Insecure primitive elements in an ElGamal signature protocol
Omar Khadir · Journal of Discrete Mathematical Sciences and Cryptography · 2015
Consider the classical ElGamal digital signature scheme based on the modular relation αm ≡ yrrs[p]. In this work, we prove that if we can compute a natural integer i such that αi mod p is smooth and divides p − 1, then it is possible to sign any given document without knowing the secret key. Therefore we extend and reinforce Bleichenbacher's attack presented at Eurocrypt'96.