Light-weight implementation options for curve-based cryptography: HECC is also ready for RFID

In this paper we describe a low footprint implementation of hyperelliptic curve cryptography (HECC) for RFID tags. This HECC processor supports divisor multiplication on a hyperelliptic curve defined over GF(2⁸³). We propose a unified GF(2^m) multiplier/inverter (UMI) which is smaller than ALUs with separated multipliers and inverters. With the UMI divisor multiplications using affine coordinates can be efficiently supported. Since affine coordinates require less registers than projective coordinates, the size of register file is also reduced. We choose hyperelliptic curves defined with the h(x) = x and f(x) = x⁵ + f₃x³ + x² + f₀. The HECC processor, synthesized with 130 nm standard cell library, uses 14.5 kGates. It consumes 13.4 ??W when running at 300 kHz. One divisor multiplication takes 450 ms, which makes our solution a feasible option for light-weight applications.