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- # P434
- e2 = 0xD8
- e3 = 0x89
- # P503
- # e2=0xFA
- # e3=0x9F
- #e2=0x174
- #e3=0xEF
-
- Nsk2_max_val = (2^e2) - 1
- Nsk2_bytes = floor(e2/8)
- Nsk3_S = ceil(RDF(log(3^e3,2)))
- Nsk3_bytes = floor(Nsk3_S/8)
- Nsk3_max_val = (2^Nsk3_S) - 1
-
- p = 2^e2 * 3^e3 - 1
- Fp = GF(p)
- R.<x> = Fp[]
- Fp2 = Fp.extension(x^2 + 1, 'i')
- i = Fp2.gen()
- E0Fp = EllipticCurve(Fp, [0,6,0,1,0])
- E0Fp2 = EllipticCurve(Fp2, [0,6,0,1,0])
-
- # Montgomery R
- # 448 = 7*(8*8)
- R = 2^448
- # P503
- # R = 2^512
-
- def calc_Y_in_Fp2(x, xi):
- fp2X= Fp2(x+xi*i)
- fp2Y2 = Fp2(fp2X^3 + fp2X)
- ret = fp2Y2.sqrt()
- return ret
-
- def calc_proj_point_A(fp2X, fp2Y): return (3^e3 * E0Fp2((fp2X, fp2Y)))
- def calc_proj_point_B(fp2X, fp2Y): return (2^e2 * E0Fp2(fp2X, fp2Y))
-
- def tau(P): return E0Fp2(-P.xy()[0], i*P.xy()[1])
- def hd(val):
- return ", 0x".join([x.hex().upper() for x in Integer(val).digits(base=2^64)])
- def hcp(point):
- print("X: "); hd(point[0])
- print("Y: "); hd(point[1])
- print("Z: "); hd(point[2])
- def print_fp2_hex(Fp2_el):
- fp2_pol = Fp2_el.polynomial()
- print("A: FpElement{0x" + hd(fp2_pol[1]) + "},")
- print("B: FpElement{0x" + hd(fp2_pol[0]) + "}}")
-
- def print_fp2_in_mont_hex(Fp2_el, text):
- print(text)
- mul = Integer(R)*Fp2_el
- fp2_pol = mul.polynomial()
- print("A: FpElement{0x" + hd(fp2_pol[0]) + "},")
- print("B: FpElement{0x" + hd(fp2_pol[1]) + "}}")
-
- Integer(2^4 - 1).digits(2)
-
- print("\n P =\n"+hd(p))
- print("\n pX2 =\n"+hd(2*p))
- print("\n p+1 =\n"+hd(p+1))
- print("\n R^2 mod p =\n"+hd((R^2) % p))
- print("\n1/2 * R mod p =\n"+hd(((1/2)*R) % p))
- print("\n R mod p =\n"+hd(R % p))
- print("\n 6 * R mod p =\n"+hd(((6*R) % p)))
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