Utility
Conversions
1 byte = 8 bit = 2 hex
int —> char
chr()char —> int
ord()bytes —> HEX
<BYTES>.hex()HEX —> bytes
bytes.fromhex(<HEX>)HEX —> int
int(<HEX>, 16)int —> HEX
format(<INT>, 'x') # ffhex(<INT>) # 0xffbytes —> int
int.from_bytes(<BYTES>, <endianes>)From Crypto.Util.number
bytes_to_long(<BYTES>)int —> bytes
<INT>.to_bytes(<nblock>, <endianes>)From Crypto.Util.number
long_to_bytes(<INT>)bytes —> Base64
From base64
b64encode(<BASE64>)Base64 —> bytes
From base64
b64decode(<BYTES>)bytes XOR bytes
From PwnTools
xor()Functions
GCD
From sympy
gcd(<A>, <B>)Modular Inverse
From Crypto.Util.number
inverse(<NUM>, <MOD>)From sympy
mod_inverse(<NUM>, <MOD>)Extended Euclidean
X*A + Y*B = GCD(A,B)
From sympy
X, Y, MCD = gcdex(<A>, <B>)Chinese Remainder Theorem
x % M1 = U1 x = U1 % M1
x % M2 = U2 x = U2 % M2
From sympy.ntheory.modular
crt([M1, M2, …], [U1, U2, …])Congruence Resolution
N1 == N2 (mod M)
Solves the modules and returns if they are congruent modulo M
From sympy.ntheory.modular
solve_congruence((N1, M), (N2, M))A*? = B mod N
x such that A*x = B mod N
From Crypto.Util.number
inverse(A, N)*B)%N)From sympy
mod_inverse(A, N)*B)%N)Discrete Logarithm
Given a prime p, g is defined to be a primitive root of p if for every y ∈ {1, .... , p-1} there exists an i such that: y = g^i mod p
From sympy.ntheory
discrete_log(p, y, g)N-th root
N-th root of v. Returns 2 values, the approximate root, and if it is perfect (with or without approximation).
From gmpy2
iroot(v, n)N-th root Extended
N-th root of A (A^(1/N))
From decimal.Decimal
int(pow(Decimal(<A>)), Decimal(Decimal('1')/Decimal(<N>))))Large Number
From decimal.Decimal, decimal.getcontext
getcontext().prec = 1000
Decimal(<N>)Modular Square Root
Find the square root of x mod p (hard problem, like factorization).
From sympy
sqrt_mod(x, p)SAT & SMT solver
From z3
pip install z3-solver# Define variables
a, b = Ints('a b')
# Define equations
equation1 = a + b == 50
equation2 = a * b == 625
# Create Solver
s = Solver()
# Add equations
s.add(equation1)
s.add(equation2)
# If there are solutions extract them
if s.check() == sat:
model = s.model()
a_val = model[a].as_long()
b_val = model[b].as_long()For my setting on macOS
import sys
sys.path.append("/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/")
from sage.all import *From sage
Discrete Logarithm
Calculate i in: RESULT = BASE^i mod M
discrete_log(Mod(<RESULT>, <M>), Mod(<BASE>, <M>), ord=<EULER_FUNCTION>)Factorization
Gets the factorization of the number n. Returns the list of factors.
factor(n)Chinese Remainder Theorem
x % M1 = U1 x = U1 % M1
x % M2 = U2 x = U2 % M2
crt([U1, U2, …], [M1, M2, …])Last updated
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