Sciweavers

Share
JOC
2010

Discrete Logarithm Problems with Auxiliary Inputs

8 years 6 months ago
Discrete Logarithm Problems with Auxiliary Inputs
Let g be an element of prime order p in an abelian group and let Zp. We show that if g, g , and gd are given for a positive divisor d of p - 1, the secret key can be computed deterministically in O( p/d + d) exponentiations by using O(max{ p/d, d}) storage. If gi (i = 0, 1, 2, . . . , 2d) is given for a positive divisor d of p + 1, can be computed in O( p/d+d) exponentiations by using O(max{ p/d, d}) storage. We also propose space-efficient, but probabilistic algorithms for the same problem, which have the same computational complexities with the deterministic algorithm. As applications of the proposed algorithms, we show that the strong Diffie-Hellman problem and its related problems with public g , . . . , gd have computational complexity up to O( d/ log p) less than the generic algorithm complexity of the discrete logarithm problem when p-1 (resp. p + 1) has a divisor d p1/2 (resp. d p1/3 ). Under the same conditions for d, the algorithm is also applicable to recovering th...
Jung Hee Cheon
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JOC
Authors Jung Hee Cheon
Comments (0)
books