Sciweavers

TIT
2010

Parameterized splitting systems for the discrete logarithm

13 years 6 months ago
Parameterized splitting systems for the discrete logarithm
Hoffstein and Silverman suggested the use of low Hamming weight product (LHWP) exponents to accelerate group exponentiation while maintaining the security level. With LHWP exponents, the computation costs on GF(2n ) or Koblitz elliptic curves can be reduced significantly, where the cost of squaring and elliptic curve doubling is much lower than that of multiplication and elliptic curve addition, respectively. In this paper, we present a parameterized splitting system with an additional property, which is a refinement version of the system introduced in PKC'08. We show that it yields an algorithm for the discrete logarithm problem (DLP) with LHWP exponents with lower complexity than that of any previously known algorithms. To demonstrate its application, we attack the GPS identification scheme modified by Coron, Lefranc, and Poupard in CHES'05 and the DLP with Hoffstein and Silverman's (2,2,11)exponent. The time complexity of our key recovery attack against
Sungwook Kim, Jung Hee Cheon
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TIT
Authors Sungwook Kim, Jung Hee Cheon
Comments (0)