FPGA Design for Algebraic Tori-Based Public-Key Cryptography

Algebraic torus-based cryptosystems are an alternative for Public-Key Cryptography (PKC). It maintains the security of a larger group while the actual computations are performed in a subgroup. Compared with RSA for the same security level, it allows faster exponentiation and much shorter bandwidth for the transmitted data. In this work we implement a torus-based cryptosystem, the so-called CEILIDH, on a multicore platform with an FPGA. This platform consists of a Xilinx MicroBlaze core and a multicore coprocessor. The platform supports CEILIDH, RSA and ECC over prime fields. The results show that one 170-bit torus T₆ exponentiation requires 20 ms, which is 5 times faster than 1024-bit RSA implementation on the same platform.