Accelerated modular arithmetic for low-performance devices

Abstract

The paper deals with efficient modular arithmetic algorithms for resource restricted devices like smart-cards or sensors. The modular arithmetic is important for a wide variety of computations in these devices, from communication to signal processing. To speed up some cryptographic operations, the most widespread devices often have some cryptographic support provided by a dedicated chip. Our goal is to use the resources of a crypto-coprocessor to accelerate general modular operations. The paper describes our implementation of modular arithmetic operations with large integers, and provides the comparison of the accelerated method with three classical methods for (modular) multiplication. The standard methods are represented by the operand-scanning multiplication algorithm (the school-book method), the product-scanning method (Comba's method) and the Montgomery multiplication. The accelerated method is based on using the RSA encryption support for multiplication tunnelling. The performance characteristics of standard methods and the advanced method called ‘RSA tunnel’ are compared and concluded.