[Cryptography] New White Paper: GhostLine - Information-Theoretically Secure Multi-Party Chat

[Ferecides de Siros]

Dear Andrew,

Thank you for the keen observation - you are absolutely correct, and I appreciate the scrutiny. This is exactly the kind of peer review that strengthens cryptographic work.

You've identified a significant mathematical error in my implementation. The hex value 0xFFFF...FFD3 indeed represents 2^256 - 45, not 2^256 - 189 as claimed. The correct hex representation of 2^256 - 189 should be 0xFFFF...FF43.

This is a clear implementation bug that contradicts my white paper's mathematical claims. While the underlying cryptographic principles (ε-ASU₂ universal hashing, Wegman-Carter construction, perfect secrecy via OTP) remain theoretically sound, the specific prime I'm using doesn't match what I documented.

I'm correcting this immediately in the codebase. The fix involves changing the prime constant from:

let p_hex = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd3";

to:

let p_hex = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff43";

This type of mathematical precision is exactly why I published the code openly - so that experts like yourself can verify the implementation matches the theoretical claims. I appreciate you taking the time to audit the work.

Best regards,

Hitokiri Battosai

Sent with [Proton Mail](https://proton.me/mail/home) secure email.

On Saturday, September 6th, 2025 at 11:00, Andrew Lee <andrew at joseon.com> wrote:

>> Source code repository: https://app.radicle.xyz/nodes/ash.radicle.garden/rad:z9NtUTymSdxnuTcnzaM5qi7cuHPN
>
> It looks like there are some hallucinations in the POC (excerpt therefrom):
>
> // This is a safe prime: p = 2^256 - 189
> let p_hex = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd3”;
>
> That said, this is a novel idea.
>
> Cheers,
> Andrew
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