Robust finite field arithmetic for fault-tolerant public-key cryptography

Abstract

We present a new approach to fault tolerant public key cryptography based on redundant arithmetic in finite rings. Redundancy is achieved by embedding non-redundant field or ring elements into larger rings via suitable homomorphisms obtained from modulus scaling. Our approach is closely related to, but not limited by the exact definition of cyclic binary and arithmetic codes. We present a framework for system-designers that allows flexible trade-offs between circuit area and desired level of fault tolerance. Our method applies to arithmetic in prime fields and extension fields of characteristic 2 where it serves two mutually beneficial purposes: The redundancy of the larger ring can be used for error detection, while its modulus has a special low Hamming-weight form, lending itself particularly well to efficient modular reduction. © Springer-Verlag Berlin Heidelberg 2006.