Novel iterative digit-serial modular division over GF(2)

Public key cryptography is a concept used by many useful functionalities such as digital signature, encryption, key agreements, ... For those needs, elliptic curve cryptography is an attractive solution: for a given level of security, it provides one of the best key sizes and amount of exchanged data. Cryptosystems based on elliptic curve necessitate a costly modular division. Depending on the choice of coordinates, this operation is needed at each step of algorithms or at the end of the whole computation. As a result, efficient modular division implementations could be useful for some area constrained designs and are required for high-speed processors with output in affine coordinates. For that purpose, an improved modular division algorithm is presented. This new design is particularly well suited for hardware implementations as illustrated by our FPGA realization. To the best of our knowledge, it is the first report about an iterative digit-serial modular division algorithm.