| Title:
|
Explicit form for the discrete logarithm over the field ${\rm GF}(p,k)$ (English) |
| Author:
|
Meletiou, Gerasimos C. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
25-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $a$ generator of the multiplicative group of the field $GF(p,k)$, the discrete logarithm of an element $b$ of the field to the base $a$, $b\ne 0$ is that integer $z:1\le z \le p^k -1$, $b=a^z$. The $p$-ary digits which represent $z$ can be described with extremely simple polynomial forms. (English) |
| Keyword:
|
discrete logarithm |
| Keyword:
|
finite fields |
| Keyword:
|
cryptography |
| MSC:
|
11T71 |
| MSC:
|
11T99 |
| MSC:
|
94A60 |
| idZBL:
|
Zbl 0818.11049 |
| idMR:
|
MR1242625 |
| . |
| Date available:
|
2008-06-06T21:23:38Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107463 |
| . |
| Reference:
|
[1] Adleman, L. M.: A subexponential algorithm for the discrete logarithm problem, with applications to cryptography.Proc. 20th IEEE Found. Comp. Sci. Symp. (1979), 55-60. |
| Reference:
|
[2] Diffie, W., Hellman, M. E.: New directions in cryptography.IEEE Trans. Inform. Theory, IT-22 (1976), 644-654. MR 0437208 |
| Reference:
|
[3] Odlyzko, A. M.: Discrete logarithms in finite fields and their cryptographic significance.Proc. of the Eurocrypt ’84. Zbl 0594.94016 |
| Reference:
|
[4] Pohling, S. C., Hellman, M. E.: An improved algorithm for computing logarithms over $GF(p)$ and its cryptographic significance.IEEE Trans. Inform. Theory, IT-24 (1978), 106-110. MR 0484737 |
| Reference:
|
[5] Pollard, S. M.: The fast Fourier transform in a finite field.Mathematics of computation 25 (1971), 365-374. Zbl 0221.12015, MR 0301966 |
| Reference:
|
[6] Wells, A. L.: A polynomial form for logarithms modulo a prime.IEEE Trans.Inform. Theory, IT-30 (1984), 845-846. Zbl 0558.12009 |
| Reference:
|
[7] Knuth, D. E.: The art of computer programming.Reading MA III (1969), Addison Wesley. Zbl 0191.18001, MR 0378456 |
| . |
