Some lattice attacks on DSA and ECDSA
In this paper, using the LLL reduction method and computing the integral points of two classes of conics, we develop attacks on DSA and ECDSA in case where the secret and the ephemeral key of a signed message or theirs modular inverses are sufficiently small and in case where the ephemeral keys or theirs modular inverses of two signed messages are sufficiently small.
public key cryptography digital signature algorithm elliptic curve algorithm lll discrete logarithm diophantine equations