2001 Fiscal Year Final Research Report Summary
A Development of Public Key Cryptosystem Based on tne Security for the Hard Problem of Number Theory and its Security Evaluation
| Project/Area Number |
12650360
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
情報通信工学
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| Research Institution | Yamagata University |
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Principal Investigator |
KOBAYASHI Kunikatsu Yamagata University, Faculty of Engineering, Professor, 工学部, 教授 (40007191)
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| Co-Investigator(Kenkyū-buntansha) |
HAYATA Takahiro Yamagata University, Faculty of Engineering, Research Assistant, 工学部, 助手 (50312757)
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| Project Period (FY) |
2000 – 2001
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| Keywords | information security / public key cryptosystem / digital signature / factoring / discrete logarithm problem / trap door / RSA cryptosystem / ElGamal signature scheme |
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| Research Abstract |
In this research, we investigated a development of public key cryptosystem based on the security for the hard problem of number theory and its security evaluation.
1. First, we made a study of digital signature scheme having the same principle as the trap door of RSA cryptosystem. With trap door of RSA cryptosystem, encryption key e and decryption key d which satisfy ed=1 (mod L) are defined over a modulus L. The trap door used in this signature scheme is identical with these definitions. Over the modulus L, for document M that is prime with regard to L, the multiplication inverse element of M is defined as K. Over the modulus n, the maximum generator g is raised to K power, and this is defined as digital signature S. Security of this signature scheme is based on a difficulty of the factorization and of the discrete logarithm problem.
2. Then, we expanded ElGamal signature scheme to the case over composite modulus. Security of this signature scheme is based on a difficulty of the discrete logarithm problem over composite modulus.
3. Next, we made a study of factoring algorithm using Jacobi symbol in regard to the composite number of n=p^2q. Because the value of Jacobi symbol of n=p^2q for arbitrary prime number pi is equal to Legendre symbol of q for the prime number p_i, whether a prime factor q is a quadratic residue or not is known by calculating the value of Jacobi symbol and remainder candidates of prime factor q for prime number p_i are obtained. The complexity of this method is about O(n^<1/3.7>).
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