Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, Tohoku University
Shuji ISOBE
Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, Tohoku University
Hiroki SHIZUYA
Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, Tohoku University The Institute of Electronics, Information and Communication Engineers
We define two functions fDL and fIF in NPMV, the class of all partial, multivalued functions computed nondeterministically in polynomial time. We prove that they are complete for NPMV, and show that (a) computing discrete logarithms modulo a prime reduces to fDL, and (b) computing integer factorization reduces to fIF. These are the first complete functions that have explicit reductions from significant cryptographic primitives.
