The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces

Nguyen and Shparlinski recently presented a polynomial-time algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of DSA), under a reasonable assumption on the hash function used in DSA. The number of required bits is about log1/2 q, and can be further decreased to 2 if one assumes access to ideal lattice basis reduction, namely an oracle for the lattice closest vector problem for the infinity norm. All previously known results were only heuristic, including those of Howgrave-Graham and Smart who introduced the topic. Here, we obtain similar results for the elliptic curve variant of DSA (ECDSA).

• Type: Conference
• Year: 2003
• Where: DCC
• Authors: Phong Q. Nguyen, Igor Shparlinski
• Keywords: Computer Graphics, DCC 2003, DSA Signatures, Lattice Closest Vector, Secret Dsa Key