New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2n)

approved: The computation of th GF(p) or GF(2), is one o applications. In this work, w the design of efficient hard inverse. We suggest a new c inverse algorithm to calcula a fast hardware algorithm proposed designs have the h on constrained areas and sti calculations, the module w module operates, can be se upper limit on the operand operands and internal resul infinite-precision Montgome We also propose a s hardware that operates in b Montgomery inverse algorit it very similar to the propose We compare all scalab inversion algorithm. All sca performance than the fully solution for computing the l AN ABSTRACT OF THE THESIS OF for the degree of Doctor of Philosophy in Electrical and nted on June 11, 2002. gorithms and Designs for Montgomery Modular Inverse s GF(p) and GF(2). Alexandre Ferreira Tenca e inverse of a number in finite fields, namely Galois Fields f the most complex arithmetic operations in cryptographic e investigate the GF(p) inversion and present several phases in ware implementations to compute the Montgomery modular orrection phase for a previously proposed almost Montgomery te the inversion in hardware. It is also presented how to obtain to compute the inverse by multi-bit shifting method. The ardware scalability feature, which means that the design can fit ll handle operands of any size. In order to have long-precision orks on small precision words. The word-size, on which the lected based on the area and performance requirements. The precision is dictated only by the available memory to store the ts. The scalable module is in principle capable of performing ry inverse computation of an integer, modulo a prime number. calable and unified architecture for a Montgomery inverse oth GF(p) and GF(2) fields. We adjust and modify a GF(2) hm to benefit from multi-bit shifting hardware features making d best design of GF(p) inversion hardware. le designs with fully parallel ones based on the same basic lable designs consumed less area and in general showed better parallel ones, which makes the scalable design a very efficient ong precision Montgomery inverse. Copyright by Adnan Abdul-Aziz Gutub June 11, 2002 All Rights Reserved New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2) by Adnan Abdul-Aziz Gutub