**Experimenting with Faults, Lattices and the DSA**

*David Naccache and Phong Q. Nguyen and Michael Tunstall and Claire Whelan*

**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.

**Category / Keywords: **implementation / DSA, public key, smart cards, faults, attacks

**Publication Info: **To be presented at PKC 2005

**Date: **received 24 Oct 2004, last revised 19 Nov 2004

**Contact author: **david naccache at gemplus com

**Available format(s): **PDF | BibTeX Citation

**Version: **20041119:111826 (All versions of this report)

**Short URL: **ia.cr/2004/277

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