def conv_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/poly.bend:280

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/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

280def conv_val(+one: Nat, +h1: {one == 1n : Nat}, +xs: List<&2, U32>, +ys: List<&2, U32>, +a: Nat, +b: Nat, +hx: {LM.lea(xs, a) == True{} : Bool}, +hy: {LM.lea(ys, b) == True{} : Bool}, +hc: {Nat.is_lt(cb(xs, Nat.mul(a, b)), WD.sc(32n, one)) == True{} : Bool}) -> {FS.value(F.conv(xs, ys)) == Nat.mul(FS.value(xs), FS.value(ys)) : Nat}:
281  match xs:
282    case Nil{}:
283      {==}
284    case Con{+x, +xt}:
285      +ab = Nat.mul(a, b)
286      +k = cb(xt, ab)
287      +Y = FS.value(ys)
288      +X = FS.value(xt)
289      +hab = N.le_lt_trans(ab, Nat.add(ab, k), WD.sc(32n, one), N.le_add_right(ab, k), hc)
290      +hk = N.le_lt_trans(k, Nat.add(ab, k), WD.sc(32n, one), le_add_l(ab, k), hc)
291      +hxh = LM.lea_head(x, xt, a, hx)
292      +hxt = LM.lea_tail(x, xt, a, hx)
293      +hs = scal_lea(one, h1, x, ys, a, b, hxh, hy, hab)
294      +hz = L.and_intro(Nat.is_le(0n, k), LM.lea(F.conv(xt, ys), k), N.zero_le(k), conv_lea(one, h1, xt, ys, a, b, hxt, hy, hk))
295      +e1 = addl_val(one, h1, F.scal(x, ys), Con{0, F.conv(xt, ys)}, ab, k, hs, hz, hc)
296      +e2 = M.cong_add(FS.value(F.scal(x, ys)), Nat.mul(v(x), Y), FS.value(Con{0, F.conv(xt, ys)}), C.shift(8n, Nat.mul(X, Y)), scal_val(one, h1, x, ys, a, b, hxh, hy, hab), M.cong_sc(8n, FS.value(F.conv(xt, ys)), Nat.mul(X, Y), conv_val(one, h1, xt, ys, a, b, hxt, hy, hk)))
297      +e3 = M.cong_r(Nat.mul(v(x), Y), C.shift(8n, Nat.mul(X, Y)), Nat.mul(C.shift(8n, X), Y), AR.sc_mul(8n, X, Y))
298      +e4 = Equal.sym(Nat, Nat.mul(Nat.add(v(x), C.shift(8n, X)), Y), Nat.add(Nat.mul(v(x), Y), Nat.mul(C.shift(8n, X), Y)), NA.mul_add_right(v(x), C.shift(8n, X), Y))
299      Equal.trans(Nat, FS.value(F.conv(Con{x, xt}, ys)), Nat.add(FS.value(F.scal(x, ys)), FS.value(Con{0, F.conv(xt, ys)})), Nat.mul(Nat.add(v(x), C.shift(8n, X)), Y), e1,
300        Equal.trans(Nat, Nat.add(FS.value(F.scal(x, ys)), FS.value(Con{0, F.conv(xt, ys)})), Nat.add(Nat.mul(v(x), Y), C.shift(8n, Nat.mul(X, Y))), Nat.mul(Nat.add(v(x), C.shift(8n, X)), Y), e2,
301          Equal.trans(Nat, Nat.add(Nat.mul(v(x), Y), C.shift(8n, Nat.mul(X, Y))), Nat.add(Nat.mul(v(x), Y), Nat.mul(C.shift(8n, X), Y)), Nat.mul(Nat.add(v(x), C.shift(8n, X)), Y), e3, e4)))