From eda7812b8b426411a024608381c8dab732db61d2 Mon Sep 17 00:00:00 2001
From: John Driscoll <john@bitgo.com>
Date: Wed, 11 Oct 2023 12:31:51 -0500
Subject: [PATCH] feat(sdk-lib-mpc): reject y not co-prime to N

TICKET: WP-132
---
 .../src/tss/ecdsa/paillierBlumProof.ts        |   14 +-
 .../test/fixtures/mockPaillierBlumProof.json  | 1956 ++++++++---------
 2 files changed, 985 insertions(+), 985 deletions(-)

diff --git a/modules/sdk-lib-mpc/src/tss/ecdsa/paillierBlumProof.ts b/modules/sdk-lib-mpc/src/tss/ecdsa/paillierBlumProof.ts
index 9ba74a5507..a17417b417 100644
--- a/modules/sdk-lib-mpc/src/tss/ecdsa/paillierBlumProof.ts
+++ b/modules/sdk-lib-mpc/src/tss/ecdsa/paillierBlumProof.ts
@@ -1,6 +1,6 @@
 import { createHash } from 'crypto';
 import { bitLength, randBits, isProbablyPrime } from 'bigint-crypto-utils';
-import { modInv, modPow } from 'bigint-mod-arith';
+import { gcd, modInv, modPow } from 'bigint-mod-arith';
 import { bigIntFromBufferBE, bigIntToBufferBE } from '../../util';
 import { DeserializedPaillierBlumProof } from './types';
 
@@ -33,7 +33,7 @@ function generateY(N, w): bigint[] {
             .update('$')
             .digest()
         );
-        if (y > BigInt(0) && y < N) {
+        if (y > BigInt(0) && y < N && gcd(y, N) === BigInt(1)) {
           return y;
         }
       }
@@ -110,14 +110,13 @@ export async function prove(p: bigint, q: bigint): Promise<DeserializedPaillierB
     y.map(async (y_i, i) => {
       // Select random a_i, b_i so that y_i' = (-1)^{a_i} * w^{b_i} * y is
       // quadratic residue of N using [HOC - Fact 2.137].
-      let t;
-      while (true) {
+      let ab_i, t;
+      for (ab_i = 0; ab_i < 4; ab_i++) {
         t = y_i;
-        ab[i] = (await randBits(2))[0];
-        if (ab[i] & 2) {
+        if (ab_i & 2) {
           t = -t;
         }
-        if (ab[i] & 1) {
+        if (ab_i & 1) {
           t *= w;
         }
         if (
@@ -127,6 +126,7 @@ export async function prove(p: bigint, q: bigint): Promise<DeserializedPaillierB
           break;
         }
       }
+      ab[i] = ab_i;
       return modPow(t, e, N);
     })
   );
diff --git a/modules/sdk-lib-mpc/test/fixtures/mockPaillierBlumProof.json b/modules/sdk-lib-mpc/test/fixtures/mockPaillierBlumProof.json
index 47776a28e5..d50574d7ab 100644
--- a/modules/sdk-lib-mpc/test/fixtures/mockPaillierBlumProof.json
+++ b/modules/sdk-lib-mpc/test/fixtures/mockPaillierBlumProof.json
@@ -1,1262 +1,1262 @@
 [
   {
-    "n": "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",
-    "p": "0186100d11e0c4c405e291617e592e0bcc5f6ecf70cae2a26e51566137bc16ab2bf2e664becbaffa0fbf9306ff20cffb4d0f5c3995d96483f1818f83fd25fb3c5586cd0d94195507efbb90367aa59ff82585402b99735b171ad91ce356e0a050f7aa4fb5fe109a42fbe2d70ef5c151994bf7c9aa8434f3e895606a7c6e2d64dedfcc7dadb247f6ea187840a73d4cbbca4f3b90a054ed5e7c290f7ce73b5c9c2d6a6b310d5e5604c92d5187658443942c9e63f9f7552e7242b9f183eadcfb57204f",
-    "q": "a1c222f627ea4d7eb1dfab4d3a1a277762da595acd0309b129ea0542c093c40ed64967b95a19f95336faf1e19c70e9720233f7bb919322cb13530916cd0c234e40857b621d1303f8c8f510ccf56ff5e45eda61f9a3c8cb078108dc1d4bc9d1b446f2a507b42c756bdd034870eea8a77688a3217b178e70791a71d413f13d786951b824a91b6f868a5f1c957c338fe35ba51f6d65be861d8cfc21df48219d216fad4a5cf5343c8188f93600b8bffb93632cf4bf12a30b5729cb900999c29c7f7f",
-    "w": "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",
+    "n": "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",
+    "p": "0102d27b325be48a23d919917751b650cba9dca57a328a0eeeef02fc3253f8c6d4e2d5266fdbc2dd490243cad04ec1362eeade853e92a3ade62c6f06869454295b83763ef6474bbea542db8ffba12bc1881c30bdaec0fd0e4cc296a7a4c45aae7aab2ba4df489a1b37d912db0baac461861935dac9ebd48b779de0baede287a8dc8f5a1a4df408768e50016d8c2caa0a42d3be536adc61c73bd4b17ad5beda32dbf23c898d0921735c713948311204ba7a8359448af30d17cf3c06b90b9dbea253",
+    "q": "d97fffce0fa4d5696fd045c6c86a2aca4abb7d740977f28478c01f8f38eb26d948ff9b3c4094816ea8e7620361234cd0ac9c6292ca02e29d7cc0246e9af05f8556b9990f87a7295d9be7e046b6b744633db4349ecf076ee3ce171816ea3182aba3a853e7c70b0aae32f6a22b3b9414ddb6aa4ba51293660bcfa6d75c346eead0946c7a2a7578a56c31a2e780a4bec180bda7f2c3e203fdb945cc1806cdb7d1c97c022f6eaa900f55a059d0f3d9154dd5015c391d7bea0151a73ac4649ef95ec7",
+    "w": "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",
     "ab": [
-      1,
       3,
       3,
-      0,
       2,
-      0,
-      0,
       2,
+      1,
+      1,
+      1,
       2,
       3,
-      3,
       1,
       0,
-      2,
-      2,
-      0,
       1,
       2,
       2,
-      0,
       1,
-      2,
-      0,
+      3,
+      3,
       1,
       1,
       0,
       2,
-      3,
-      1,
-      0,
-      1,
-      1,
       1,
+      3,
       1,
       1,
       2,
+      2,
       0,
-      1,
-      3,
       0,
       1,
-      2,
       1,
       0,
+      2,
+      2,
       1,
       0,
+      3,
+      0,
+      3,
+      3,
+      0,
+      2,
       1,
       1,
-      3,
+      2,
+      1,
+      2,
+      2,
       2,
       3,
       3,
-      1,
+      2,
       3,
       1,
       1,
-      0,
-      0,
-      1,
       2,
       0,
+      0,
       1,
       3,
       3,
-      3,
-      3,
       0,
       1,
+      1,
       3,
+      0,
       2,
+      1,
       2,
       2,
-      3,
+      1,
+      2,
       0,
+      1,
+      3,
+      1,
       3,
-      0,
-      0,
-      0,
+      2,
       2,
       1
     ],
     "x": [
-      "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",
-      "0bf41b8636f87b75d895cf8b5d60cec75aa5dd29aaedb9781e204c60731301ffec483ac78b8cf199317cf95b62f8337ba8b76fe8fed2e10246288001bf515998f02bc138ea24de3fd9eb623a7dc11f878d2f4ff8a9b1707a7a8b4a1a58a8655af8f5c08344e90c426b8429bf33c130cd811e70bafa87c1c0286ba3b9af92523eb0e4a50343ec0dd4f54ab04f9a8548f67940a3f663e13d89a12c6c4821e1e576951ba10189cf8468c7b6f1f0d3f29db88f3c205fd47969fad79912511a7a9b38a9573f965613faac14cf7ba90fa07ce1043fe15486fe2369ad8caf244e21d0b3fab0d06cc6fbb7109a0bf11242635814ceeffa00e0078d6b511d2efe0fc4d5a898be881cedb61eca555dc1ad105e621563928ebfd2e4ddb56d1b2249441fb1b6143f5e63ab5a21641f7858db795b03dd49e3f694bb818814ab6023c29be206a78c5e81b752a343c558fc90b64f2ea88d3eb53fc52b9d1501505cf689af3b70a962d2ead841329c0f089be51f284e96cdca789854a08caa0a4d09c75626c32107",
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   }
 ]
\ No newline at end of file