GiacomoPope

sage -t --long --random-seed=286735480429121101562228604801325644303 src/sage/modular/arithgroup/congroup_gammaH.py
**********************************************************************
File "src/sage/modular/arithgroup/congroup_gammaH.py", line 200, in sage.modular.arithgroup.congroup_gammaH.GammaH_class
Failed example:
    GammaH(20, [9]).dimension_cusp_forms(1)
Exception raised:
    Traceback (most recent call last):
      File "sage/misc/cachefunc.pyx", line 1007, in sage.misc.cachefunc.CachedFunction.__call__
        return self.cache[k]
    KeyError: ((Congruence Subgroup Gamma_H(20) with H generated by [9],), ())

GiacomoPope

"""
This gist is a minimal example showing that the KAT data for Dilithiuim
does not seem to match the specification.

KAT data was downloaded from:
https://pq-crystals.org/dilithium/data/dilithium-submission-nist-round3.zip

On Friday the 16th of September, 2022

We consider here the first set of data for Dilithium2

GiacomoPope

from fastecdsa.curve import P256
from fastecdsa.point import Point
from Crypto.Util.number import inverse
from hashlib import sha256

# Generator and curve order
G, q = P256.G, P256.q

# Public key
Px = 0x0214c15785655baffd69912ca80332441746322daf99f3a9bfc08852efe24c2f 

GiacomoPope

"""
Written to help twitter user @mukesh_tiwari
understand

https://asecuritysite.com/zero/ped

This implementation however is broken, as 
q is not a prime... 

Below is showing how we can sign a message m2 which

GiacomoPope

from Crypto.Util.number import isPrime
import math
import time

primes = []

def find_primes(max_val):
    N = math.ceil(math.sqrt(max_val))
    for n in range(0,N,2):
        p = n**2 + 1

GiacomoPope

# http://www.monnerat.info/publications/anomalous.pdf

def anon_prime(m):
    while True:
        p = (19*m*(m + 1)) + 5
        if is_prime(p):
            return p
        m += 1

GiacomoPope

def find_Hilbert_roots(upper):
    """
    Examples of D s.t. D%4 == 0
    and the corresponding roots of 
    the Hilbert Class Polynomial

    D=4, root=2^6 * 3^3
    D=8, root=2^6 * 5^3
    D=12, root=0
    D=16, root=2^6 * 3^3

GiacomoPope

Keybase proof

I hereby claim:

• I am jack4818 on github.
• I am jack4818 (https://keybase.io/jack4818) on keybase.
• I have a public key ASCvf5k_zyIHBXblLj1ehKcdgYbB5pDXCno4WJFMy2vHXwo

To claim this, I am signing this object: