http://iet.metastore.ingenta.com
1887

Square root algorithm in 𝔽 q for q ≡ 2 s + 1 (mod 2 s+1)

Square root algorithm in 𝔽 q for q ≡ 2 s + 1 (mod 2 s+1)

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
Electronics Letters — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Presented is a square root algorithm in 𝔽 q which generalises Atkins's square root algorithm [see reference 6] for q ≡ 5 (mod 8) and Müller's algorithm [see reference 7] for q ≡ 9 (mod 16). The presented algorithm precomputes a primitive 2 s -th root of unity ξ where s is the largest positive integer satisfying 2 s |q−1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favourably compared with the algorithms of Atkin, Müuller and Kong et al.

References

    1. 1)
      • Shanks, D.: `Five number-theoretic algorithms', Proc. 2nd Manitoba Conf. of Numerical Mathematics, Winnipeg, Manitoba, Canada, 1972, p. 51–70.
    2. 2)
      • D.H. Lehmer . (1969) Computer technology applied to the theory of numbers.
    3. 3)
      • S. Lindhurst . An analysis for computing square roots in finite fields. CRM Proc Lect. Notes , 231 - 242
    4. 4)
    5. 5)
      • N. Nishihara , R. Harasawa , Y. Sueyoshi , A. Kudo . A remark on the computation of cube roots in finite fields.
    6. 6)
      • A.O.L. Atkin . (1992) Probabilistic primality testing.
    7. 7)
    8. 8)
http://iet.metastore.ingenta.com/content/journals/10.1049/el.2012.4239
Loading

Related content

content/journals/10.1049/el.2012.4239
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address