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Diffstat (limited to 'security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst')
| -rw-r--r-- | security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst | 168 |
1 files changed, 0 insertions, 168 deletions
diff --git a/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst b/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst deleted file mode 100644 index af4035b09..000000000 --- a/security/nss/lib/freebl/verified/specs/Spec.Curve25519.fst +++ /dev/null @@ -1,168 +0,0 @@ -/* 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 |