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;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
;; PRE: A is not alias-free | ||
;; POST: The result B is not alias-free (on MAP) | ||
;; | ||
;; invFnSecp256k1: | ||
;; in: A | ||
;; out: B = A⁻¹ (mod n) | ||
;; | ||
;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
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; RESOURCES: | ||
; non-normalized: 2 ariths + 2 binaries + 13 steps | ||
; normalized: 2 ariths + 1 binaries + 12 steps | ||
; TOTAL (worst case): 2 ariths + 2 binaries + 13 steps | ||
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VAR GLOBAL invFnSecp256k1_tmp | ||
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invFnSecp256k1: | ||
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; Reduction of A | ||
%SECP256K1_N => B | ||
$ :LT, JMPC(invFnSecp256k1_normalized) | ||
$ => A :SUB | ||
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invFnSecp256k1_normalized: | ||
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; 1] Compute and check the inverse over Z | ||
; A·A⁻¹ + 0 = [D]·2²⁵⁶ + [E] | ||
0 => C | ||
${var _invFnSecp256k1_A = inverseFnEc(A)} => B :MSTORE(invFnSecp256k1_tmp) | ||
$${var _invFnSecp256k1_AB = A * _invFnSecp256k1_A} | ||
${_invFnSecp256k1_AB >> 256} => D | ||
${_invFnSecp256k1_AB} => E :ARITH | ||
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; 2] Check it over Fn, that is, it must be satisfied that: | ||
; n·[(A·A⁻¹) / n] + 1 = D·2²⁵⁶ + E | ||
%SECP256K1_N => A | ||
${_invFnSecp256k1_AB / const.SECP256K1_N} => B | ||
1 => C | ||
E :ARITH | ||
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$ => B :MLOAD(invFnSecp256k1_tmp), RETURN |
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Original file line number | Diff line number | Diff line change |
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
;; PRE: A,B are not alias-free | ||
;; POST: The result C is not alias-free (on MAP) | ||
;; | ||
;; mulFnSecp256k1: | ||
;; in: A,B | ||
;; out: C = A·B (mod n) | ||
;; | ||
;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
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; RESOURCES: | ||
; 2 arith + 8 steps | ||
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mulFnSecp256k1: | ||
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; 1] Compute and check the multiplication over Z | ||
; A·B + 0 = [D]·2²⁵⁶ + [E] | ||
0 => C | ||
$${var _mulFnSecp256k1_AB = A * B} | ||
${_mulFnSecp256k1_AB >> 256} => D | ||
${_mulFnSecp256k1_AB} => E :ARITH | ||
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; 2] Check it over Fn, that is, it must be satisfied that: | ||
; n·[(A·B) / n] + [(A·B) % n] = D·2²⁵⁶ + E | ||
%SECP256K1_N => A | ||
${_mulFnSecp256k1_AB / const.SECP256K1_N} => B ; quotient (256 bits) | ||
${_mulFnSecp256k1_AB % const.SECP256K1_N} => C ; residue (256 bits) | ||
E :ARITH, RETURN |
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
;; PRE: A,C are not alias-free | ||
;; POST: The result C is not alias-free (on MAP) | ||
;; | ||
;; addFpSecp256k1: | ||
;; in: A,C | ||
;; out: C = A + C (mod p) | ||
;; | ||
;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
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; RESOURCES: | ||
; 2 ariths + 8 steps | ||
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addFpSecp256k1: | ||
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; 1] Compute and check the sum over Z | ||
; A·[1] + C = [D]·2²⁵⁶ + [E] | ||
1 => B | ||
$${var _addFpSecp256k1_AC = A + C} | ||
${_addFpSecp256k1_AC >> 256} => D | ||
${_addFpSecp256k1_AC} => E :ARITH | ||
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; 2] Check it over Fp, that is, it must be satisfied that: | ||
; p·[(A+C) / p] + [(A+C) % p] = D·2²⁵⁶ + E | ||
%SECP256K1_P => A | ||
${_addFpSecp256k1_AC / const.SECP256K1_P} => B ; quotient (256 bits) | ||
${_addFpSecp256k1_AC % const.SECP256K1_P} => C ; residue (256 bits) | ||
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E :ARITH, RETURN |
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