The complexity of breaking cryptosystems of which security is based on the discrete logarithm problem is explored. The cryptosystems mainly discussed are the Diffie-Hellman key exchange scheme (DH), the Bellare-Micali noninteractive oblivious transfer scheme (EM), the ElGamal public-key cryptosystem (EG), the Okamoto conference-key sharing scheme (CONF), and the Shamir 3-pass key-transmission scheme (3PASS). The obtained relation among these cryptosystems is that 3 PASS < CONF < EG =£" BM s DH, where <JJdenotes the polynomial-time functionally many-to-one reducibility, i.e., a function version of the <£ -reducibility. We further give some condition in which these algorithms have equivalent difficulty. One of such conditions suggest another advantage of the discrete logarithm associated with ordinary elliptic curves.
|Number of pages||15|
|Journal||Journal of Cryptology|
|Publication status||Published - Jan 1 1998|
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Applied Mathematics