Unbridle the bit-length of a crypto-coprocessor with montgomery multiplication

Abstract

We present a novel approach for computing 2n-bit Montgomery multiplications with n-bit hardware Montgomery multipliers. Smartcards are usually equipped with such hardware Montgomery multipliers; however, due to progresses in factoring algorithms, the recommended bit length of public-key schemes such as RSA is steadily increasing, making the hardware quickly obsolete. Thanks to our double-size technique, one can re-use the existing hardware while keeping pace with the latest security requirements. Unlike the other double-size techniques which rely on classical n-bit modular multipliers, our idea is tailored to take advantage of n-bit Montgomery multipliers. Thus, our technique increases the perenniality of existing products without compromises in terms of security. © Springer-Verlag Berlin Heidelberg 2007.