Sliding Windows Succumbs to Big Mac Attack

Abstract

Sliding Windows is a general technique for obtaining an efficient exponentiation scheme. Big Mac is a specific form of attack on a cryptosystem in which bits of a secret key can be deduced independently, or almost so, of the others. Here such an attack on an implementation of the RSA cryptosystem is described. It assumes digit-by-digit computations are performed sequentially on a single k-bit multiplier and uses information which leaks through differential power analysis (DPA). With sufficiently powerful monitoring equipment, only a small number of exponentiations, independent of the key length, is enough to reveal the secret exponent from unknown plaintext inputs. Since the technique may work for a single exponentiation, many blinding techniques currently under consideration may be rendered useless. This is particularly relevant to implementations with single processors where a digit multiplication cannot be masked by other simultaneous processing. Moreover, the longer the key length, the easier the attacks becomes.