def sq_cb

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldpow.bend:277

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as BV

277# hv(bits of p + 1) + d + one = 2^256 with d = (c_p - 2)
278def sq_cb(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(Nat.add(BV.hv(L.cbits(L.bits(L.norm16([975n, 0n, 1n]))), one, 0n), FS.digits(one, L.norm16([975n, 0n, 1n]))), one) == C.shift(256n, one) : Nat}:
279  +bs = L.bits(L.norm16([975n, 0n, 1n]))
280  +hcb = BV.cb(one, bs, 0n, 0n, BV.bits01(L.norm16([975n, 0n, 1n])))
281  %Equal.sym(Nat, FS.digits(one, L.norm16([975n, 0n, 1n])), BV.hv(L.bits(L.norm16([975n, 0n, 1n])), one, 0n), Equal.sym(Nat, BV.hv(L.bits(L.norm16([975n, 0n, 1n])), one, 0n), FS.digits(one, L.norm16([975n, 0n, 1n])), yp_hv(one, h1))) : {Nat.add(Nat.add(BV.hv(L.cbits(L.bits(L.norm16([975n, 0n, 1n]))), one, 0n), _), one) == C.shift(256n, one) : Nat}
282  hcb