,....

static/js/modules/crypto/paillier.js

@@ -16,11 +16,11 @@ class Ciphertext {
         let gm = (1n + key.n * plainText) % key.n2;
 
         // Compute g^m r^n from crt.
-        this.cyphertext = (gm * mod_exp(r, key.n, key.n2)) % key.n2;
+        this.cipherText = (gm * mod_exp(r, key.n, key.n2)) % key.n2;
 
         // Force into range.
-        while (this.cyphertext < 0n) {
-            this.cyphertext += key.n2;
+        while (this.cipherText < 0n) {
+            this.cipherText += key.n2;
         }
 
         this.r = r;
@@ -31,30 +31,69 @@ class Ciphertext {
     }
 
     update(c) {
-        this.cyphertext = (this.cyphertext * c.cyphertext) % this.pubKey.n2;
+        this.cipherText = (this.cipherText * c.cipherText) % this.pubKey.n2;
         this.r = (this.r * c.r) % this.pubKey.n2;
         this.plainText += c.plainText;
 
         // Force into range
-        while (this.cyphertext < 0n) {
-            this.cyphertext += this.pubKey.n2;
+        while (this.cipherText < 0n) {
+            this.cipherText += this.pubKey.n2;
         }
     }
 
     toString() {
-        return "0x" + this.cyphertext.toString(16);
+        return "0x" + this.cipherText.toString(16);
     }
 
     prove() {
-        return new ZeroProofSessionProver(this);
+        return new ValueProofSessionProver(this);
     }
 
-    asReadOnlyCyphertext() {
-        return new ReadOnlyCiphertext(this.pubKey, this.cyphertext);
+    // Construct a non-interactive proof
+    proveNI() {
+        let rp = cryptoRandom(4096);
+        while (rp >= this.pubKey.n) {
+            rp = cryptoRandom(4096);
+        }
+
+        let a = mod_exp(rp, this.pubKey.n, this.pubKey.n2);
+        let hasher = new jsSHA("SHAKE256", "HEX");
+
+        let plainText = this.plainText.toString(16);
+        if (plainText.length % 2 !== 0) {
+            plainText = "0" + plainText;
+        }
+
+        let aStr = a.toString(16);
+        if (aStr.length % 2 !== 0) {
+            aStr = "0" + aStr;
+        }
+
+        hasher.update(this.pubKey.g.toString(16));
+        hasher.update(plainText);
+        hasher.update(aStr);
+
+        let challenge = BigInt("0x" + hasher.getHash("HEX", { outputLen: 2048 }));
+
+        return {
+            plainText: "0x" + this.plainText.toString(16),
+            a: "0x" + a.toString(16),
+            challenge: "0x" + challenge.toString(16),
+            proof:
+                "0x" +
+                (
+                    ((rp % this.pubKey.n) * mod_exp(this.r, challenge, this.pubKey.n)) %
+                    this.pubKey.n
+                ).toString(16),
+        };
+    }
+
+    asReadOnlyCiphertext() {
+        return new ReadOnlyCiphertext(this.pubKey, this.cipherText);
     }
 }
 
-class ZeroProofSessionProver {
+class ValueProofSessionProver {
     constructor(cipherText) {
         this.cipherText = cipherText;
 
@@ -82,46 +121,63 @@ class ZeroProofSessionProver {
 
     asVerifier() {
         return this.cipherText
-            .asReadOnlyCyphertext()
+            .asReadOnlyCiphertext()
             .prove(this.cipherText.plainText, this.noise());
     }
 }
 
-window.Cyphertext = Ciphertext;
+window.Ciphertext = Ciphertext;
 
 export class ReadOnlyCiphertext {
-    constructor(key, cyphertext) {
-        this.cyphertext = cyphertext;
+    constructor(key, cipherText) {
+        this.cipherText = cipherText;
         this.pubKey = key;
 
         this.readOnly = true;
     }
 
     update(c) {
-        this.cyphertext = (this.cyphertext * c.cyphertext) % this.pubKey.n2;
+        this.cipherText = (this.cipherText * c.cipherText) % this.pubKey.n2;
 
         // Force into range
-        while (this.cyphertext < 0n) {
-            this.cyphertext += this.pubKey.n2;
+        while (this.cipherText < 0n) {
+            this.cipherText += this.pubKey.n2;
         }
     }
 
     prove(plainText, a) {
-        return new ZeroProofSessionVerifier(this, plainText, a);
+        return new ValueProofSessionVerifier(this, plainText, a);
+    }
+
+    verifyNI(statement) {
+        let verifier = new ValueProofSessionVerifier(
+            this,
+            BigInt(statement.plainText),
+            BigInt(statement.a),
+            BigInt(statement.challenge)
+        );
+
+        return verifier.verify(BigInt(statement.proof));
     }
 
     clone() {
-        return new ReadOnlyCiphertext(this.pubKey, this.cyphertext);
+        return new ReadOnlyCiphertext(this.pubKey, this.cipherText);
     }
 }
 
-class ZeroProofSessionVerifier {
-    constructor(cipherText, plainText, a) {
+class ValueProofSessionVerifier {
+    constructor(cipherText, plainText, a, challenge) {
         // Clone, otherwise the update below will mutate the original value
         this.cipherText = cipherText.clone();
         this.cipherText.update(this.cipherText.pubKey.encrypt(-1n * plainText, 1n));
-        // Shift the challenge down by 1 to ensure it is smaller than either prime factor.
-        this.challenge = cryptoRandom(2048) << 1n;
+
+        if (challenge === undefined) {
+            // Shift the challenge down by 1 to ensure it is smaller than either prime factor.
+            this.challenge = cryptoRandom(2048) << 1n;
+        } else {
+            this.challenge = challenge;
+        }
+
         this.a = a;
 
         this.plainText = plainText;
@@ -130,14 +186,14 @@ class ZeroProofSessionVerifier {
     verify(proof) {
         // check coprimality
         if (gcd(proof, this.cipherText.pubKey.n) !== 1n) return -1;
-        if (gcd(this.cipherText.cyphertext, this.cipherText.pubKey.n) !== 1n) return -2;
+        if (gcd(this.cipherText.cipherText, this.cipherText.pubKey.n) !== 1n) return -2;
         if (gcd(this.a, this.cipherText.pubKey.n) !== 1n) return -3;
 
         // check exp
         return mod_exp(proof, this.cipherText.pubKey.n, this.cipherText.pubKey.n2) ===
             (this.a *
                 mod_exp(
-                    this.cipherText.cyphertext,
+                    this.cipherText.cipherText,
                     this.challenge,
                     this.cipherText.pubKey.n2
                 )) %
@@ -147,7 +203,7 @@ class ZeroProofSessionVerifier {
     }
 }
 
-window.ReadOnlyCyphertext = ReadOnlyCiphertext;
+window.ReadOnlyCiphertext = ReadOnlyCiphertext;
 
 export class PaillierPubKey {
     constructor(n) {

static/js/modules/interface/main.js

@@ -5,6 +5,7 @@ import { Packet } from "./packet.js";
 import { Game } from "./game.js";
 import { Region } from "./map.js";
 import "./dom.js";
+import "./proofs.js";
 
 export const ID = window.crypto.randomUUID();
 export const game = new Game();

static/js/modules/interface/proofs.js

@@ -0,0 +1,17 @@
+function cryptoShuffle(l) {
+    for (let i = 0; i < l.length - 1; i++) {}
+}
+
+window.cryptoShuffle = cryptoShuffle;
+
+function proveRegions(regions) {
+    // Construct prover coins
+    let regionNames = Object.keys(regions.keys());
+    let psi = [regionNames];
+
+    // Construct verifier coins
+    let hasher = new jsSHA("SHA3-256", "TEXT");
+    hasher.update(JSON.stringify(regions));
+
+    // Construct prover proofs
+}