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escalar renamed to the correct scalar
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,155 @@ | ||
| ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
| ;; PRE: P ∈ E'(Fp2) | ||
| ;; POST: The resulting coordinates are in the range [0,BN254_P) because if falls back to addPointBN254 | ||
| ;; | ||
| ;; | ||
| ;; scalarMulBN254: | ||
| ;; in: k, P = (P.x1 + P.x2·u, P.y1 + P.y2·u) ∈ E'(Fp2), where k ∈ [0,r-1] | ||
| ;; out: k·P = (Q.x1 + Q.x2·u, Q.y1 + Q.y2·u) ∈ E'(Fp2) | ||
| ;; | ||
| ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; | ||
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| ; scalarMulBN254 assumes P belong to E'(Fp2), since it is checked in the pairing. | ||
| ; However, it must be implemented if scalarMulBN254 wants to be used independently. | ||
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| ; Since the curve is E'/Fp2: y² = x³ + 3/(9+u), there is no issue in representing the point at infinity as (0, 0). | ||
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| VAR GLOBAL scalarMulBN254_k | ||
| VAR GLOBAL scalarMulBN254_P_x1 | ||
| VAR GLOBAL scalarMulBN254_P_x2 | ||
| VAR GLOBAL scalarMulBN254_P_y1 | ||
| VAR GLOBAL scalarMulBN254_P_y2 | ||
| VAR GLOBAL scalarMulBN254_Q_x1 | ||
| VAR GLOBAL scalarMulBN254_Q_x2 | ||
| VAR GLOBAL scalarMulBN254_Q_y1 | ||
| VAR GLOBAL scalarMulBN254_Q_y2 | ||
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| VAR GLOBAL scalarMulBN254_RR | ||
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| scalarMulBN254: | ||
| RR :MSTORE(scalarMulBN254_RR) | ||
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| ; Is P = 𝒪? | ||
| 0n => B | ||
| $ => A :MLOAD(scalarMulBN254_P_x1) | ||
| $ :EQ, JMPNC(__scalarMulBN254_P_continue) | ||
| $ => A :MLOAD(scalarMulBN254_P_x2) | ||
| $ :EQ, JMPNC(__scalarMulBN254_P_continue) | ||
| $ => A :MLOAD(scalarMulBN254_P_y1) | ||
| $ :EQ, JMPNC(__scalarMulBN254_P_continue) | ||
| $ => A :MLOAD(scalarMulBN254_P_y2) | ||
| $ :EQ, JMPC(scalarMulBN254_P_is_zero) | ||
| __scalarMulBN254_P_continue: | ||
|
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||
| ; Is k = 0? | ||
| $ => B :MLOAD(scalarMulBN254_k), CALL(reduceFrBN254) | ||
| A :MSTORE(scalarMulBN254_k) | ||
| 0n => B | ||
| $ :EQ, JMPC(scalarMulBN254_k_is_zero) | ||
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| 257 => RCX | ||
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| $ => A :MLOAD(scalarMulBN254_P_x1) | ||
| $ => B :MLOAD(scalarMulBN254_P_x2) | ||
| $ => C :MLOAD(scalarMulBN254_P_y1) | ||
| $ => D :MLOAD(scalarMulBN254_P_y2) | ||
| A :MSTORE(scalarMulBN254_Q_x1) | ||
| B :MSTORE(scalarMulBN254_Q_x2) | ||
| C :MSTORE(scalarMulBN254_Q_y1) | ||
| D :MSTORE(scalarMulBN254_Q_y2) | ||
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| :JMP(scalarMulBN254_find_MSB_k) | ||
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| scalarMulBN254_P_is_zero: | ||
| ; Q = 𝒪 | ||
| 0n :MSTORE(scalarMulBN254_Q_x1) | ||
| 0n :MSTORE(scalarMulBN254_Q_x2) | ||
| 0n :MSTORE(scalarMulBN254_Q_y1) | ||
| 0n :MSTORE(scalarMulBN254_Q_y2) | ||
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| :JMP(scalarMulBN254_end) | ||
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| scalarMulBN254_k_is_zero: | ||
| ; Q = 𝒪 | ||
| 0n :MSTORE(scalarMulBN254_Q_x1) | ||
| 0n :MSTORE(scalarMulBN254_Q_x2) | ||
| 0n :MSTORE(scalarMulBN254_Q_y1) | ||
| 0n :MSTORE(scalarMulBN254_Q_y2) | ||
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| :JMP(scalarMulBN254_end) | ||
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| scalarMulBN254_find_MSB_k: | ||
| RCX - 1 => RCX | ||
| $ => A,B :MLOAD(scalarMulBN254_k) | ||
| ; E = 2A | ||
| $ => E :ADD,MSTORE(scalarMulBN254_k), JMPNC(scalarMulBN254_find_MSB_k) | ||
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| scalarMulBN254_loop: | ||
| RCX - 1 => RCX :JMPZ(scalarMulBN254_end) | ||
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| ; We always double | ||
| $ => A :MLOAD(scalarMulBN254_Q_x1) | ||
| $ => B :MLOAD(scalarMulBN254_Q_x2) | ||
| $ => C :MLOAD(scalarMulBN254_Q_y1) | ||
| $ => D :MLOAD(scalarMulBN254_Q_y2) | ||
| A :MSTORE(addPointBN254_P1_x1) | ||
| B :MSTORE(addPointBN254_P1_x2) | ||
| C :MSTORE(addPointBN254_P1_y1) | ||
| D :MSTORE(addPointBN254_P1_y2) | ||
| A :MSTORE(addPointBN254_P2_x1) | ||
| B :MSTORE(addPointBN254_P2_x2) | ||
| C :MSTORE(addPointBN254_P2_y1) | ||
| D :MSTORE(addPointBN254_P2_y2), CALL(addPointBN254) | ||
| ; Q = Q + Q | ||
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| $ => A :MLOAD(addPointBN254_P3_x1) | ||
| $ => B :MLOAD(addPointBN254_P3_x2) | ||
| $ => C :MLOAD(addPointBN254_P3_y1) | ||
| $ => D :MLOAD(addPointBN254_P3_y2) | ||
| A :MSTORE(scalarMulBN254_Q_x1) | ||
| B :MSTORE(scalarMulBN254_Q_x2) | ||
| C :MSTORE(scalarMulBN254_Q_y1) | ||
| D :MSTORE(scalarMulBN254_Q_y2) | ||
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| ; We check if the MSB b of k is either 1 or 0. If b==1, we should add P to Q. | ||
| ; Then, update the value of k. | ||
| $ => A,B :MLOAD(scalarMulBN254_k) | ||
| ; E = 2A | ||
| $ => E :ADD,MSTORE(scalarMulBN254_k), JMPNC(scalarMulBN254_loop) | ||
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| scalarMulBN254_add: | ||
| ; We add | ||
| $ => A :MLOAD(scalarMulBN254_Q_x1) | ||
| $ => B :MLOAD(scalarMulBN254_Q_x2) | ||
| $ => C :MLOAD(scalarMulBN254_Q_y1) | ||
| $ => D :MLOAD(scalarMulBN254_Q_y2) | ||
| A :MSTORE(addPointBN254_P1_x1) | ||
| B :MSTORE(addPointBN254_P1_x2) | ||
| C :MSTORE(addPointBN254_P1_y1) | ||
| D :MSTORE(addPointBN254_P1_y2) | ||
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| $ => A :MLOAD(scalarMulBN254_P_x1) | ||
| $ => B :MLOAD(scalarMulBN254_P_x2) | ||
| $ => C :MLOAD(scalarMulBN254_P_y1) | ||
| $ => D :MLOAD(scalarMulBN254_P_y2) | ||
| A :MSTORE(addPointBN254_P2_x1) | ||
| B :MSTORE(addPointBN254_P2_x2) | ||
| C :MSTORE(addPointBN254_P2_y1) | ||
| D :MSTORE(addPointBN254_P2_y2), CALL(addPointBN254) | ||
| ; Q = Q + P | ||
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| $ => A :MLOAD(addPointBN254_P3_x1) | ||
| $ => B :MLOAD(addPointBN254_P3_x2) | ||
| $ => C :MLOAD(addPointBN254_P3_y1) | ||
| $ => D :MLOAD(addPointBN254_P3_y2) | ||
| A :MSTORE(scalarMulBN254_Q_x1) | ||
| B :MSTORE(scalarMulBN254_Q_x2) | ||
| C :MSTORE(scalarMulBN254_Q_y1) | ||
| D :MSTORE(scalarMulBN254_Q_y2), JMP(scalarMulBN254_loop) | ||
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| scalarMulBN254_end: | ||
| $ => RR :MLOAD(scalarMulBN254_RR) | ||
| :RETURN |
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