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| Original file line number | Diff line number | Diff line change |
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| from starkware.cairo.common.cairo_secp.bigint import ( | ||
| BigInt3, | ||
| UnreducedBigInt3, | ||
| nondet_bigint3, | ||
| ) | ||
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| from cairo_programs.compute_slope_v2 import verify_zero | ||
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| const BASE = 2 ** 86; | ||
| const SECP_REM = 19; | ||
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| struct EcPoint { | ||
| x: BigInt3, | ||
| y: BigInt3, | ||
| } | ||
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| func unreduced_mul(a: BigInt3, b: BigInt3) -> (res_low: UnreducedBigInt3) { | ||
| // The result of the product is: | ||
| // sum_{i, j} a.d_i * b.d_j * BASE**(i + j) | ||
| // Since we are computing it mod secp256k1_prime, we replace the term | ||
| // a.d_i * b.d_j * BASE**(i + j) | ||
| // where i + j >= 3 with | ||
| // a.d_i * b.d_j * BASE**(i + j - 3) * 4 * SECP_REM | ||
| // since BASE ** 3 = 4 * SECP_REM (mod secp256k1_prime). | ||
| return ( | ||
| UnreducedBigInt3( | ||
| d0=a.d0 * b.d0 + (a.d1 * b.d2 + a.d2 * b.d1) * (8 * SECP_REM), | ||
| d1=a.d0 * b.d1 + a.d1 * b.d0 + (a.d2 * b.d2) * (8 * SECP_REM), | ||
| d2=a.d0 * b.d2 + a.d1 * b.d1 + a.d2 * b.d0), | ||
| ); | ||
| } | ||
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| // Computes the square of a big integer, given in BigInt3 representation, modulo the | ||
| // secp256k1 prime. | ||
| // | ||
| // Has the same guarantees as in unreduced_mul(a, a). | ||
| func unreduced_sqr(a: BigInt3) -> (res_low: UnreducedBigInt3) { | ||
| tempvar twice_d0 = a.d0 * 2; | ||
| return ( | ||
| UnreducedBigInt3( | ||
| d0=a.d0 * a.d0 + (a.d1 * a.d2) * (2 * 8 * SECP_REM), | ||
| d1=twice_d0 * a.d1 + (a.d2 * a.d2) * (8 * SECP_REM), | ||
| d2=twice_d0 * a.d2 + a.d1 * a.d1), | ||
| ); | ||
| } | ||
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| // Computes the slope of the elliptic curve at a given point. | ||
| // The slope is used to compute point + point. | ||
| // | ||
| // Arguments: | ||
| // point - the point to operate on. | ||
| // | ||
| // Returns: | ||
| // slope - the slope of the curve at point, in BigInt3 representation. | ||
| // | ||
| // Assumption: point != 0. | ||
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| func compute_doubling_slope{range_check_ptr}(point: EcPoint) -> (slope: BigInt3) { | ||
| alloc_locals; | ||
| // Note that y cannot be zero: assume that it is, then point = -point, so 2 * point = 0, which | ||
| // contradicts the fact that the size of the curve is odd. | ||
| %{ | ||
| from starkware.python.math_utils import ec_double_slope | ||
| from starkware.cairo.common.cairo_secp.secp_utils import pack | ||
| SECP_P = 2**255-19 | ||
| # Compute the slope. | ||
| x = pack(ids.point.x, PRIME) | ||
| y = pack(ids.point.y, PRIME) | ||
| value = slope = ec_double_slope(point=(x, y), alpha=42204101795669822316448953119945047945709099015225996174933988943478124189485, p=SECP_P) | ||
| %} | ||
| let (slope: BigInt3) = nondet_bigint3(); | ||
| // let alpha = Uint256( | ||
| // 143186476941636880901214103594843510573, 124026708105846590725274683684370988502 | ||
| // ); | ||
| let (x_sqr: UnreducedBigInt3) = unreduced_sqr(point.x); | ||
| let (slope_y: UnreducedBigInt3) = unreduced_mul(slope, point.y); | ||
| let to_assert = UnreducedBigInt3( | ||
| d0=3 * x_sqr.d0 - 2 * slope_y.d0 + 44933163489768861888943917, | ||
| d1=3 * x_sqr.d1 - 2 * slope_y.d1 + 5088459194227531129123890, | ||
| d2=3 * x_sqr.d2 - 2 * slope_y.d2 + 7050102118787810395887998, | ||
| ); | ||
| // let to_assert256 = bigint_to_uint256(to_assert); | ||
| // %{ print_u_256_info(ids.to_assert256, 'to_assert') %} | ||
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| verify_zero(to_assert); | ||
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| return (slope=slope); | ||
| } | ||
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| func main{range_check_ptr}() { | ||
| let point_1 = EcPoint(BigInt3(512, 2412, 133), BigInt3(64, 0, 6546)); | ||
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| let (slope) = compute_doubling_slope(point_1); | ||
| assert slope = BigInt3(50745345459537348646984154, 66221251087242098185359002 ,8063180118678125382645462); | ||
| return (); | ||
| } |
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