Imai Laboratory Introduction

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Imai Laboratory Introduction Quantum Computation
and Information
Introduction
Current Our Research Fields
Our Motivation

Quantum Computation
Quantum Cryptography
By utilizing Quantum Power, We want to design
efficient algorithms and secure protocols which
have not been accomplished in todays
computational and cryptographic model.
Quantum Walk Algorithms
Quantum Key Distribution
Algorithms for Hidden Subgroup Problem (HSP)
Quantum Digital Signature
Quantum Cryptography
Quantum Computation
Achievements
Shors Integer factorization algorithm
BB84 Protocol
BB84 protocol Is unconditional secure key
distribution protocol!! (Even though the
adversary having unlimited computational
resources)
classical algorithm
The best known algorithm takes sub exponential
time.
Sub exponential gap!!
quantum algorithm
Shors algorithm can solve it in polynomial time.
secure
Bob
Alice
Adversary
Future Works
Designing new cryptographic application
Designing Algorithms for Non-Abelian HSP
HSP
Shortest Vector
Graph Isomorphism
We want to design new cryptographic Applications
by using quantum one-way functions which are
related to Graph Isomorphism and Shortest Vector
problems.
There are no polynomial time quantum algorithms
for Graph Isomorphism and Shortest Vector
Problems in which are included Non-Abelian HSP.
Non-Abelian HSP
References 1 P. W. Shor. Algorithms for quantum
computation discrete logarithms and factoring.
In Proceedings, 35th Annual Symposium on
Foundation of Computer Science, IEEE Press, Los
Alamitos, CA, 1994. 2 C. H. Bennett and G.
Brassard. Quantum cryptography Public key
distribution and coin tossing. In proceedings of
IEEE International Conference on Computers,
Systems and Signal Processing, pages 175-179,
IEEE, New York, 1984. Bangalore, India, December
1984. 3 C. Moore, A. Russel, and U. Vazirani. A
classical one-way function to confound quantum
adversaries. Preprint, quant-ph/07115v2,2007.