Concurrent algorithm for high-speed point multiplication in elliptic curve cryptography

The paper explores the concurrent property, inherent in point multiplication, to speed up the operations of encryption and decryption in elliptic curve cryptography (ECC) under limited hardware resources. To decrease computation time further, we employed the nonadjacent form of a binary sequence to reduce the number of 1s in an operand so as to decrease the total number of additions in ECC encryption/decryption. With the developed interleaving schemes, we can fully use the idle time of hardware resources by relaxing the data dependency on those arithmetic operations performed to accomplish point multiplication. As a result, by way of increasing hardware utilization, we can achieve the performance of radix-4 arithmetic in the existing work by employing only the radix-2 hardware realization.