSecretAliceP503(b *testing.B) {
	aPr := convToPrv(tdata[FP_503].PrA, KeyVariant_SIDH_A, FP_503)
	bPk := convToPub(tdata[FP_503].PkB, KeyVariant_SIDH_B, FP_503)
	for n := 0; n < b.N; n++ {
		DeriveSecret(aPr, bPk)
	}
}

func BenchmarkSharedSecretBobP751(b *testing.B) {
	// m_B = 3*randint(0,3^238)
	aPk := convToPub(tdata[FP_751].PkA, KeyVariant_SIDH_A, FP_751)
	bPr := convToPrv(tdata[FP_751].PrB, KeyVariant_SIDH_B, FP_751)
	for n := 0; n < b.N; n++ {
		DeriveSecret(bPr, aPk)
	}
}

func BenchmarkSharedSecretBobP503(b *testing.B) {
	// m_B = 3*randint(0,3^238)
	aPk := convToPub(tdata[FP_503].PkA, KeyVariant_SIDH_A, FP_503)
	bPr := convToPrv(tdata[FP_503].PrB, KeyVariant_SIDH_B, FP_503)
	for n := 0; n < b.N; n++ {
		DeriveSecret(bPr, aPk)
	}
}