mirror of
https://github.com/status-im/nim-eth-keys.git
synced 2025-02-19 12:47:13 +00:00
77 lines
2.2 KiB
Nim
77 lines
2.2 KiB
Nim
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# Copyright (c) 2018 Status Research & Development GmbH
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# Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).
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import ./constants, ./mod_arithmetic
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import ttmath
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proc to_jacobian(p: array[2, UInt256]): array[3, UInt256] {.noInit.}=
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[p[0], p[1], 1.u256]
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proc jacobian_double(p: array[3, UInt256]): array[3, UInt256] {.noInit.}=
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if p[1] == 0.u256:
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return [0.u256, 0.u256, 0.u256]
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modulo(SECPK1_P):
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let
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ysq = p[1] ** 2.u256
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S = 4.u256 * p[0] * ysq
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M = 3.u256 * (p[0] ** 2.u256) + SECPK1_A * (p[2] ** 4.u256)
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nx = M ** 2.u256 - 2.u256 * S
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ny = M * (S - nx) - 8.u256 * (ysq ** 2.u256)
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nz = 2.u256 * p[1] * p[2]
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result = [nx, ny, nz]
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proc jacobian_add*(p, q: array[3, UInt256]): array[3, UInt256] {.noInit.}=
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if p[1] == 0.u256:
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return q
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if q[1] == 0.u256:
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return p
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modulo(SECPK1_P):
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let
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U1 = p[0] * (q[2] ** 2.u256)
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U2 = q[0] * (p[2] ** 2.u256)
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S1 = p[1] * (q[2] ** 2.u256)
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S2 = q[1] * (p[2] ** 2.u256)
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if U1 == U2:
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if S1 == S2:
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return [0.u256, 0.u256, 1.u256]
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return jacobian_double(p)
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modulo(SECPK1_P):
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let
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H = U2 - U1
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R = S2 - S1
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H2 = H * H
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H3 = H * H2
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U1H2 = U1 * H2
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nx = R ** 2.u256 - H3 - 2.u256 * U1H2
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ny = R * (U1H2 - nx) - S1 * H3
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nz = H * p[2] * q[2]
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result = [nx, ny, nz]
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proc from_jacobian*(p: array[3, UInt256]): array[2, UInt256] =
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let z = invmod(p[2], SECPK1_P)
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modulo(SECPK1_P):
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result = [p[0] * (z ** 2.u256), p[1] * (z ** 3.u256)]
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proc jacobian_multiply*(a: array[3, UInt256], n: UInt256): array[3, UInt256] =
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if a[1] == 0.u256 or n == 0.u256:
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return [0.u256, 0.u256, 1.u256]
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elif n == 1.u256:
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return a
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elif n >= SECPK1_N: # note n cannot be < 0 in Nim
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return jacobian_multiply(a, n mod SECPK1_N)
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elif n.isEven:
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return jacobian_double jacobian_multiply(a, n div 2.u256)
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else: # n.isOdd
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return jacobian_add(jacobian_double jacobian_multiply(a, n div 2.u256), a)
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proc fast_multiply*(a: array[2, UInt256], n: UInt256): array[2,UInt256] =
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return from_jacobian jacobian_multiply(a.to_jacobian, n)
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proc fast_add*(a, b: array[2, UInt256]): array[2, UInt256] =
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return from_jacobian jacobian_add(a.to_jacobian, b.to_jacobian)
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