The Insecurity of the Digital Signature Algorithm with Partially Known Nonces

@article{Nguyen2002TheIO,
  title={The Insecurity of the Digital Signature Algorithm with Partially Known Nonces
},
  author={Phong Q. Nguyen and Igor E. Shparlinski},
  journal={Journal of Cryptology},
  year={2002},
  volume={15},
  pages={151-176}
}
Abstract. We present a polynomial-time algorithm that provably recovers the signer's secret DSA key when a few consecutive 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. For most significant or least significant bits, the number of required bits is about log1/2 q , but can be decreased to log log q with a… 

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