On the DSA Key Recovery Attack with Variable Partial Nonces Known

The security of Digital Signature Algorithm is based on the proven hardness of the number theoretic problem of discrete logarithm. However, in practice, this public key based digital signature algorithm is prone to side channel based attacks. In this work, we consider the cryptanalysis of Digital Signature Algorithm, when partial information on ephemeral keys can be obtained. We present a variant of the existing lattice based cryptanalytic method for DSA and further extend our work by analysing the scenario when variable number of least significant bits per ephemeral keys are known for a set of signatures pertaining to a signatory.