proofs/crypto/secp256k1/ptwo.bend
bend-collections-laws-crypto@1.0.0.0 · 24 lines · 2 definitions
1
2import Base
3import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
4import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend as CV
5import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend as P
6import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT
7import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as SL
8import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pmul.bend as PM
9import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/paff.bend as PA
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13
14def two_r(+one: Nat, +h1: {one == 1n : Nat}, +u1: List<&2, Nat>, +hu1: {FS.reduced(one, FS.order(one), u1) == True{} : Bool}, +u2: List<&2, Nat>, +hu2: {FS.reduced(one, FS.order(one), u2) == True{} : Bool}, +pr: P.Point, +hpr: {PT.pred(one, pr) == True{} : Bool}) -> {PT.pred(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))) == True{} : Bool}:
15 PT.padd_r(one, h1, P.mul(u1, P.g()), P.mul(u2, pr), PM.mul_r(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1)), PM.mul_r(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr))
16
17def two_v(+one: Nat, +h1: {one == 1n : Nat}, +u1: List<&2, Nat>, +hu1: {FS.reduced(one, FS.order(one), u1) == True{} : Bool}, +u2: List<&2, Nat>, +hu2: {FS.reduced(one, FS.order(one), u2) == True{} : Bool}, +pr: P.Point, +hpr: {PT.pred(one, pr) == True{} : Bool}) -> {PT.pv(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}:
18 +hp1 = PM.mul_r(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1))
19 +hp2 = PM.mul_r(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr)
20 %Equal.sym(CV.SPoint, PT.pv(one, P.add(P.mul(u1, P.g()), P.mul(u2, pr))), CV.padd(FS.prime(one), PT.pv(one, P.mul(u1, P.g())), PT.pv(one, P.mul(u2, pr))), PT.padd_v(one, h1, P.mul(u1, P.g()), P.mul(u2, pr), hp1, hp2)) : {_ == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
21 %Equal.sym(CV.SPoint, PT.pv(one, P.mul(u1, P.g())), CV.pmul(FS.prime(one), FS.value(one, u1), PT.pv(one, P.g())), PM.mul_v(one, h1, u1, P.g(), SL.sl16(one, u1, hu1), PA.g_r(one, h1))) : {CV.padd(FS.prime(one), _, PT.pv(one, P.mul(u2, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
22 %Equal.sym(CV.SPoint, PT.pv(one, P.mul(u2, pr)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr)), PM.mul_v(one, h1, u2, pr, SL.sl16(one, u2, hu2), hpr)) : {CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), PT.pv(one, P.g())), _) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
23 %Equal.sym(CV.SPoint, PT.pv(one, P.g()), CV.g(one), PA.g_v(one, h1)) : {CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), _), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) == CV.padd(FS.prime(one), CV.pmul(FS.prime(one), FS.value(one, u1), CV.g(one)), CV.pmul(FS.prime(one), FS.value(one, u2), PT.pv(one, pr))) : CV.SPoint}
24 {==}