Paper 2004/123 Original: eprint.iacr.org/2004/123 ↗

On security of XTR public key cryptosystems against Side Channel Attacks

Abstract

The XTR public key system was introduced at Crypto 2000. Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security. It is regarded that XTR is suitable for a variety of environments, including low-end smart cards, and XTR is the excellent alternative to either RSA or ECC. In \cite{LV00a,SL01}, authors remarked that XTR single exponentiation (XTR-SE) is less susceptible than usual exponentiation routines to environmental attacks such as timing attacks and Differential Power Analysis (DPA). In this paper, however, we investigate the security of side channel attack (SCA) on XTR. This paper shows that XTR-SE is immune against simple power analysis (SPA) under assumption that the order of the computation of XTR-SE is carefully considered. However we show that XTR-SE is vulnerable to Data-bit DPA (DDPA)\cite{Cor99}, Address-bit DPA (ADPA)\cite{IIT02}, and doubling attack \cite{FV03}. Moreover, we propose two countermeasures that prevent from DDPA and a countermeasure against ADPA. One of the countermeasures using randomization of the base element proposed to defeat DDPA, i.e., randomization of the base element using field isomorphism, could be used to break doubling attack. Thus if we only deal with SPA, DDPA, ADPA, and doubling attack as the attack algorithm for XTR-SE, XTR-SE should be added following countermeasures: randomization of the base element using field isomorphism (DDPA and doubling attack) + randomized addressing (ADPA). But the proposed countermeasure against doubling attack is very inefficient. So to maintain the advantage of efficiency of XTR a good countermeasure against doubling attack is actually necessary.