상세정보
학술지
Improved Computation of Square Roots in Specific Finite Fields
- 발행일
- 200902
- 출처
- IEEE Transactions on Computers, v.58 no.2, pp.188-196
- ISSN
- 0018-9340
- 출판사
- IEEE
- 협약과제
- 08MS2200, 안전한 RFID/USN을 위한 정보보호 기술 개발, 정교일
- 초록
- In this paper, we study exponentiation in the specific finite fields F q with very special exponents such as those that occur in algorithms for computing square roots. Here, q is a prime power, q = pk, where k > 1, and k is odd. Our algorithmic approach improves the corresponding exponentiation resulted from the better rewritten exponent. To the best of our knowledge, it is the first major improvement to the Tonelli-Shanks algorithm, for example, the number of multiplications can be reduced to at least 60 percent on the average when p = 1 (mod 16). Several numerical examples are given that show the speedup of the proposed methods. © 2006 IEEE.
- KSP 제안 키워드
- Algorithmic approach, Finite fields, Numerical examples, Square root