From e10349ab8dda8a3f11be6aa19f2b6e29fe814044 Mon Sep 17 00:00:00 2001 From: wolfbeast Date: Fri, 23 Feb 2018 11:04:39 +0100 Subject: Update NSS to 3.35-RTM --- .../lib/freebl/verified/specs/Spec.Curve25519.fst | 168 +++++++++++++++++++++ 1 file changed, 168 insertions(+) create mode 100644 security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst (limited to 'security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst') diff --git a/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst b/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst new file mode 100644 index 0000000000..af4035b09f --- /dev/null +++ b/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst @@ -0,0 +1,168 @@ +/* Copyright 2016-2017 INRIA and Microsoft Corporation + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +module Spec.Curve25519 + +module ST = FStar.HyperStack.ST + +open FStar.Mul +open FStar.Seq +open FStar.UInt8 +open FStar.Endianness +open Spec.Lib +open Spec.Curve25519.Lemmas + +#reset-options "--initial_fuel 0 --max_fuel 0 --z3rlimit 20" + +(* Field types and parameters *) +let prime = pow2 255 - 19 +type elem : Type0 = e:int{e >= 0 /\ e < prime} +let fadd e1 e2 = (e1 + e2) % prime +let fsub e1 e2 = (e1 - e2) % prime +let fmul e1 e2 = (e1 * e2) % prime +let zero : elem = 0 +let one : elem = 1 +let ( +@ ) = fadd +let ( *@ ) = fmul + +(** Exponentiation *) +let rec ( ** ) (e:elem) (n:pos) : Tot elem (decreases n) = + if n = 1 then e + else + if n % 2 = 0 then op_Star_Star (e `fmul` e) (n / 2) + else e `fmul` (op_Star_Star (e `fmul` e) ((n-1)/2)) + +(* Type aliases *) +type scalar = lbytes 32 +type serialized_point = lbytes 32 +type proj_point = | Proj: x:elem -> z:elem -> proj_point + +let decodeScalar25519 (k:scalar) = + let k = k.[0] <- (k.[0] &^ 248uy) in + let k = k.[31] <- ((k.[31] &^ 127uy) |^ 64uy) in k + +let decodePoint (u:serialized_point) = + (little_endian u % pow2 255) % prime + +let add_and_double qx nq nqp1 = + let x_1 = qx in + let x_2, z_2 = nq.x, nq.z in + let x_3, z_3 = nqp1.x, nqp1.z in + let a = x_2 `fadd` z_2 in + let aa = a**2 in + let b = x_2 `fsub` z_2 in + let bb = b**2 in + let e = aa `fsub` bb in + let c = x_3 `fadd` z_3 in + let d = x_3 `fsub` z_3 in + let da = d `fmul` a in + let cb = c `fmul` b in + let x_3 = (da `fadd` cb)**2 in + let z_3 = x_1 `fmul` ((da `fsub` cb)**2) in + let x_2 = aa `fmul` bb in + let z_2 = e `fmul` (aa `fadd` (121665 `fmul` e)) in + Proj x_2 z_2, Proj x_3 z_3 + +let ith_bit (k:scalar) (i:nat{i < 256}) = + let q = i / 8 in let r = i % 8 in + (v (k.[q]) / pow2 r) % 2 + +let rec montgomery_ladder_ (init:elem) x xp1 (k:scalar) (ctr:nat{ctr<=256}) + : Tot proj_point (decreases ctr) = + if ctr = 0 then x + else ( + let ctr' = ctr - 1 in + let (x', xp1') = + if ith_bit k ctr' = 1 then ( + let nqp2, nqp1 = add_and_double init xp1 x in + nqp1, nqp2 + ) else add_and_double init x xp1 in + montgomery_ladder_ init x' xp1' k ctr' + ) + +let montgomery_ladder (init:elem) (k:scalar) : Tot proj_point = + montgomery_ladder_ init (Proj one zero) (Proj init one) k 256 + +let encodePoint (p:proj_point) : Tot serialized_point = + let p = p.x `fmul` (p.z ** (prime - 2)) in + little_bytes 32ul p + +let scalarmult (k:scalar) (u:serialized_point) : Tot serialized_point = + let k = decodeScalar25519 k in + let u = decodePoint u in + let res = montgomery_ladder u k in + encodePoint res + + +(* ********************* *) +(* RFC 7748 Test Vectors *) +(* ********************* *) + +let scalar1 = [ + 0xa5uy; 0x46uy; 0xe3uy; 0x6buy; 0xf0uy; 0x52uy; 0x7cuy; 0x9duy; + 0x3buy; 0x16uy; 0x15uy; 0x4buy; 0x82uy; 0x46uy; 0x5euy; 0xdduy; + 0x62uy; 0x14uy; 0x4cuy; 0x0auy; 0xc1uy; 0xfcuy; 0x5auy; 0x18uy; + 0x50uy; 0x6auy; 0x22uy; 0x44uy; 0xbauy; 0x44uy; 0x9auy; 0xc4uy +] + +let scalar2 = [ + 0x4buy; 0x66uy; 0xe9uy; 0xd4uy; 0xd1uy; 0xb4uy; 0x67uy; 0x3cuy; + 0x5auy; 0xd2uy; 0x26uy; 0x91uy; 0x95uy; 0x7duy; 0x6auy; 0xf5uy; + 0xc1uy; 0x1buy; 0x64uy; 0x21uy; 0xe0uy; 0xeauy; 0x01uy; 0xd4uy; + 0x2cuy; 0xa4uy; 0x16uy; 0x9euy; 0x79uy; 0x18uy; 0xbauy; 0x0duy +] + +let input1 = [ + 0xe6uy; 0xdbuy; 0x68uy; 0x67uy; 0x58uy; 0x30uy; 0x30uy; 0xdbuy; + 0x35uy; 0x94uy; 0xc1uy; 0xa4uy; 0x24uy; 0xb1uy; 0x5fuy; 0x7cuy; + 0x72uy; 0x66uy; 0x24uy; 0xecuy; 0x26uy; 0xb3uy; 0x35uy; 0x3buy; + 0x10uy; 0xa9uy; 0x03uy; 0xa6uy; 0xd0uy; 0xabuy; 0x1cuy; 0x4cuy +] + +let input2 = [ + 0xe5uy; 0x21uy; 0x0fuy; 0x12uy; 0x78uy; 0x68uy; 0x11uy; 0xd3uy; + 0xf4uy; 0xb7uy; 0x95uy; 0x9duy; 0x05uy; 0x38uy; 0xaeuy; 0x2cuy; + 0x31uy; 0xdbuy; 0xe7uy; 0x10uy; 0x6fuy; 0xc0uy; 0x3cuy; 0x3euy; + 0xfcuy; 0x4cuy; 0xd5uy; 0x49uy; 0xc7uy; 0x15uy; 0xa4uy; 0x93uy +] + +let expected1 = [ + 0xc3uy; 0xdauy; 0x55uy; 0x37uy; 0x9duy; 0xe9uy; 0xc6uy; 0x90uy; + 0x8euy; 0x94uy; 0xeauy; 0x4duy; 0xf2uy; 0x8duy; 0x08uy; 0x4fuy; + 0x32uy; 0xecuy; 0xcfuy; 0x03uy; 0x49uy; 0x1cuy; 0x71uy; 0xf7uy; + 0x54uy; 0xb4uy; 0x07uy; 0x55uy; 0x77uy; 0xa2uy; 0x85uy; 0x52uy +] +let expected2 = [ + 0x95uy; 0xcbuy; 0xdeuy; 0x94uy; 0x76uy; 0xe8uy; 0x90uy; 0x7duy; + 0x7auy; 0xaduy; 0xe4uy; 0x5cuy; 0xb4uy; 0xb8uy; 0x73uy; 0xf8uy; + 0x8buy; 0x59uy; 0x5auy; 0x68uy; 0x79uy; 0x9fuy; 0xa1uy; 0x52uy; + 0xe6uy; 0xf8uy; 0xf7uy; 0x64uy; 0x7auy; 0xacuy; 0x79uy; 0x57uy +] + +let test () = + assert_norm(List.Tot.length scalar1 = 32); + assert_norm(List.Tot.length scalar2 = 32); + assert_norm(List.Tot.length input1 = 32); + assert_norm(List.Tot.length input2 = 32); + assert_norm(List.Tot.length expected1 = 32); + assert_norm(List.Tot.length expected2 = 32); + let scalar1 = createL scalar1 in + let scalar2 = createL scalar2 in + let input1 = createL input1 in + let input2 = createL input2 in + let expected1 = createL expected1 in + let expected2 = createL expected2 in + scalarmult scalar1 input1 = expected1 + && scalarmult scalar2 input2 = expected2 -- cgit v1.2.3