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Preference of Efficient Architectures for GF(p) Elliptic Curve Crypto Operations using Multiple Parallel Multipliers
Adnan Abdul-Aziz Gutub
Pages - 46 - 63     |    Revised - 30-08-2010     |    Published - 30-10-2010
Volume - 4   Issue - 4    |    Publication Date - October  Table of Contents
Modulo multipliers, Cryptography Hardware, Elliptic curve cryptography, Jacobian projective coordinates, Parallel multipliers crypto hardware
This paper explores architecture possibilities to utilize more than one multiplier to speedup the computation of GF(p) elliptic curve crypto systems. The architectures considers projective coordinates to reduce the GF(p) inversion complexity through additional multiplication operations. The study compares the standard projective coordinates (X/Z,Y/Z) with the Jacobian coordinates (X/Z2,Y/Z3) exploiting their multiplication operations parallelism. We assume using 2, 3, 4, and 5 parallel multipliers and accordingly choose the appropriate projective coordinate efficiently. The study proved that the Jacobian coordinates (X/Z2,Y/Z3) is preferred when single or two multipliers are used. Whenever 3 or 4 multipliers are available, the standard projective coordinates (X/Z,Y/Z) are favored. We found that designs with 5 multipliers have no benefit over the 4 multipliers because of the data dependency. These architectures study are particularly attractive for elliptic curve cryptosystems when hardware area optimization is the key concern.
CITED BY (2)  
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Dr. Adnan Abdul-Aziz Gutub
Umm Al-Qura University - Saudi Arabia