Name
Abstract | ||
|---|---|---|
Let k = F-q be a finite field of odd characteristic. We find a closed formula for the number of k-isomorphism classes of pointed, and non-pointed, hyperelliptic curves of genus g over k, admitting a Koblitz model. These numbers are expressed as a polynomial in q with integer coefficients (for pointed curves) and rational coefficients (for non-pointed curves). The coefficients depend on g and the set of divisors of q - 1 and q + 1. These formulas show that the number of hyperelliptic curves of genus g suitable (in principle) for cryptographic applications is asymptotically (1 - e(-1)) 2q(2g-1), and not 2q(2g-1) as it was believed. The curves of genus g = 2 and g = 3 are more resistant to the attacks to the DLP; for these values of g the number of curves is respectively (91/72)q(3) + O(q(2)) and (3641/2880)q(5) + O(q(4)). |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1515/JMC.2008.008 | JOURNAL OF MATHEMATICAL CRYPTOLOGY |
Keywords | Field | DocType |
Finite field, hyperelliptic curve, hyperelliptic cryptosystem, Koblitz model, Weierstrass point, rational n-set | Integer,Discrete mathematics,Combinatorics,Hyperelliptic curve,Finite field,Family of curves,Polynomial,Hyperelliptic curve cryptography,Divisor,Mathematics | Journal |
Volume | Issue | ISSN |
2 | 2 | 1862-2976 |
Citations | PageRank | References |
1 | 0.50 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cevahir Demirkiran | 1 | 1 | 0.50 |
| Enric Nart | 2 | 25 | 5.92 |