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SquareRootOfTwentyThree avatar Crypto

Test vectors (points) for Ed25519

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SquareRootOfTwentyThree

I am trying to verify an Ed25519 implementation, but I can't find any test vectors for the curve points. All test vectors focus directly on signature constructions (EdDSA).

I tried to use https://asecuritysite.com/ecc/nacl07 but that seems to give the wrong results. For instance, it reports that the affine coordinates of the point 5G are:

x = 49384254074273129950593193138861175954739393969723597783743362437597626495704

y = 100993238402330024465140605900252962566919016078863090678826226962847795431661

but that's not even on the curve... Are there any reliable, reference test vectors to validate generic operations on Ed25519?

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kelalaka avatar
in flag
kelalaka
There is already python code in the Ed25519 section Section 6
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knaccc avatar Crypto
es flag
knaccc

Just use a reliable library to generate your test vectors. For example, using elliptic:

const elliptic = require('elliptic');
const ed25519 = new require('elliptic').eddsa('ed25519');
const BN = require('bn.js');

function printPointInfo(desc, P) {
  console.log(`${desc}: hex:     ` + elliptic.utils.toHex(ed25519.encodePoint(P)));
  console.log(`${desc}: x-coord: ` + P.getX());
  console.log(`${desc}: y-coord: ` + P.getY());
  console.log();
}

let G = ed25519.curve.g;
let a = '12581e70a192aeb9ac1411b36d11fc06393db55998190491c063807a6b4d730d';
let b = '0c2340b974bebfb9cb3f14e991bca432b57fb33f7c4d79e15f64209076afcd00';
let aG = G.mul(elliptic.utils.intFromLE(a));
let bG = G.mul(elliptic.utils.intFromLE(b));
printPointInfo('G', G);
printPointInfo('2G', G.mul(new BN(2)));
printPointInfo('5G', G.mul(new BN(5)));
printPointInfo('aG', aG);
printPointInfo('bG', bG);

Expected output:

G: hex:     5866666666666666666666666666666666666666666666666666666666666666
G: x-coord: 15112221349535400772501151409588531511454012693041857206046113283949847762202
G: y-coord: 46316835694926478169428394003475163141307993866256225615783033603165251855960

2G: hex:     c9a3f86aae465f0e56513864510f3997561fa2c9e85ea21dc2292309f3cd6022
2G: x-coord: 24727413235106541002554574571675588834622768167397638456726423682521233608206
2G: y-coord: 15549675580280190176352668710449542251549572066445060580507079593062643049417

5G: hex:     edc876d6831fd2105d0b4389ca2e283166469289146e2ce06faefe98b22548df
5G: x-coord: 33467004535436536005251147249499675200073690106659565782908757308821616914995
5G: y-coord: 43097193783671926753355113395909008640284023746042808659097434958891230611693

aG: hex:     14e35209936de59710e4a3a55b1887a6f3a390c0b1b2d132a0158ff3b60581e0
aG: x-coord: 46953515626174660128743374276590207025464948126956050456964432034683890442435
aG: y-coord: 43649996176441760651255662656482711906128939437336752974722489909985414406932

bG: hex:     cca4cc575d5eb9057834ad8b759272d37feb95c9f7197bf251814f37a4413f1d
bG: x-coord: 48108495825706412711799803692360228025391948835486250305831184019146948949994
bG: y-coord: 13228837014764440841117560545823854143168584625415590819123131242008409842892
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