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readme, benchmarks, fix verification

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jude
2023-04-15 14:28:13 +01:00
parent 35dbf321e9
commit ad26788927
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31
README.md Normal file
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# Riskless
### Undergraduate dissertation
**Paper: https://judesouthworth.xyz/Dissertation.pdf**
## Running the demo
1. `pip install -r requirements.txt`
2. `python3 app.py`
3. Navigate browser to `http://localhost:5000`
### Running the benchmarks
1. Press F12
2. Type the name of the benchmark to run:
- `RSABench`
- `PaillierBench`
- `ZeroProofBench`
- `ZeroProofVerifierBench`
- `ZeroProofSizeBench`
- `Protocol4Bench`
- `Protocol4VerifierBench`
- `Protocol4SizeBench`
3. Wait for results to output in milliseconds
### Changing the key size
The key size is determined by the variable `KEY_SIZE` in `random_primes.js`. This
variable dictates the size of _each_ prime used in the modulus, so the total key size
is twice this value. Recommend selecting one of 512, 1024, or 2048. In fact, I recommend
selecting 512 if you want the program to run in less than 3-5 business days.

309
static/js/lz-string.js Normal file
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@@ -0,0 +1,309 @@
var LZString = (function () {
var r = String.fromCharCode,
o = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",
n = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+-$",
e = {};
function t(r, o) {
if (!e[r]) {
e[r] = {};
for (var n = 0; n < r.length; n++) e[r][r.charAt(n)] = n;
}
return e[r][o];
}
var i = {
compressToBase64: function (r) {
if (null == r) return "";
var n = i._compress(r, 6, function (r) {
return o.charAt(r);
});
switch (n.length % 4) {
default:
case 0:
return n;
case 1:
return n + "===";
case 2:
return n + "==";
case 3:
return n + "=";
}
},
decompressFromBase64: function (r) {
return null == r
? ""
: "" == r
? null
: i._decompress(r.length, 32, function (n) {
return t(o, r.charAt(n));
});
},
compressToUTF16: function (o) {
return null == o
? ""
: i._compress(o, 15, function (o) {
return r(o + 32);
}) + " ";
},
decompressFromUTF16: function (r) {
return null == r
? ""
: "" == r
? null
: i._decompress(r.length, 16384, function (o) {
return r.charCodeAt(o) - 32;
});
},
compressToUint8Array: function (r) {
for (
var o = i.compress(r),
n = new Uint8Array(2 * o.length),
e = 0,
t = o.length;
e < t;
e++
) {
var s = o.charCodeAt(e);
(n[2 * e] = s >>> 8), (n[2 * e + 1] = s % 256);
}
return n;
},
decompressFromUint8Array: function (o) {
if (null == o) return i.decompress(o);
for (var n = new Array(o.length / 2), e = 0, t = n.length; e < t; e++)
n[e] = 256 * o[2 * e] + o[2 * e + 1];
var s = [];
return (
n.forEach(function (o) {
s.push(r(o));
}),
i.decompress(s.join(""))
);
},
compressToEncodedURIComponent: function (r) {
return null == r
? ""
: i._compress(r, 6, function (r) {
return n.charAt(r);
});
},
decompressFromEncodedURIComponent: function (r) {
return null == r
? ""
: "" == r
? null
: ((r = r.replace(/ /g, "+")),
i._decompress(r.length, 32, function (o) {
return t(n, r.charAt(o));
}));
},
compress: function (o) {
return i._compress(o, 16, function (o) {
return r(o);
});
},
_compress: function (r, o, n) {
if (null == r) return "";
var e,
t,
i,
s = {},
u = {},
a = "",
p = "",
c = "",
l = 2,
f = 3,
h = 2,
d = [],
m = 0,
v = 0;
for (i = 0; i < r.length; i += 1)
if (
((a = r.charAt(i)),
Object.prototype.hasOwnProperty.call(s, a) ||
((s[a] = f++), (u[a] = !0)),
(p = c + a),
Object.prototype.hasOwnProperty.call(s, p))
)
c = p;
else {
if (Object.prototype.hasOwnProperty.call(u, c)) {
if (c.charCodeAt(0) < 256) {
for (e = 0; e < h; e++)
(m <<= 1),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++;
for (t = c.charCodeAt(0), e = 0; e < 8; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
} else {
for (t = 1, e = 0; e < h; e++)
(m = (m << 1) | t),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t = 0);
for (t = c.charCodeAt(0), e = 0; e < 16; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
}
0 == --l && ((l = Math.pow(2, h)), h++), delete u[c];
} else
for (t = s[c], e = 0; e < h; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
0 == --l && ((l = Math.pow(2, h)), h++),
(s[p] = f++),
(c = String(a));
}
if ("" !== c) {
if (Object.prototype.hasOwnProperty.call(u, c)) {
if (c.charCodeAt(0) < 256) {
for (e = 0; e < h; e++)
(m <<= 1),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++;
for (t = c.charCodeAt(0), e = 0; e < 8; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
} else {
for (t = 1, e = 0; e < h; e++)
(m = (m << 1) | t),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t = 0);
for (t = c.charCodeAt(0), e = 0; e < 16; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
}
0 == --l && ((l = Math.pow(2, h)), h++), delete u[c];
} else
for (t = s[c], e = 0; e < h; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
0 == --l && ((l = Math.pow(2, h)), h++);
}
for (t = 2, e = 0; e < h; e++)
(m = (m << 1) | (1 & t)),
v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
(t >>= 1);
for (;;) {
if (((m <<= 1), v == o - 1)) {
d.push(n(m));
break;
}
v++;
}
return d.join("");
},
decompress: function (r) {
return null == r
? ""
: "" == r
? null
: i._decompress(r.length, 32768, function (o) {
return r.charCodeAt(o);
});
},
_decompress: function (o, n, e) {
var t,
i,
s,
u,
a,
p,
c,
l = [],
f = 4,
h = 4,
d = 3,
m = "",
v = [],
g = { val: e(0), position: n, index: 1 };
for (t = 0; t < 3; t += 1) l[t] = t;
for (s = 0, a = Math.pow(2, 2), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position && ((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
switch (s) {
case 0:
for (s = 0, a = Math.pow(2, 8), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position && ((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
c = r(s);
break;
case 1:
for (s = 0, a = Math.pow(2, 16), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position && ((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
c = r(s);
break;
case 2:
return "";
}
for (l[3] = c, i = c, v.push(c); ; ) {
if (g.index > o) return "";
for (s = 0, a = Math.pow(2, d), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position && ((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
switch ((c = s)) {
case 0:
for (s = 0, a = Math.pow(2, 8), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position &&
((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
(l[h++] = r(s)), (c = h - 1), f--;
break;
case 1:
for (s = 0, a = Math.pow(2, 16), p = 1; p != a; )
(u = g.val & g.position),
(g.position >>= 1),
0 == g.position &&
((g.position = n), (g.val = e(g.index++))),
(s |= (u > 0 ? 1 : 0) * p),
(p <<= 1);
(l[h++] = r(s)), (c = h - 1), f--;
break;
case 2:
return v.join("");
}
if ((0 == f && ((f = Math.pow(2, d)), d++), l[c])) m = l[c];
else {
if (c !== h) return null;
m = i + i.charAt(0);
}
v.push(m),
(l[h++] = i + m.charAt(0)),
(i = m),
0 == --f && ((f = Math.pow(2, d)), d++);
}
},
};
return i;
})();
"function" == typeof define && define.amd
? define(function () {
return LZString;
})
: "undefined" != typeof module && null != module
? (module.exports = LZString)
: "undefined" != typeof angular &&
null != angular &&
angular.module("LZString", []).factory("LZString", function () {
return LZString;
});

45
static/js/modules/crypto/paillier.js
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@@ -4,6 +4,25 @@ import { gcd, mod_exp } from "./math.js";
const PAILLIER = 0;
const JURIK = 1;
function RSTransform(g, a, p) {
let plainText = p.toString(16);
if (plainText.length % 2 !== 0) {
plainText = "0" + plainText;
}
let aStr = a.toString(16);
if (aStr.length % 2 !== 0) {
aStr = "0" + aStr;
}
let hasher = new jsSHA("SHAKE256", "HEX");
hasher.update(g.toString(16));
hasher.update(plainText);
hasher.update(aStr);
return BigInt("0x" + hasher.getHash("HEX", { outputLen: 2048 }));
}
class Ciphertext {
constructor(key, plainText, r, set) {
if (set !== undefined) {
@@ -93,28 +112,12 @@ class Ciphertext {
}
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 }));
let challenge = RSTransform(this.pubKey.g, a, this.plainText);
return {
plainText: "0x" + this.plainText.toString(16),
a: "0x" + a.toString(16),
challenge: "0x" + challenge.toString(16),
proof:
"0x" +
(
@@ -195,11 +198,17 @@ export class ReadOnlyCiphertext {
}
verifyNI(statement) {
let challenge = RSTransform(
this.pubKey.g,
BigInt(statement.a),
BigInt(statement.plainText)
);
let verifier = new ValueProofSessionVerifier(
this,
BigInt(statement.plainText),
BigInt(statement.a),
BigInt(statement.challenge)
challenge
);
if (verifier.verify(BigInt(statement.proof))) {

2
static/js/modules/crypto/random_primes.js
View File

@@ -1,6 +1,6 @@
import { mod_exp } from "./math.js";
export const KEY_SIZE = 512;
export const KEY_SIZE = 2048;
export function cryptoRandom(bits) {
if (bits === undefined) {

1
static/js/modules/interface/proofs.js
View File

@@ -135,7 +135,6 @@ export function verifyRegions(obj, key) {
let plaintext = c.verifyNI(verification.zeroProofs[regionName]);
if (plaintext !== 0n) {
console.log(plaintext);
return false;
}
}

165
templates/index.html
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@@ -7,7 +7,8 @@
<script src="https://cdn.socket.io/4.5.4/socket.io.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/crypto-js/4.1.1/crypto-js.min.js"></script>
<script src="{{ url_for('static', filename='js/sha3.js') }}" type="module"></script>
<script src="{{ url_for('static', filename='js/lz-string.js') }}"></script>
<script src="{{ url_for('static', filename='js/sha3.js') }}"></script>
<script src="{{ url_for('static', filename='js/modules/interface/main.js') }}" type="module"></script>
<script src="{{ url_for('static', filename='js/modules/crypto/main.js') }}" type="module"></script>
</head>
@@ -188,6 +189,8 @@
function RSABench() {
console.log("Warming up")
const ROUNDS = 250;
for (let i = 0n; i < 100n; i++) {
window.rsa.pubKey.encrypt(i);
}
@@ -195,17 +198,19 @@
console.log("Benching")
performance.mark("rsa-start")
for (let i = 0n; i < 250n; i++) {
for (let i = 0n; i < BigInt(ROUNDS); i++) {
window.rsa.pubKey.encrypt(i);
}
performance.mark("rsa-end")
console.log(`Bench done. Duration: ${performance.measure("rsa-duration", "rsa-start", "rsa-end").duration}`)
console.log(`Bench done. Time per encrypt: ${performance.measure("rsa-duration", "rsa-start", "rsa-end").duration / ROUNDS}`)
}
function PaillierBench() {
console.log("Warming up")
const ROUNDS = 250
for (let i = 0n; i < 100n; i++) {
window.paillier.pubKey.encrypt(i);
}
@@ -213,12 +218,162 @@
console.log("Benching")
performance.mark("paillier-start")
for (let i = 0n; i < 250n; i++) {
for (let i = 0n; i < BigInt(ROUNDS); i++) {
window.paillier.pubKey.encrypt(i);
}
performance.mark("paillier-end")
console.log(`Bench done. Duration: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration}`)
console.log(`Bench done. Time per encrypt: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration / ROUNDS}`)
}
function ZeroProofBench() {
console.log("Warming up")
const cipherText = paillier.pubKey.encrypt(0n)
const ROUNDS = 20;
for (let i = 0; i < 5; i++) {
cipherText.proveNI();
}
console.log("Benching")
performance.mark("paillier-start")
for (let i = 0; i < ROUNDS; i++) {
cipherText.proveNI()
}
performance.mark("paillier-end")
console.log(`Bench done. Time per proof: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration / ROUNDS}`)
}
function ZeroProofVerifierBench() {
console.log("Warming up")
const ROUNDS = 20
const cipherText = paillier.pubKey.encrypt(1n)
const readOnly = cipherText.asReadOnlyCiphertext();
const proof = cipherText.proveNI()
for (let i = 0; i < 5; i++) {
readOnly.verifyNI(proof)
}
console.log("Benching")
performance.mark("paillier-start")
for (let i = 0; i < ROUNDS; i++) {
readOnly.verifyNI(proof)
}
performance.mark("paillier-end")
console.log(`Bench done. Time per verification: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration / ROUNDS}`)
}
function Protocol4Bench() {
console.log("Warming up")
const regions = {
A: paillier.pubKey.encrypt(0n),
B: paillier.pubKey.encrypt(1n),
C: paillier.pubKey.encrypt(0n),
D: paillier.pubKey.encrypt(0n),
E: paillier.pubKey.encrypt(0n)
}
const ROUNDS = 20;
for (let i = 0; i < 5; i++) {
proveRegions(regions)
}
console.log("Benching")
performance.mark("paillier-start")
for (let i = 0; i < ROUNDS; i++) {
proveRegions(regions)
}
performance.mark("paillier-end")
console.log(`Bench done. Time per proof: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration / ROUNDS}`)
}
function Protocol4VerifierBench() {
console.log("Warming up")
const ROUNDS = 20;
const regions = {
A: paillier.pubKey.encrypt(0n),
B: paillier.pubKey.encrypt(1n),
C: paillier.pubKey.encrypt(0n),
D: paillier.pubKey.encrypt(0n),
E: paillier.pubKey.encrypt(0n)
}
let proof = proveRegions(regions)
for (let i = 0; i < 5; i++) {
verifyRegions(proof, paillier.pubKey)
}
console.log("Benching")
performance.mark("paillier-start")
for (let i = 0; i < ROUNDS; i++) {
verifyRegions(proof, paillier.pubKey)
}
performance.mark("paillier-end")
console.log(`Bench done. Time per verification: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration / ROUNDS}`)
}
// https://gist.github.com/kawanet/352a2ed1d1656816b2bc
function string_to_buffer(src) {
return (new Uint16Array([].map.call(src, function(c) {
return c.charCodeAt(0)
}))).buffer;
}
function Protocol4Size() {
const regions = {
A: paillier.pubKey.encrypt(0n),
B: paillier.pubKey.encrypt(1n),
C: paillier.pubKey.encrypt(0n),
D: paillier.pubKey.encrypt(0n),
E: paillier.pubKey.encrypt(0n)
}
let ROUNDS = 10;
let size = 0;
let compressedSize = 0;
for (let x = 0; x < ROUNDS; x++) {
let s = JSON.stringify(proveRegions(regions));
size += string_to_buffer(s).byteLength;
compressedSize += LZString.compressToUint8Array(s).length;
}
return {
size: size / ROUNDS,
compressedSize: compressedSize / ROUNDS
};
}
function ZeroProofSize() {
const ROUNDS = 100;
const cipherText = paillier.pubKey.encrypt(0n)
let size = 0;
let compressedSize = 0;
for (let x = 0; x < ROUNDS; x++) {
let s = JSON.stringify(cipherText.proveNI());
size += string_to_buffer(s).byteLength;
compressedSize += LZString.compressToUint8Array(s).length;
}
return {
size: size / ROUNDS,
compressedSize: compressedSize / ROUNDS
};
}
</script>
</body>

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whitepaper/Dissertation.pdf
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55
whitepaper/Dissertation.tex
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@@ -8,6 +8,11 @@
\usepackage{amsthm}
\usepackage{tikz}
\usepackage{minted}
\usepackage{multirow}
\usepackage{tabularx}
\usepackage{booktabs}
\usepackage{ragged2e}
\usepackage[alph]{parnotes}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\id}{id}
@@ -598,18 +603,52 @@ The other proofs do not translate so trivially to this structure however. In fac
\subsection{Complexity results}
All measurements taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, using a Ryzen 5 3600 CPU.
All measurements taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, using a Ryzen 5 3600 CPU. Absolute timings are extremely dependent on the browser engine: for example Firefox 111.0.1 was typically 4 times slower than the results shown.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Modulus size & Na\"ive encrypt & Jacobi encrypt & RSA encrypt \\\hline
\begin{table}[htp]
\fontsize{10pt}{10pt}\selectfont
\caption{Time to encrypt}
\begin{tabularx}{\textwidth}{c *3{>{\Centering}X}}
\toprule
Modulus size & Na\"ive encrypt & Jacobi encrypt & RSA encrypt \\
\midrule
$|n| = 1024$ & 6ms & 4ms & <1ms \\
$|n| = 2048$ & 34ms & 22ms & <1ms \\
$|n| = 4096$ & 189ms & 128ms & <1ms \\
\hline
\end{tabular}
\end{center}
\bottomrule
\end{tabularx}
\end{table}
\begin{table}[htp]
\fontsize{10pt}{10pt}\selectfont
\caption{Time to process proofs}
\begin{tabularx}{\textwidth}{c *4{>{\Centering}X}}
\toprule
\multirow{2}{*}{Modulus size} & \multicolumn{2}{c}{Proof-of-zero non-interactive} & \multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol1}} with $t = 24$} \tabularnewline \cmidrule(l){2-3}\cmidrule(l){4-5}
& Prover & Verifier & Prover & Verifier \\
\midrule
$|n| = 1024$ & 10ms & 18ms & 1,740ms & 2,190ms \\
$|n| = 2048$ & 44ms & 68ms & 8,170ms & 8,421ms \\
$|n| = 4096$ & 225ms & 292ms & 41,500ms & 34,405ms \\
\bottomrule
\end{tabularx}
\end{table}
\begin{table}[htp]
\fontsize{10pt}{10pt}\selectfont
\caption{Byte size\parnote{1 UTF-16 character, as used by ECMAScript, is 2 or more bytes} of encoded proofs}
\begin{tabularx}{\textwidth}{c *4{>{\Centering}X}}
\toprule
\multirow{2}{*}{Modulus size} & \multicolumn{2}{c}{Proof-of-zero non-interactive} & \multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol1}} with $t = 24$} \tabularnewline \cmidrule(l){2-3}\cmidrule(l){4-5}
& JSON & with LZ-String & JSON & with LZ-String \\
\midrule
$|n| = 1024$ & 1,617B & 576B (35.62\%) & 338,902B & 95,738B (28.25\%) \\
$|n| = 2048$ & 3,153B & 1,050B (33.30\%) & 662,233B & 187,333B (28.29\%) \\
$|n| = 4096$ & 6,226B & 1,999B (32.11\%) & 1,315,027B & 368,646B (28.03\%) \\
\bottomrule
\end{tabularx}
\parnotes
\end{table}
\subsection{Quantum resistance}