A timing attack against RSA with the chinese remainder theorem

Abstract

We introduce a new type of timing attack which enables the factorization of an RSA-modulus if the exponentiation with the secret exponent uses the Chinese Remainder Theorem and Montgomery's algorithm. Its standard variant assumes that both exponentiations are carried out with a simple square and multiply algorithm. However, although its efficiency decreases, our attack can also be adapted to more advanced exponentiation algorithms. The previously known timing attacks do not work if the Chinese Remainder Theorem is used. © Springer-Verlag Berlin Heidelberg 2000.