On the Vulnerability of Exponent Recodings for the Exponentiation against Side Channel Attacks

Yasuyuki SAKAI  Kouichi SAKURAI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E88-A  No.1  pp.154-160
Publication Date: 2005/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Tamper-Resistance
Keyword: 
side channel attack,  exponent recoding,  RSA cryptosystems,  elliptic curve cryptosystems, 

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Summary: 
In this paper we propose a new side channel attack, where exponent recodings for public key cryptosystems such as RSA and ECDSA are considered. The known side channel attacks and countermeasures for public key cryptosystems were against the main stage (square and multiply stage) of the modular exponentiation (or the point multiplication on an elliptic curve). We have many algorithms which achieve fast computation of exponentiations. When we compute an exponentiation, the exponent recoding has to be carried out before the main stage. There are some exponent recoding algorithms including conditional branches, in which instructions depend on the given exponent value. Consequently exponent recoding can constitute an information channel, providing the attacker with valuable information on the secret exponent. In this paper we show new algorithms of attack on exponent recoding. The proposed algorithms can recover the secret exponent, when the width-w NAF and the unsigned/signed fractional window representation are used.