Add BLS12-381 operations (to FATE)
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priv/stdlib/BLS12_381.aes
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68
priv/stdlib/BLS12_381.aes
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@ -0,0 +1,68 @@
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namespace BLS12_381 =
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type fr = MCL_BLS12_381.fr
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type fp = MCL_BLS12_381.fp
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record fp2 = { x1 : fp, x2 : fp }
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record g1 = { x : fp, y : fp, z : fp }
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record g2 = { x : fp2, y : fp2, z : fp2 }
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record gt = { x1 : fp, x2 : fp, x3 : fp, x4 : fp, x5 : fp, x6 : fp,
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x7 : fp, x8 : fp, x9 : fp, x10 : fp, x11 : fp, x12 : fp }
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function pairing_check(xs : list(g1), ys : list(g2)) =
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switch((xs, ys))
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([], []) => true
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(x :: xs, y :: ys) => pairing_check_(pairing(x, y), xs, ys)
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function pairing_check_(acc : gt, xs : list(g1), ys : list(g2)) =
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switch((xs, ys))
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([], []) => gt_is_one(acc)
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(x :: xs, y :: ys) =>
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pairing_check_(gt_mul(acc, pairing(x, y)), xs, ys)
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function int_to_fr(x : int) = MCL_BLS12_381.int_to_fr(x)
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function int_to_fp(x : int) = MCL_BLS12_381.int_to_fp(x)
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function fr_to_int(x : fr) = MCL_BLS12_381.fr_to_int(x)
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function fp_to_int(x : fp) = MCL_BLS12_381.fp_to_int(x)
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function mk_g1(x : int, y : int, z : int) : g1 =
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{ x = int_to_fp(x), y = int_to_fp(y), z = int_to_fp(z) }
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function mk_g2(x1 : int, x2 : int, y1 : int, y2 : int, z1 : int, z2 : int) : g2 =
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{ x = {x1 = int_to_fp(x1), x2 = int_to_fp(x2)},
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y = {x1 = int_to_fp(y1), x2 = int_to_fp(y2)},
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z = {x1 = int_to_fp(z1), x2 = int_to_fp(z2)} }
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function pack_g1(t) = switch(t)
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(x, y, z) => {x = x, y = y, z = z} : g1
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function pack_g2(t) = switch(t)
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((x1, x2), (y1, y2), (z1, z2)) =>
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{x = {x1 = x1, x2 = x2}, y = {x1 = y1, x2 = y2}, z = {x1 = z1, x2 = z2}} : g2
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function pack_gt(t) = switch(t)
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(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) =>
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{x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = x5, x6 = x6,
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x7 = x7, x8 = x8, x9 = x9, x10 = x10, x11 = x11, x12 = x12} : gt
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function g1_neg(p : g1) = pack_g1(MCL_BLS12_381.g1_neg((p.x, p.y, p.z)))
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function g1_norm(p : g1) = pack_g1(MCL_BLS12_381.g1_norm((p.x, p.y, p.z)))
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function g1_valid(p : g1) = MCL_BLS12_381.g1_valid((p.x, p.y, p.z))
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function g1_is_zero(p : g1) = MCL_BLS12_381.g1_is_zero((p.x, p.y, p.z))
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function g1_add(p : g1, q : g1) = pack_g1(MCL_BLS12_381.g1_add((p.x, p.y, p.z), (q.x, q.y, q.z)))
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function g1_mul(k : fr, p : g1) = pack_g1(MCL_BLS12_381.g1_mul(k, (p.x, p.y, p.z)))
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function g2_neg(p : g2) = pack_g2(MCL_BLS12_381.g2_neg(((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2))))
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function g2_norm(p : g2) = pack_g2(MCL_BLS12_381.g2_norm(((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2))))
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function g2_valid(p : g2) = MCL_BLS12_381.g2_valid(((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2)))
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function g2_is_zero(p : g2) = MCL_BLS12_381.g2_is_zero(((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2)))
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function g2_add(p : g2, q : g2) = pack_g2(MCL_BLS12_381.g2_add(((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2)),
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((q.x.x1, q.x.x2), (q.y.x1, q.y.x2), (q.z.x1, q.z.x2))))
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function g2_mul(k : fr, p : g2) = pack_g2(MCL_BLS12_381.g2_mul(k, ((p.x.x1, p.x.x2), (p.y.x1, p.y.x2), (p.z.x1, p.z.x2))))
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function gt_inv(p : gt) = pack_gt(MCL_BLS12_381.gt_inv((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12)))
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function gt_add(p : gt, q : gt) = pack_gt(MCL_BLS12_381.gt_add((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12),
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(q.x1, q.x2, q.x3, q.x4, q.x5, q.x6, q.x7, q.x8, q.x9, q.x10, q.x11, q.x12)))
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function gt_mul(p : gt, q : gt) = pack_gt(MCL_BLS12_381.gt_mul((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12),
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(q.x1, q.x2, q.x3, q.x4, q.x5, q.x6, q.x7, q.x8, q.x9, q.x10, q.x11, q.x12)))
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function gt_pow(p : gt, k : fr) = pack_gt(MCL_BLS12_381.gt_pow((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12), k))
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function gt_is_one(p : gt) = MCL_BLS12_381.gt_is_one((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12))
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function pairing(p : g1, q : g2) = pack_gt(MCL_BLS12_381.pairing((p.x, p.y, p.z), ((q.x.x1, q.x.x2), (q.y.x1, q.y.x2), (q.z.x1, q.z.x2))))
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function miller_loop(p : g1, q : g2) = pack_gt(MCL_BLS12_381.miller_loop((p.x, p.y, p.z), ((q.x.x1, q.x.x2), (q.y.x1, q.y.x2), (q.z.x1, q.z.x2))))
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function final_exp(p : gt) = pack_gt(MCL_BLS12_381.final_exp((p.x1, p.x2, p.x3, p.x4, p.x5, p.x6, p.x7, p.x8, p.x9, p.x10, p.x11, p.x12)))
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@ -2,7 +2,7 @@
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{erl_opts, [debug_info]}.
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{deps, [ {aebytecode, {git, "https://github.com/aeternity/aebytecode.git", {ref,"b040dcc"}}}
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{deps, [ {aebytecode, {git, "https://github.com/aeternity/aebytecode.git", {ref,"e4b09d7"}}}
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, {getopt, "1.0.1"}
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, {eblake2, "1.0.0"}
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, {jsx, {git, "https://github.com/talentdeficit/jsx.git",
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@ -1,7 +1,7 @@
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{"1.1.0",
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[{<<"aebytecode">>,
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{git,"https://github.com/aeternity/aebytecode.git",
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{ref,"b040dccdefb0713198986264bc2d19d3fb84398d"}},
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{ref,"e4b09d7c5c85030636b3b88df7dd9f89f3d1e2cb"}},
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0},
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{<<"aeserialization">>,
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{git,"https://github.com/aeternity/aeserialization.git",
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@ -390,6 +390,12 @@ global_env() ->
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SignFun = fun(Ts, T) -> {type_sig, [stateful|Ann], none, [Signature], Ts, T} end,
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TTL = {qid, Ann, ["Chain", "ttl"]},
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Pointee = {qid, Ann, ["AENS", "pointee"]},
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Fr = {qid, Ann, ["MCL_BLS12_381", "fr"]},
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Fp = {qid, Ann, ["MCL_BLS12_381", "fp"]},
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Fp2 = {tuple_t, Ann, [Fp, Fp]},
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G1 = {tuple_t, Ann, [Fp, Fp, Fp]},
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G2 = {tuple_t, Ann, [Fp2, Fp2, Fp2]},
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GT = {tuple_t, Ann, lists:duplicate(12, Fp)},
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Fee = Int,
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[A, Q, R, K, V] = lists:map(TVar, ["a", "q", "r", "k", "v"]),
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@ -493,6 +499,40 @@ global_env() ->
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{"sha256", Fun1(A, Hash)},
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{"blake2b", Fun1(A, Hash)}]) },
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%% Fancy BLS12-381 crypto operations
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MCL_BLS12_381_Scope = #scope
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{ funs = MkDefs(
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[{"g1_neg", Fun1(G1, G1)},
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{"g1_norm", Fun1(G1, G1)},
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{"g1_valid", Fun1(G1, Bool)},
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{"g1_is_zero", Fun1(G1, Bool)},
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{"g1_add", Fun ([G1, G1], G1)},
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{"g1_mul", Fun ([Fr, G1], G1)},
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{"g2_neg", Fun1(G2, G2)},
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{"g2_norm", Fun1(G2, G2)},
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{"g2_valid", Fun1(G2, Bool)},
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{"g2_is_zero", Fun1(G2, Bool)},
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{"g2_add", Fun ([G2, G2], G2)},
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{"g2_mul", Fun ([Fr, G2], G2)},
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{"gt_inv", Fun1(GT, GT)},
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{"gt_add", Fun ([GT, GT], GT)},
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{"gt_mul", Fun ([GT, GT], GT)},
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{"gt_pow", Fun ([GT, Fr], GT)},
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{"gt_is_one", Fun1(GT, Bool)},
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{"pairing", Fun ([G1, G2], GT)},
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{"miller_loop", Fun ([G1, G2], GT)},
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{"final_exp", Fun1(GT, GT)},
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{"int_to_fr", Fun1(Int, Fr)},
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{"int_to_fp", Fun1(Int, Fp)},
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{"fr_to_int", Fun1(Fr, Int)},
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{"fp_to_int", Fun1(Fp, Int)}
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]),
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types = MkDefs(
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[{"fr", 0}, {"fp", 0}]) },
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%% Authentication
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AuthScope = #scope
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{ funs = MkDefs(
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@ -547,12 +587,15 @@ global_env() ->
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, ["Map"] => MapScope
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, ["Auth"] => AuthScope
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, ["Crypto"] => CryptoScope
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, ["MCL_BLS12_381"] => MCL_BLS12_381_Scope
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, ["String"] => StringScope
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, ["Bits"] => BitsScope
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, ["Bytes"] => BytesScope
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, ["Int"] => IntScope
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, ["Address"] => AddressScope
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} }.
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}
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}.
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option_t(As, T) -> {app_t, As, {id, As, "option"}, [T]}.
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map_t(As, K, V) -> {app_t, As, {id, As, "map"}, [K, V]}.
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@ -34,7 +34,14 @@
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bits_intersection | bits_union | bits_difference |
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contract_to_address | address_to_contract | crypto_verify_sig | crypto_verify_sig_secp256k1 |
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crypto_sha3 | crypto_sha256 | crypto_blake2b |
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crypto_ecverify_secp256k1 | crypto_ecrecover_secp256k1.
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crypto_ecverify_secp256k1 | crypto_ecrecover_secp256k1 |
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mcl_bls12_381_g1_neg | mcl_bls12_381_g1_norm | mcl_bls12_381_g1_valid |
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mcl_bls12_381_g1_is_zero | mcl_bls12_381_g1_add | mcl_bls12_381_g1_mul |
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mcl_bls12_381_g2_neg | mcl_bls12_381_g2_norm | mcl_bls12_381_g2_valid |
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mcl_bls12_381_g2_is_zero | mcl_bls12_381_g2_add | mcl_bls12_381_g2_mul |
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mcl_bls12_381_gt_inv | mcl_bls12_381_gt_add | mcl_bls12_381_gt_mul | mcl_bls12_381_gt_pow |
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mcl_bls12_381_gt_is_one | mcl_bls12_381_pairing | mcl_bls12_381_miller_loop | mcl_bls12_381_final_exp |
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mcl_bls12_381_int_to_fr | mcl_bls12_381_int_to_fp | mcl_bls12_381_fr_to_int | mcl_bls12_381_fp_to_int.
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-type flit() :: {int, integer()}
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| {string, binary()}
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@ -197,6 +204,11 @@ builtins() ->
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{["Crypto"], [{"verify_sig", 3}, {"verify_sig_secp256k1", 3},
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{"ecverify_secp256k1", 3}, {"ecrecover_secp256k1", 2},
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{"sha3", 1}, {"sha256", 1}, {"blake2b", 1}]},
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{["MCL_BLS12_381"], [{"g1_neg", 1}, {"g1_norm", 1}, {"g1_valid", 1}, {"g1_is_zero", 1}, {"g1_add", 2}, {"g1_mul", 2},
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{"g2_neg", 1}, {"g2_norm", 1}, {"g2_valid", 1}, {"g2_is_zero", 1}, {"g2_add", 2}, {"g2_mul", 2},
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{"gt_inv", 1}, {"gt_add", 2}, {"gt_mul", 2}, {"gt_pow", 2}, {"gt_is_one", 1},
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{"pairing", 2}, {"miller_loop", 2}, {"final_exp", 1},
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{"int_to_fr", 1}, {"int_to_fp", 1}, {"fr_to_int", 1}, {"fp_to_int", 1}]},
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{["Auth"], [{"tx_hash", none}]},
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{["String"], [{"length", 1}, {"concat", 2}, {"sha3", 1}, {"sha256", 1}, {"blake2b", 1}]},
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{["Bits"], [{"set", 2}, {"clear", 2}, {"test", 2}, {"sum", 1}, {"intersection", 2},
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@ -229,7 +241,9 @@ init_type_env() ->
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["map"] => ?type(K, V, {map, K, V}),
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["option"] => ?type(T, {variant, [[], [T]]}),
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["Chain", "ttl"] => ?type({variant, [[integer], [integer]]}),
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["AENS", "pointee"] => ?type({variant, [[address], [address], [address]]})
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["AENS", "pointee"] => ?type({variant, [[address], [address], [address]]}),
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["MCL_BLS12_381", "fr"] => ?type({bytes, 32}),
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["MCL_BLS12_381", "fp"] => ?type({bytes, 48})
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}.
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is_no_code(Env) ->
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@ -910,7 +924,14 @@ op_builtins() ->
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bits_difference, int_to_str, address_to_str, crypto_verify_sig,
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address_to_contract,
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crypto_verify_sig_secp256k1, crypto_sha3, crypto_sha256, crypto_blake2b,
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crypto_ecverify_secp256k1, crypto_ecrecover_secp256k1
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crypto_ecverify_secp256k1, crypto_ecrecover_secp256k1,
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mcl_bls12_381_g1_neg, mcl_bls12_381_g1_norm, mcl_bls12_381_g1_valid,
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mcl_bls12_381_g1_is_zero, mcl_bls12_381_g1_add, mcl_bls12_381_g1_mul,
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mcl_bls12_381_g2_neg, mcl_bls12_381_g2_norm, mcl_bls12_381_g2_valid,
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mcl_bls12_381_g2_is_zero, mcl_bls12_381_g2_add, mcl_bls12_381_g2_mul,
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mcl_bls12_381_gt_inv, mcl_bls12_381_gt_add, mcl_bls12_381_gt_mul, mcl_bls12_381_gt_pow,
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mcl_bls12_381_gt_is_one, mcl_bls12_381_pairing, mcl_bls12_381_miller_loop, mcl_bls12_381_final_exp,
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mcl_bls12_381_int_to_fr, mcl_bls12_381_int_to_fp, mcl_bls12_381_fr_to_int, mcl_bls12_381_fp_to_int
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].
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builtin_to_fcode(require, [Cond, Msg]) ->
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@ -570,7 +570,31 @@ op_to_scode(crypto_sha256) -> aeb_fate_ops:sha256(?a, ?a);
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op_to_scode(crypto_blake2b) -> aeb_fate_ops:blake2b(?a, ?a);
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op_to_scode(string_sha3) -> aeb_fate_ops:sha3(?a, ?a);
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op_to_scode(string_sha256) -> aeb_fate_ops:sha256(?a, ?a);
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op_to_scode(string_blake2b) -> aeb_fate_ops:blake2b(?a, ?a).
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op_to_scode(string_blake2b) -> aeb_fate_ops:blake2b(?a, ?a);
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op_to_scode(mcl_bls12_381_g1_neg) -> aeb_fate_ops:bls12_381_g1_neg(?a, ?a);
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op_to_scode(mcl_bls12_381_g1_norm) -> aeb_fate_ops:bls12_381_g1_norm(?a, ?a);
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op_to_scode(mcl_bls12_381_g1_valid) -> aeb_fate_ops:bls12_381_g1_valid(?a, ?a);
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op_to_scode(mcl_bls12_381_g1_is_zero) -> aeb_fate_ops:bls12_381_g1_is_zero(?a, ?a);
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op_to_scode(mcl_bls12_381_g1_add) -> aeb_fate_ops:bls12_381_g1_add(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_g1_mul) -> aeb_fate_ops:bls12_381_g1_mul(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_g2_neg) -> aeb_fate_ops:bls12_381_g2_neg(?a, ?a);
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op_to_scode(mcl_bls12_381_g2_norm) -> aeb_fate_ops:bls12_381_g2_norm(?a, ?a);
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op_to_scode(mcl_bls12_381_g2_valid) -> aeb_fate_ops:bls12_381_g2_valid(?a, ?a);
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op_to_scode(mcl_bls12_381_g2_is_zero) -> aeb_fate_ops:bls12_381_g2_is_zero(?a, ?a);
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op_to_scode(mcl_bls12_381_g2_add) -> aeb_fate_ops:bls12_381_g2_add(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_g2_mul) -> aeb_fate_ops:bls12_381_g2_mul(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_gt_inv) -> aeb_fate_ops:bls12_381_gt_inv(?a, ?a);
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op_to_scode(mcl_bls12_381_gt_add) -> aeb_fate_ops:bls12_381_gt_add(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_gt_mul) -> aeb_fate_ops:bls12_381_gt_mul(?a, ?a, ?a);
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op_to_scode(mcl_bls12_381_gt_pow) -> aeb_fate_ops:bls12_381_gt_pow(?a, ?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_gt_is_one) -> aeb_fate_ops:bls12_381_gt_is_one(?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_pairing) -> aeb_fate_ops:bls12_381_pairing(?a, ?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_miller_loop) -> aeb_fate_ops:bls12_381_miller_loop(?a, ?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_final_exp) -> aeb_fate_ops:bls12_381_final_exp(?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_int_to_fr) -> aeb_fate_ops:bls12_381_int_to_fr(?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_int_to_fp) -> aeb_fate_ops:bls12_381_int_to_fp(?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_fr_to_int) -> aeb_fate_ops:bls12_381_fr_to_int(?a, ?a);
|
||||
op_to_scode(mcl_bls12_381_fp_to_int) -> aeb_fate_ops:bls12_381_fp_to_int(?a, ?a).
|
||||
|
||||
%% PUSH and STORE ?a are the same, so we use STORE to make optimizations
|
||||
%% easier, and specialize to PUSH (which is cheaper) at the end.
|
||||
@ -843,6 +867,30 @@ attributes(I) ->
|
||||
{'AENS_UPDATE', A, B, C, D, E, F} -> Impure(none, [A, B, C, D, E, F]);
|
||||
{'AENS_TRANSFER', A, B, C, D} -> Impure(none, [A, B, C, D]);
|
||||
{'AENS_REVOKE', A, B, C} -> Impure(none, [A, B, C]);
|
||||
{'BLS12_381_G1_NEG', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G1_NORM', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G1_VALID', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G1_IS_ZERO', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G1_ADD', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_G1_MUL', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_G2_NEG', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G2_NORM', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G2_VALID', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G2_IS_ZERO', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_G2_ADD', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_G2_MUL', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_GT_INV', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_GT_ADD', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_GT_MUL', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_GT_POW', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_GT_IS_ONE', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_PAIRING', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_MILLER_LOOP', A, B, C} -> Pure(A, [B, C]);
|
||||
{'BLS12_381_FINAL_EXP', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_INT_TO_FR', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_INT_TO_FP', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_FR_TO_INT', A, B} -> Pure(A, [B]);
|
||||
{'BLS12_381_FP_TO_INT', A, B} -> Pure(A, [B]);
|
||||
{'ABORT', A} -> Impure(pc, A);
|
||||
{'EXIT', A} -> Impure(pc, A);
|
||||
'NOP' -> Pure(none, [])
|
||||
|
@ -161,11 +161,12 @@ compilable_contracts() ->
|
||||
"list_comp",
|
||||
"payable",
|
||||
"unapplied_builtins",
|
||||
"underscore_number_literals"
|
||||
"underscore_number_literals",
|
||||
"pairing_crypto"
|
||||
].
|
||||
|
||||
not_yet_compilable(fate) -> [];
|
||||
not_yet_compilable(aevm) -> [].
|
||||
not_yet_compilable(aevm) -> ["pairing_crypto"].
|
||||
|
||||
%% Contracts that should produce type errors
|
||||
|
||||
|
30
test/contracts/pairing_crypto.aes
Normal file
30
test/contracts/pairing_crypto.aes
Normal file
@ -0,0 +1,30 @@
|
||||
include "BLS12_381.aes"
|
||||
|
||||
contract GrothVerify =
|
||||
type fr = BLS12_381.fr
|
||||
type g1 = BLS12_381.g1
|
||||
type g2 = BLS12_381.g2
|
||||
|
||||
record proof = { a : g1, b : g2, c : g1 }
|
||||
record verify_key = { a : g1, b : g2, c : g2, d : g2, ic : list(g1) }
|
||||
|
||||
record state = { vk : verify_key }
|
||||
|
||||
entrypoint init(vk0 : verify_key) = {vk = vk0}
|
||||
|
||||
entrypoint verify_proof(p : proof, input : list(fr)) =
|
||||
let vk = state.vk
|
||||
let vk_x = calc_vk_x(vk.ic, input)
|
||||
|
||||
BLS12_381.pairing_check([BLS12_381.g1_neg(p.a), vk.a, vk_x, p.c],
|
||||
[p.b, vk.b, vk.c, vk.d])
|
||||
|
||||
function calc_vk_x(ics : list(g1), xs : list(fr)) =
|
||||
switch(ics)
|
||||
(ic :: ics) => calc_vk_x_(ic, ics, xs)
|
||||
|
||||
function calc_vk_x_(vk_x : g1, ics : list(g1), xs : list(fr)) =
|
||||
switch((ics, xs))
|
||||
([], []) => vk_x
|
||||
(ic :: ics, x :: xs) => calc_vk_x_(BLS12_381.g1_add(vk_x, BLS12_381.g1_mul(x, ic)), ics, xs)
|
||||
|
Loading…
x
Reference in New Issue
Block a user