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

@article{Nguyen2003TheIO,
  title={The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces},
  author={Phong Q. Nguyen and Igor E. Shparlinski},
  journal={Des. Codes Cryptography},
  year={2003},
  volume={30},
  pages={201-217}
}
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 log q, and can be further decreased to 2 if one assumes access to ideal lattice basis… CONTINUE READING
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