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