ctf-crypto-attacks

To factor an RSA modulus with noisy samples, you can use lattice reduction techniques like LLL or Gaussian integer Coppersmith to recover the hidden prime p and factor the RSA modulus.

Recovering parameters from a linear congruential generator (LCG) involves applying lattice reduction techniques to its outputs to reconstruct the underlying hidden state and modulus values.

A lattice attack on supersingular ECDH works by applying Pohlig-Hellman and MOV attacks to exploit supersingular elliptic curve properties and recover the shared secret.

Yes, you can use sympy and gmpy2 to execute Coppersmith attacks, applying joint lattices to factor RSA moduli when they share exponents across different ciphertext samples.

Yes, you need Sage alongside sympy and gmpy2, as these Python libraries are required dependencies for executing advanced cryptographic operations and lattice algorithms.

Use Gaussian integer Coppersmith for specific lattice attacks on RSA and ECDH challenges where standard LLL or BDD approaches are insufficient for recovering hidden primes.