Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.11/site-packages/starkbank_ecdsa-2.3.1-py3.11.egg/ellipticcurve/curve.py: 77%

1# coding: utf-8 

2# 

3# Elliptic Curve Equation 

4# 

5# y^2 = x^3 + A*x + B (mod P) 

6# 

7from .math import Math 

8from .point import Point 

9 

10 

11class CurveFp: 

12 

13 def __init__(self, A, B, P, N, Gx, Gy, name, oid, nistName=None, glvParams=None): 

14 self.A = A 

15 self.B = B 

16 self.P = P 

17 self.N = N 

18 self.nBitLength = N.bit_length() 

19 self.G = Point(Gx, Gy) 

20 self.name = name 

21 self.nistName = nistName 

22 self.oid = oid # ASN.1 Object Identifier 

23 # GLV endomorphism parameters (only for curves that support one, 

24 # e.g. secp256k1). None means no endomorphism; fall back to Shamir+JSF. 

25 self.glvParams = glvParams 

26 

27 def contains(self, p): 

28 """ 

29 Verify if the point `p` is on the curve 

30 

31 :param p: Point p = Point(x, y) 

32 :return: boolean 

33 """ 

34 if not 0 <= p.x <= self.P - 1: 

35 return False 

36 if not 0 <= p.y <= self.P - 1: 

37 return False 

38 if (p.y**2 - (p.x**3 + self.A * p.x + self.B)) % self.P != 0: 

39 return False 

40 return True 

41 

42 def length(self): 

43 return (1 + len("%x" % self.N)) // 2 

44 

45 def y(self, x, isEven): 

46 ySquared = (pow(x, 3, self.P) + self.A * x + self.B) % self.P 

47 y = Math.modularSquareRoot(ySquared, self.P) 

48 if isEven != (y % 2 == 0): 

49 y = self.P - y 

50 return y 

51 

52 

53_curvesByOid = {tuple(curve.oid): curve for curve in []} 

54 

55 

56def add(curve): 

57 _curvesByOid[tuple(curve.oid)] = curve 

58 

59 

60def getByOid(oid): 

61 if oid not in _curvesByOid: 

62 raise Exception("Unknown curve with oid {oid}; The following are registered: {names}".format( 

63 oid=".".join([str(number) for number in oid]), 

64 names=", ".join([curve.name for curve in _curvesByOid.values()]), 

65 )) 

66 return _curvesByOid[oid] 

67 

68 

69secp256k1 = CurveFp( 

70 name="secp256k1", 

71 A=0x0000000000000000000000000000000000000000000000000000000000000000, 

72 B=0x0000000000000000000000000000000000000000000000000000000000000007, 

73 P=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f, 

74 N=0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141, 

75 Gx=0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, 

76 Gy=0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8, 

77 oid=[1, 3, 132, 0, 10], 

78 # GLV endomorphism φ((x,y)) = (β·x, y), equivalent to λ·P. 

79 # Basis vectors from Gauss reduction; used to split a 256-bit scalar k 

80 # into two ~128-bit scalars (k1, k2) with k ≡ k1 + k2·λ (mod N). 

81 glvParams={ 

82 "beta": 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee, 

83 "lambda": 0x5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72, 

84 "a1": 0x3086d221a7d46bcde86c90e49284eb15, 

85 "b1": -0xe4437ed6010e88286f547fa90abfe4c3, 

86 "a2": 0x114ca50f7a8e2f3f657c1108d9d44cfd8, 

87 "b2": 0x3086d221a7d46bcde86c90e49284eb15, 

88 }, 

89) 

90 

91prime256v1 = CurveFp( 

92 name="prime256v1", 

93 nistName="P-256", 

94 A=0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc, 

95 B=0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b, 

96 P=0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff, 

97 N=0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551, 

98 Gx=0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, 

99 Gy=0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5, 

100 oid=[1, 2, 840, 10045, 3, 1, 7], 

101) 

102 

103p256 = prime256v1 

104 

105add(secp256k1) 

106add(prime256v1)