| Presentation | 1995/12/14 On the Cardinality of Elements each with a Given Order in Z^*_n Hideo Suzuki, Tadao Nakamura, |
|---|---|
| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | There are three functions for expressing properties of the multiplicative group Z^*_n: φ(n) for the cardinality of all elements, λ(n) for the maximum order of elements, and ψ_n(d) for the cardinality of elements each with a given order d, where φ(・) denotes Euler's totient function, λ(・) denotes Carmicael's function, and d is a divisor of λ(n). Euler showed the function φ(n) for any composite n. Carmicael showed the function λ(n) for any composite n. Gauss showed the equation ψ_p(d)=φ(d) that holds for an odd prime p. In this paper, we show a new function ψ_n(d) for the cardinality of elements each with a given order d in Z^*_n for any composite n, where d is a divisor of λ(n). And we show that this new function can be used counting the cardinality of k-ic power residue/nonresidue elements in Z^*_n. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | order modulo a composite / universal exponent / Euler's totient function |
| Paper # | ISEC95-31 |
| Date of Issue |
| Conference Information | |
| Committee | ISEC |
|---|---|
| Conference Date | 1995/12/14(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | |
| Vice Chair | |
| Secretary | |
| Assistant | |
| Paper Information | |
| Registration To | Information Security (ISEC) |
|---|---|
| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On the Cardinality of Elements each with a Given Order in Z^*_n |
| Sub Title (in English) | |
| Keyword(1) | order modulo a composite |
| Keyword(2) | universal exponent |
| Keyword(3) | Euler's totient function |
| 1st Author's Name | Hideo Suzuki |
| 1st Author's Affiliation | Dept. of Electrical Communications, Tohoku University() |
| 2nd Author's Name | Tadao Nakamura |
| 2nd Author's Affiliation | Graduate School of Information Sciences, Tohoku University |
| Date | 1995/12/14 |
| Paper # | ISEC95-31 |
| Volume (vol) | vol.95 |
| Number (no) | 422 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |