View : 95 Download: 0
On the Cipolla–Lehmer type algorithms in finite fields
- On the Cipolla–Lehmer type algorithms in finite fields
- Cho G.H.; Go B.; Kim C.H.; Koo N.; Kwon S.
- Ewha Authors
- Issue Date
- Journal Title
- Applicable Algebra in Engineering, Communications and Computing
- Applicable Algebra in Engineering, Communications and Computing vol. 30, no. 2, pp. 135 - 145
- Adleman–Manders–Miller algorithm; Cipolla–Lehmer algorithm; Finite field; Primitive root; r-th root
- Springer Verlag
- SCIE; SCOPUS
- Document Type
- In this paper, we present a refinement of the Cipolla–Lehmer type algorithm given by H. C. Williams in 1972, and later improved by K. S. Williams and K. Hardy in 1993. For a given r-th power residue c∈ F q where r is an odd prime, the algorithm of H. C. Williams determines a solution of X r = c in O(r 3 log q) multiplications in F q , and the algorithm of K. S. Williams and K. Hardy finds a solution in O(r 4 + r 2 log q) multiplications in F q . Our refinement finds a solution in O(r 3 + r 2 log q) multiplications in F q . Therefore our new method is better than the previously proposed algorithms independent of the size of r, and the implementation result via SageMath shows a substantial speed-up compared with the existing algorithms. It should be mentioned that our method also works for a composite r. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
- Files in This Item:
There are no files associated with this item.
- RIS (EndNote)
- XLS (Excel)
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.