GF(2191) Elliptic Curve Processor using Montgomery Ladder and High Speed Finite Field Arithmetic Unit

This paper describes hardware implementation of GF(2¹⁹¹) elliptic curve cryptographic(ECC) coprocessor. It supports 6 operations such as scalar multiplication(kP), Menezes-Vanstone(MV) elliptic curve cipher/decipher, point addition(P+Q), point doubling(2P), and finite-field multiplication/division. The ECC processor adopts the Montgomery scalar multiplication scheme in which main loop can be executed using only x-coordinate. It also takes advantage of concurrent operations among arithmetic units, such as GF_ALU, GF_MUL, and GF_DIV to achieve high cipher rate. The processor has about 68,000 gates using 0.35 um CMOS technology, and its worst case delay time is about 7.8-ns. It can be efficiently applied to various elliptic curve cryptographic applications due to high cipher rate (about 647 kbps) and the possible 6 operations.