Name
Abstract | ||
|---|---|---|
XTR appeared in 2000 is a very promising alternative to elliptic curve cryptosystem. Though the basic idea behind XTR is very elegant and universal, one needs to restrict the primes p such as p ≡ 2 mod3 for optimal normal bases since it involves many multiplications in GF(p2). Moreover the restriction p ≡ 2 mod3 is consistently used to improve the time complexity for irreducibility testing for XTR polynomials. In this paper, we propose that a Gaussian normal basis of type (2,k) for small k can also be used for efficient field arithmetic for XTR when p ≢ 2(mod 3). Furthermore we give a new algorithm for fast irreducibility testing and finding a generator of XTR group when p ≡ 1 mod 3. Also we present an explicit generator of XTR group which does not need any irreducibility testing when there is a Gaussian normal basis of type (2,3) in GF(p2). We show that our algorithms are simple to implement and the time complexity of our methods are comparable to the best ones proposed so far. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1007/978-3-540-30564-4_10 | Selected Areas in Cryptography |
Keywords | Field | DocType |
basic idea,optimal normal base,low complexity,explicit generator,restriction p,xtr polynomial,gaussian normal basis,fast irreducibility testing,irreducibility testing,xtr group,time complexity,roots of unity,normal basis | Discrete mathematics,Polynomial,XTR,Irreducibility,Root of unity,Field arithmetic,Normal basis,Time complexity,Gaussian normal basis,Mathematics | Conference |
Volume | ISSN | ISBN |
3357 | 0302-9743 | 3-540-24327-5 |
Citations | PageRank | References |
0 | 0.34 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Soonhak Kwon | 1 | 170 | 22.00 |
| Chang Hoon Kim | 2 | 73 | 9.02 |
| Chun Pyo Hong | 3 | 73 | 9.02 |