Efficient algorithms for NMR quantum computers with small qubits

The security of the RSA cryptosystems is based on the difficulty of factoring a large composite integer. In 1994, Shor showed that factoring a large composite is executable in polynomial time if we use a quantum Turing machine. Since this algorithm is complicated, straightforward implementations seem impractical judging from current technologies. In this paper, we propose simple and efficient algorithms for factoring and discrete logarithm problem based on NMR quantum computers. Our algorithms are easier to implement if we consider NMR quantum computers with small qubits. A part of this work was done while both authors were with NTT Communication Science Laboratories. Noboru Kunihiro, Ph.D.: He is Assistant Professor of the University of Electro-Communications. He received his B.E., M.E. and Ph.D. in mathematical engineering and information physics from the University of Tokyo in 1994, 1996 and 2001, respectively. He had been engaged in the research on cryptography and information security at NTT Communication Science Laboratories from 1996 to 2002. Since 2002, he has been working for Department of Information and Communication Engineering of the University of Elector-Communications. His research interest includes cryptography, information security and quantum computations. He was awarded the SCIS’97 paper prize. Shigeru Yamashita, Ph.D.: Associate Professor of Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan. He received his B.E., M.E. and Ph.D. degrees in information science from Kyoto University, Kyoto, Japan, in 1993, 1995 and 2001, respectively. His research interests include new type of computer architectures and quantum computation. He received the 2000 IEEE Circuits and Systems Society Transactions on Computer-Aided Design of Integrated Circuits and Systems Best Paper Award.