Optimal tower fields for hyperelliptic curve cryptosystems

Cryptographic primitives have increasingly emerged into embedded systems such as mobile phones, smart cards, and personal digital assistants. Elliptic Curve Cryptosystems (ECC) and Hyperelliptic curve cryptosystems (HECC) are the cryptosystems of choice for asymmetric data encryption in environments where processor power and storage are limited [T. Wollinger et al. (2003)]. We introduce the first cryptographic implementation of Optimal Tower Fields (OTF) [S. Baktir (2003)], [S. Baktir et al. (2004)] for HECC. Furthermore, we introduce the first implementation of HECC over an extension field of odd characteristic on an embedded processor. With our implementation, a scalar multiplication for a 160 bit group order can be performed in 44 ms on the ARM processor which is 57% faster than the best previously known implementation on the same processor. Our implementations also target a general purpose processor.