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Characteristic Polynomial of 90 UCA and Synthesis of CA using Transition Rule Blocks

90 UCA의 특성다항식과 전이규칙 블록을 이용한 CA 합성법

  • 최언숙 (동명대학교 정보통신공학과) ;
  • 조성진 (부경대학교 응용수학과)
  • Received : 2018.03.22
  • Accepted : 2018.06.15
  • Published : 2018.06.30

Abstract

Cellular automata (CA) have been applied to effective cryptographic system design. CA is superior in randomness to LFSR due to the fact that its state is updated simultaneously by local interaction. To apply these CAs to the cryptosystem, a study has been performed how to synthesize CA corresponding to given polynomials. In this paper, we analyze the recurrence relations of the characteristic polynomial of the 90 UCA and the characteristic polynomial of the 90/150 CA whose transition rule is <$00{\cdots}001$>. And we synthesize the 90/150 CA corresponding to the trinomials $x^{2^n}+x+1(n{\geq}2)$ satisfying f(x)=f(x+1) using the 90 UCA transition rule blocks and the special transition rule block. We also analyze the properties of the irreducible factors of trinomials $x^{2^n}+x+1$ and propose a 90/150 CA synthesis algorithm corresponding to $x^{2^n}+x^{2^m}+1(n{\geq}2,n-m{\geq}2)$.

효과적인 암호시스템 설계에 셀룰라 오토마타(이하 CA)가 적용되고 있다. CA는 국소적 상호작용에 의해 상태가 동시에 업데이트되는 성질이 있어서 LFSR보다 랜덤성이 우수하다. 이런 CA를 암호 시스템에 적용하기 위해 주어진 다항식에 대응하는 CA를 합성하는 방법에 대한 연구가 진행되었다. 본 논문에서는 90 UCA의 특성다항식과 전이규칙이 <$00{\cdots}001$>인 90/150 CA의 특성다항식의 점화관계를 분석한다. 또한 f(x)=f(x+1)을 만족하는 삼항다항식 $x^{2^n}+x+1$에 대응하는 90/150 CA를 90 UCA 전이규칙 블록과 특별한 전이규칙 블록을 이용하여 합성한다. 또한 $x^{2^n}+x+1$의 기약인수에 관한 성질을 분석한 후 $x^{2^n}+x^{2^m}+1(n{\geq}2,n-m{\geq}2)$에 대응하는 90/150 CA 합성 알고리즘을 제안한다.

Keywords

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