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ON THE POCKLINGTON-PERALTA SQUARE ROOT ALGORITHM IN FINITE FIELDS
- Title
- ON THE POCKLINGTON-PERALTA SQUARE ROOT ALGORITHM IN FINITE FIELDS
- Authors
- Kim, Chang Heon; Koo, Namhun; Kwon, Soonhak
- Ewha Authors
- 구남훈
- SCOPUS Author ID
- 구남훈
- Issue Date
- 2022
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- ISSN
- 1015-8634
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY vol. 59, no. 6, pp. 1523 - 1537
- Keywords
- Square root algorithm; finite field; Pocklington-Peralta algorithm; Tonelli-Shanks algorithm; Cipolla-Lehmer algorithm
- Publisher
- KOREAN MATHEMATICAL SOC
- Indexed
- SCIE; SCOPUS; KCI
- Document Type
- Article
- Abstract
- We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.
- DOI
- 10.4134/BKMS.b210870
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
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