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:

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

# 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

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

"""
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 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

"""
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

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],), ())