Abstract
Evaluation of cube roots in characteristic three finite fields is required for Tate (or modified Tate) pairing computation. The Hamming weight of x1 /3 means that the number of nonzero coefficients in the polynomial representation of x1/3 in F3m= F3[x]/(f), where fâ̂̂F3[x] is an irreducible polynomial. The Hamming weight of x1/3 determines the efficiency of cube roots computation for characteristic three finite fields. Ahmadi et al. found the Hamming weight of x1/3 using polynomial basis [4]. In this paper, we observe that shifted polynomial basis (SPB), a variation of polynomial basis, can reduce Hamming weights of x1/3 and x2 /3. Moreover, we provide the suitable SPB that eliminates modular reduction process in cube roots computation.
Original language | English |
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Pages (from-to) | 331-337 |
Number of pages | 7 |
Journal | Information Processing Letters |
Volume | 114 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 Jun |
Keywords
- Cryptography
- Cube roots
- Finite field arithmetic
- Shifted polynomial basis
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications