International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Experimenting with Faults, Lattices and the DSA

David Naccache
Phong Q. Nguyen
Michael Tunstall
Claire Whelan
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Abstract: We present an attack on DSA smart-cards which combines physical fault injection and lattice reduction techniques. This seems to be the first (publicly reported) physical experiment allowing to concretely pull-out DSA keys out of smart-cards. We employ a particular type of fault attack known as a glitch attack, which will be used to actively modify the DSA nonce k used for generating the signature: k will be tampered with so that a number of its least significant bytes will flip to zero. Then we apply well-known lattice attacks on El Gamal-type signatures which can recover the private key, given sufficiently many signatures such that a few bits of each corresponding k are known. In practice, when one byte of each k is zeroed, 27 signatures are sufficient to disclose the private key. The more bytes of k we can reset, the fewer signatures will be required. This paper presents the theory, methodology and results of the attack as well as possible countermeasures.
  title={Experimenting with Faults, Lattices and the DSA},
  booktitle={IACR Eprint archive},
  keywords={implementation / DSA, public key, smart cards, faults, attacks},
  note={To be presented at PKC 2005 12741 received 24 Oct 2004, last revised 19 Nov 2004},
  author={David Naccache and Phong Q. Nguyen and Michael Tunstall and Claire Whelan},