* [Enough Polynomials and Linear Algebra to Implement Kyber](https://words.filippo.io/kyber-math/)

* [Basic Lattice Cryptography. The concepts behind Kyber (ML-KEM) and Dilithium (ML-DSA)](https://eprint.iacr.org/2024/1287.pdf)

* [A Complete Beginner Guide to the Number Theoretic Transform (NTT)](https://eprint.iacr.org/2024/585.pdf)

Comments URL: https://news.ycombinator.com/item?id=48334607

Points: 2

# Comments: 2

I am using it daily to drive Claude and it works really-well for me (much better than macOS dictation mode).

    char string[10000];
    strp = string;
    for (i=0; i<9; i++)
        *strp++ = "/usr/bin/"[i];
    p = *argv++;
    while(*strp++ = *p++);

    // string == "/usr/bin/foo"
    execv(string+9, args); // foo (execv returns only in case of error, i.e. when foo does not exist)
    execv(string+4, args); // /bin/foo
    execv(string, args);   // /usr/bin/foo

   % wireguard-vanity-key -prefix=NAS/
   private                                      public                                       attempts   duration   attempts/s
   EiBsDB8zt/G4+VWGvxW2ZznNXYmcslcIyJimNR2PpF4= NAS/aex8+IFzLePBYVNGMsSo/1/XeUZcam+Hn8wbNB4= 22619537   0s         112587360

This tool uses proper crypto/rand initialisation of the starting key https://github.com/AlexanderYastrebov/onion-vanity-address/b...

Check out my other vanity generators (they all use crypto/rand):

https://github.com/AlexanderYastrebov/wireguard-vanity-key

https://github.com/AlexanderYastrebov/age-vanity-keygen

https://github.com/AlexanderYastrebov/ethereum-vanity-addres...

  // hashItem computes the slot an item hashes to, given a total number of slots.
  func hashItem(item string, nslots uint64) uint64 {
    digest := md5.Sum([]byte(item))
    digestHigh := binary.BigEndian.Uint64(digest[8:16])
    digestLow := binary.BigEndian.Uint64(digest[:8])
    return (digestHigh | digestLow) % nslots
  }

Wildcard support has low value for the use case in my opinion, compare:

    helloyebjctfjivalxn343gppksrzdpm33qzmeeq4qnqwgrgqy75zoqd.onion
    qbtlzwabvvkvmogjy2wdvnn6gq55463jhellobwtnjsinvtxsur67oad.onion

In short: I got obsessed by making it as fast as possible and read a ton of elliptic curve cryptography papers.

It was a journey that started from reading WireGuard kernel sources, then I was thinking about deriving IPv6 address from peer key, left a random comment on a dated gist https://gist.github.com/artizirk/c91e4f8c237dec07e3ad1b286f1... from which I learned about vanity key concept.

I naturally enjoy doing performance optimization work so when I discovered incremental approach idea here https://github.com/warner/wireguard-vanity-address/pull/15 I decided to create my own tool.

I've implemented first version of https://github.com/AlexanderYastrebov/wireguard-vanity-key and then continuously profiled it to improve performance. From profiling I saw that field inversion and multiplication are the main operations.

I realized I need to reduce unnecessary computation to make it faster and for that I need to understand the underlying math which is actually quite simple.

I read RFCs for Curve25519 and papers from D. J. Bernstein who invented it.

You can see how my understanding evolved from the commit history https://github.com/AlexanderYastrebov/wireguard-vanity-key/c...

Once I have the fastest algorithm to generate vanity Curve25519 keypairs I can apply it to other things that use Curve25519 (https://ianix.com/pub/curve25519-deployment.html) or Ed25519 (https://ianix.com/pub/ed25519-deployment.html) which is an equivalent curve.

See also my other related projects: * [age-vanity-keygen](https://github.com/AlexanderYastrebov/age-vanity-keygen) — Fast vanity age X25519 identity generator. * [vanity25519](https://github.com/AlexanderYastrebov/vanity25519) — Efficient Curve25519 vanity key generator.

I've built the tool to generate vanity Tor Onion Service addresses:

    $ onion-vanity-address allium
    Found allium... in 12s after 558986486 attempts (48529996 attempts/s)
    ---
    hostname: alliumdye3it7ko4cuftoni4rlrupuobvio24ypz55qpzjzpvuetzhyd.onion
    hs_ed25519_public_key: PT0gZWQyNTUxOXYxLXB1YmxpYzogdHlwZTAgPT0AAAAC1ooweCbRP6ncFQs3NRyK40fRwaodrmH572D8py+tCQ==
    hs_ed25519_secret_key: PT0gZWQyNTUxOXYxLXNlY3JldDogdHlwZTAgPT0AAAAQEW4Rhot7oroPaETlAEG3GPAntvJ1agF2c7A2AXmBW3WqAH0oUZ1hySvvZl3hc9dSAIc49h1UuCPZacOWp4vQ

I've explained key performance difference here https://github.com/AlexanderYastrebov/onion-vanity-address?t...

Would love your feedback, thanks!

Comments URL: https://news.ycombinator.com/item?id=45216630

Points: 16

# Comments: 6

    $ wireguard-vanity-key --prefix=mac/
    private                                      public                                       attempts   duration   attempts/s
    Mtvsq5urRK/HRE1EfqTkZ9dtBNNBjSVPbqYBZ/BL4Qw= mac/t3wcAUhyZUti7OM4KsGQ7/V00HPRmzI3agaSplM= 37258118   1s         70119328

    $ wireguard-vanity-key --prefix=ipad/
    private                                      public                                       attempts   duration   attempts/s
    hJXdv5FKyem2WqWzduSaEhEw1H4b+6BGTIqJeYu9H1c= ipad/s6w2nBEDhmuEl/xyLeohEbfc5MWUy5D8dJHgAs= 158299886  2s         69564916

I built a tool that generates age (modern file encryption https://github.com/FiloSottile/age) keys with vanity prefixes.

The key innovation is using the fastest search algorithm available – it can check ~40'000'000 keys per second on a laptop, finding 6-character prefixes within a minute.

For example, running `age-vanity-keygen hacker` will find a key like:

  $ age-vanity-keygen hacker
  Found age1hacker... in 23s after 973647953 attempts (42686172 attempts/s)
  # created: 2025-08-18T22:22:22+02:00
  # public key: age1hackerxf9wukrzxfjt56xmq7c3y5ua5ylgrk0pmhlmdsg3773q8qh3ym6v
  AGE-SECRET-KEY-1K9G5Y6DRJPSXUFE2ELZULCG6SET7YC0676KR33WXSULW2CDHLGGS0EMJA2

I've packaged it as both a Go binary and Docker image. The core algorithm is in a separate library (https://github.com/AlexanderYastrebov/vanity25519) if anyone wants to use it for other X25519-based systems.

Would love your feedback, thanks!

Comments URL: https://news.ycombinator.com/item?id=44945227

Points: 3

# Comments: 0