readme, benchmarks, fix verification
This commit is contained in:
jude
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31
README.md
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31
README.md
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@ -0,0 +1,31 @@
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# Riskless
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### Undergraduate dissertation
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**Paper: https://judesouthworth.xyz/Dissertation.pdf**
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## Running the demo
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1. `pip install -r requirements.txt`
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2. `python3 app.py`
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3. Navigate browser to `http://localhost:5000`
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### Running the benchmarks
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1. Press F12
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2. Type the name of the benchmark to run:
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- `RSABench`
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- `PaillierBench`
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- `ZeroProofBench`
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- `ZeroProofVerifierBench`
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- `ZeroProofSizeBench`
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- `Protocol4Bench`
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- `Protocol4VerifierBench`
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- `Protocol4SizeBench`
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3. Wait for results to output in milliseconds
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### Changing the key size
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The key size is determined by the variable `KEY_SIZE` in `random_primes.js`. This
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variable dictates the size of _each_ prime used in the modulus, so the total key size
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is twice this value. Recommend selecting one of 512, 1024, or 2048. In fact, I recommend
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selecting 512 if you want the program to run in less than 3-5 business days.
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309
static/js/lz-string.js
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309
static/js/lz-string.js
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var LZString = (function () {
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var r = String.fromCharCode,
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o = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",
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n = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+-$",
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e = {};
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function t(r, o) {
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if (!e[r]) {
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e[r] = {};
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for (var n = 0; n < r.length; n++) e[r][r.charAt(n)] = n;
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}
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return e[r][o];
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}
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var i = {
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compressToBase64: function (r) {
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if (null == r) return "";
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var n = i._compress(r, 6, function (r) {
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return o.charAt(r);
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});
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switch (n.length % 4) {
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default:
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case 0:
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return n;
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case 1:
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return n + "===";
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case 2:
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return n + "==";
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case 3:
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return n + "=";
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}
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},
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decompressFromBase64: function (r) {
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return null == r
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? ""
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: "" == r
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? null
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: i._decompress(r.length, 32, function (n) {
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return t(o, r.charAt(n));
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});
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},
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compressToUTF16: function (o) {
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return null == o
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? ""
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: i._compress(o, 15, function (o) {
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return r(o + 32);
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}) + " ";
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},
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decompressFromUTF16: function (r) {
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return null == r
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? ""
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: "" == r
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? null
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: i._decompress(r.length, 16384, function (o) {
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return r.charCodeAt(o) - 32;
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});
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},
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compressToUint8Array: function (r) {
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for (
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var o = i.compress(r),
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n = new Uint8Array(2 * o.length),
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e = 0,
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t = o.length;
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e < t;
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e++
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) {
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var s = o.charCodeAt(e);
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(n[2 * e] = s >>> 8), (n[2 * e + 1] = s % 256);
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}
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return n;
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},
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decompressFromUint8Array: function (o) {
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if (null == o) return i.decompress(o);
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for (var n = new Array(o.length / 2), e = 0, t = n.length; e < t; e++)
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n[e] = 256 * o[2 * e] + o[2 * e + 1];
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var s = [];
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return (
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n.forEach(function (o) {
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s.push(r(o));
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}),
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i.decompress(s.join(""))
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);
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},
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compressToEncodedURIComponent: function (r) {
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return null == r
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? ""
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: i._compress(r, 6, function (r) {
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return n.charAt(r);
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});
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},
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decompressFromEncodedURIComponent: function (r) {
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return null == r
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? ""
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: "" == r
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? null
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: ((r = r.replace(/ /g, "+")),
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i._decompress(r.length, 32, function (o) {
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return t(n, r.charAt(o));
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}));
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},
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compress: function (o) {
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return i._compress(o, 16, function (o) {
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return r(o);
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});
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},
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_compress: function (r, o, n) {
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if (null == r) return "";
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var e,
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t,
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i,
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s = {},
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u = {},
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a = "",
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p = "",
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c = "",
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l = 2,
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f = 3,
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h = 2,
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d = [],
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m = 0,
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v = 0;
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for (i = 0; i < r.length; i += 1)
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if (
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((a = r.charAt(i)),
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Object.prototype.hasOwnProperty.call(s, a) ||
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((s[a] = f++), (u[a] = !0)),
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(p = c + a),
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Object.prototype.hasOwnProperty.call(s, p))
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)
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c = p;
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else {
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if (Object.prototype.hasOwnProperty.call(u, c)) {
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if (c.charCodeAt(0) < 256) {
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for (e = 0; e < h; e++)
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(m <<= 1),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++;
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for (t = c.charCodeAt(0), e = 0; e < 8; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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} else {
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for (t = 1, e = 0; e < h; e++)
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(m = (m << 1) | t),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t = 0);
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for (t = c.charCodeAt(0), e = 0; e < 16; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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}
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0 == --l && ((l = Math.pow(2, h)), h++), delete u[c];
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} else
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for (t = s[c], e = 0; e < h; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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0 == --l && ((l = Math.pow(2, h)), h++),
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(s[p] = f++),
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(c = String(a));
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}
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if ("" !== c) {
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if (Object.prototype.hasOwnProperty.call(u, c)) {
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if (c.charCodeAt(0) < 256) {
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for (e = 0; e < h; e++)
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(m <<= 1),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++;
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for (t = c.charCodeAt(0), e = 0; e < 8; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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} else {
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for (t = 1, e = 0; e < h; e++)
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(m = (m << 1) | t),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t = 0);
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for (t = c.charCodeAt(0), e = 0; e < 16; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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}
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0 == --l && ((l = Math.pow(2, h)), h++), delete u[c];
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} else
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for (t = s[c], e = 0; e < h; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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0 == --l && ((l = Math.pow(2, h)), h++);
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}
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for (t = 2, e = 0; e < h; e++)
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(m = (m << 1) | (1 & t)),
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v == o - 1 ? ((v = 0), d.push(n(m)), (m = 0)) : v++,
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(t >>= 1);
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for (;;) {
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if (((m <<= 1), v == o - 1)) {
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d.push(n(m));
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break;
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}
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v++;
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}
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return d.join("");
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},
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decompress: function (r) {
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return null == r
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? ""
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: "" == r
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? null
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: i._decompress(r.length, 32768, function (o) {
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return r.charCodeAt(o);
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});
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},
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_decompress: function (o, n, e) {
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var t,
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i,
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s,
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u,
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a,
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p,
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c,
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l = [],
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f = 4,
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h = 4,
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d = 3,
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m = "",
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v = [],
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g = { val: e(0), position: n, index: 1 };
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for (t = 0; t < 3; t += 1) l[t] = t;
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for (s = 0, a = Math.pow(2, 2), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position && ((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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switch (s) {
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case 0:
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for (s = 0, a = Math.pow(2, 8), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position && ((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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c = r(s);
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break;
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case 1:
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for (s = 0, a = Math.pow(2, 16), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position && ((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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c = r(s);
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break;
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case 2:
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return "";
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}
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for (l[3] = c, i = c, v.push(c); ; ) {
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if (g.index > o) return "";
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for (s = 0, a = Math.pow(2, d), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position && ((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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switch ((c = s)) {
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case 0:
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for (s = 0, a = Math.pow(2, 8), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position &&
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((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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(l[h++] = r(s)), (c = h - 1), f--;
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break;
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case 1:
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for (s = 0, a = Math.pow(2, 16), p = 1; p != a; )
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(u = g.val & g.position),
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(g.position >>= 1),
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0 == g.position &&
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((g.position = n), (g.val = e(g.index++))),
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(s |= (u > 0 ? 1 : 0) * p),
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(p <<= 1);
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(l[h++] = r(s)), (c = h - 1), f--;
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break;
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case 2:
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return v.join("");
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}
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if ((0 == f && ((f = Math.pow(2, d)), d++), l[c])) m = l[c];
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else {
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if (c !== h) return null;
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m = i + i.charAt(0);
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}
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v.push(m),
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(l[h++] = i + m.charAt(0)),
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(i = m),
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0 == --f && ((f = Math.pow(2, d)), d++);
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}
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},
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};
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return i;
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})();
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"function" == typeof define && define.amd
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? define(function () {
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return LZString;
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})
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: "undefined" != typeof module && null != module
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? (module.exports = LZString)
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: "undefined" != typeof angular &&
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null != angular &&
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angular.module("LZString", []).factory("LZString", function () {
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return LZString;
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});
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@ -4,6 +4,25 @@ import { gcd, mod_exp } from "./math.js";
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const PAILLIER = 0;
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const JURIK = 1;
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function RSTransform(g, a, p) {
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let plainText = p.toString(16);
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if (plainText.length % 2 !== 0) {
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plainText = "0" + plainText;
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}
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let aStr = a.toString(16);
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if (aStr.length % 2 !== 0) {
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aStr = "0" + aStr;
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}
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let hasher = new jsSHA("SHAKE256", "HEX");
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hasher.update(g.toString(16));
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hasher.update(plainText);
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hasher.update(aStr);
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return BigInt("0x" + hasher.getHash("HEX", { outputLen: 2048 }));
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}
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class Ciphertext {
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constructor(key, plainText, r, set) {
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if (set !== undefined) {
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@ -93,28 +112,12 @@ class Ciphertext {
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}
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let a = mod_exp(rp, this.pubKey.n, this.pubKey.n2);
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let hasher = new jsSHA("SHAKE256", "HEX");
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let plainText = this.plainText.toString(16);
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if (plainText.length % 2 !== 0) {
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plainText = "0" + plainText;
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}
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let aStr = a.toString(16);
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if (aStr.length % 2 !== 0) {
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aStr = "0" + aStr;
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}
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hasher.update(this.pubKey.g.toString(16));
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hasher.update(plainText);
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hasher.update(aStr);
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let challenge = BigInt("0x" + hasher.getHash("HEX", { outputLen: 2048 }));
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let challenge = RSTransform(this.pubKey.g, a, this.plainText);
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return {
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plainText: "0x" + this.plainText.toString(16),
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a: "0x" + a.toString(16),
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challenge: "0x" + challenge.toString(16),
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proof:
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"0x" +
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(
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@ -195,11 +198,17 @@ export class ReadOnlyCiphertext {
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}
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verifyNI(statement) {
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let challenge = RSTransform(
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this.pubKey.g,
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BigInt(statement.a),
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BigInt(statement.plainText)
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);
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let verifier = new ValueProofSessionVerifier(
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this,
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BigInt(statement.plainText),
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BigInt(statement.a),
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BigInt(statement.challenge)
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challenge
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);
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if (verifier.verify(BigInt(statement.proof))) {
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@ -1,6 +1,6 @@
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import { mod_exp } from "./math.js";
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export const KEY_SIZE = 512;
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export const KEY_SIZE = 2048;
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export function cryptoRandom(bits) {
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if (bits === undefined) {
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@ -135,7 +135,6 @@ export function verifyRegions(obj, key) {
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let plaintext = c.verifyNI(verification.zeroProofs[regionName]);
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if (plaintext !== 0n) {
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console.log(plaintext);
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return false;
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}
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}
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@ -7,7 +7,8 @@
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<script src="https://cdn.socket.io/4.5.4/socket.io.min.js"></script>
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<script src="https://cdnjs.cloudflare.com/ajax/libs/crypto-js/4.1.1/crypto-js.min.js"></script>
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<script src="{{ url_for('static', filename='js/sha3.js') }}" type="module"></script>
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<script src="{{ url_for('static', filename='js/lz-string.js') }}"></script>
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<script src="{{ url_for('static', filename='js/sha3.js') }}"></script>
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<script src="{{ url_for('static', filename='js/modules/interface/main.js') }}" type="module"></script>
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<script src="{{ url_for('static', filename='js/modules/crypto/main.js') }}" type="module"></script>
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</head>
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@ -188,6 +189,8 @@
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function RSABench() {
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console.log("Warming up")
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const ROUNDS = 250;
|
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for (let i = 0n; i < 100n; i++) {
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window.rsa.pubKey.encrypt(i);
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}
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@ -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>
|
||||
|
||||
Binary file not shown.
@ -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}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user