High radix parallel architecture for GF(p) elliptic curve processor

Abstract

A new GF@) cryptographic processor architecture for elliptic curve encryptionidecryption is proposed in this paper. The architecture takes advantage of projective coordinates to convert GF(p) inversion needed in elliptic point operations into several multiplication steps. Unlike existing sequential designs, we show that projecting into (X/Z,Y/Z) leads to a much better improved perfomance than conventional choice of projecting into the current (X/Z2,Y/Z3). We also propose to use high radix modulo multipliers which give a wide range of area-time trade-offs. The proposed architecture is a significant challenger for implementing data security systems based on elliptic c w e cryptogwhy.

Pipelining GF(P) Elliptic Curve Cryptography Computation

“…As mentioned earlier, the points operations over elliptic curve requires inversion [10]. This inversion is the most expensive operation [13,[18][19][20] within all ECC calculations.…”

“…Assume the base point is (x,y) is noted as P. The ECC algorithm is to calculate nP from P, which is performed by the binary method, since it is known to be efficient and practical to implement in hardware [2,5,7,9,10]. The binary method for scalar multiplication over an elliptic curve can be easily adapted form the corresponding algorithms used in exponentiation, and are summarized below:…”

“…Another technique [10] is to try to parallelize the computation on several multipliers as visualized in the dataflow graphs of Figures 1 and 2, for point addition and doubling respectively. The parallelization is performed depending on the multiplications since their computation complexity makes the addition and subtraction operations negligible.…”

“…He can be contacted through email: ibrahim@dmu.ac.uk purpose programmable processors. It also provides higher security than software solutions [10].…”

“…RSA [17]) is found in the significant reduction in its key size [2,5,8], which results in a substantial faster system. Several GF(p) ECC processors have been proposed in the literature [4,7,10,12]. The gain of using dedicated hardware as crypto-systems is that it results in a considerable speed improvement and power reduction when compared to software solutions on general _______________________ * Professor Mohammad K. Ibrahim is now with the DE MONTFORT University at the United Kingdom.…”