정보보호학회논문지 (Journal of the Korea Institute of Information Security & Cryptology)

  • 제9권3호
  • /
  • Pages.3-12
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  • 1999
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  • 1598-3986(pISSN)
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  • 2288-2715(eISSN)
한국정보보호학회 (Korea Institute of Information Security and Cryptology)
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GF($2^n$) 위에서의 다항식 일수분해

The polynomial factorization over GF($2^n$)

  • 김창한 (세명대학교 컴퓨터응용수학과)
  • 발행 : 1999.09.01
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초록

공개키 암호법은 정수 인수분해의 어려움에 바탕을 둔 RSA와 이산대수문제의 어려움에 근거한 EIGamal 암호법을 대표된다. GF(qn)*에서 index-calculus 이산대수 알고리즘을 다항식 인수분해를 필요로 한다. 최근에 Niederreiter에 의하여 유한체위에서의 다항식 인수분해 알고리즘이 제안되었다. 이 논문에서는 정규기저(normal basis)를 이용한 유한체의 연산을 c-언어로 구현하고, 이것을 이용한 Niederreiter의 알고리즘을 기반으로 유한체위에서의 다항식 인수분해 알고리즘과 구현한 결과를 제시한다. The public key crytptosystem is represented by RSA based on the difficulty of integer factorization and ElGamal cryptosystem based on the intractability of the discrete logarithm problem in a cyclic group G. The index-calculus algorithm for discrete logarithms in GF(qn)* requires an polynomial factorization. The Niederreiter recently developed deterministic facorization algorithm for polynomial over GF(qn) In this paper we implemented the arithmetic of finite field with c-language and gibe an implementation of the Niederreiter's algorithm over GF(2n) using normal bases.

The public key crytptosystem is represented by RSA based on the difficulty of integer factorization and ElGamal cryptosystem based on the intractability of the discrete logarithm problem in a cyclic group G. The index-calculus algorithm for discrete logarithms in GF${$q^n$}^+$ requires an polynomial factorization. The Niederreiter recently developed deterministic facorization algorithm for polynomial over GF$q^n$ In this paper we implemented the arithmetic of finite field with c-language and gibe an implementation of the Niederreiter's algorithm over GF$2^n$ using normal bases.

키워드

참고문헌

  1. Math. Comp. 62 An accelleration of the Niederreiter's factorization algorithm in characteristic 2 R. Gottfert
  2. Math. of Computation v.48 Elliptic curve cryptosystem N. Koblitz
  3. Computational method in number theory, part 1, Mathematical Centre Tracts v.154 Factorization of polynomials A.K. Lenstra
  4. Introduction to finite fields and their applications R. Lidl;H. Niederreiter
  5. Applications of finite fields A.J. Menezes
  6. Handbook of applied cryptography A.J. Menezes
  7. CRYPTO' 85, LNCS218 Use of elliptic curve in cryptography V.S. Miller
  8. Linear Algebra Appl. 192 Factorization of polynomials and linear-algebra problems over finite fields H. Niederreiter
  9. Math. Comp. 62 Factoring polynomials over finite fields using differential equations and normal bases H. Niederreiter