DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 이주영 | - |
dc.contributor.author | Cho, Mingyu | - |
dc.contributor.author | 조민규 | - |
dc.date.accessioned | 2024-08-08T19:30:26Z | - |
dc.date.available | 2024-08-08T19:30:26Z | - |
dc.date.issued | 2024 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1097365&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/321833 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 정보보호대학원, 2024.2,[i, 22 p. :] | - |
dc.description.abstract | One of the important factors that determines the security of an S-box on the point of view of algebraic attacks is the number of linearly independent multivariate quadratic equations on $\mathbb{F}_2$ it satisfies. Many previous researches analyzed the equations on $\mathbb{F}_2$ of S-boxes based on power functions, as they can be used to build an S-box of an arbitrary size. Courtois et al.\ proved the number of equations for an inverse S-box of arbitrary size, and expanding upon that, Nawaz et al.\ presented an algorithm to count the number of equations for an S-box based on an arbitrary power function. In this paper, we extend the previous results to apply to $\mathbb{F}_{2^m}(m \ne 1, m|n)$, a subfield of $\mathbb{F}_{2^n}$. We first present an algorithm to count the number of quadratic equations of an S-box on the subfield. Next, we give proof that for one of the most frequently used S-boxes, the inverse S-box set on $\mathbb{F}_{2^n}$, the number of linearly independent quadratic equations on $\mathbb{F}_{2^m}$ is given as $n/m-1$. We expect to be able to apply the principles of algebraic attacks and analysis on subfields to new types of attacks which has not been researched before. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 지수함수▼aS-box▼a대수적 공격▼a부분체 상의 다변수 방정식 | - |
dc.subject | Power functions▼aS-boxes▼aAlgebraic attacks▼aMultivariate equations over subfields | - |
dc.title | On the number of linearly independent quadratic equations for S-boxes based on power mappings | - |
dc.title.alternative | 지수함수 기반 S-Box의 선형 독립 이차 방정식의 수에 관한 연구 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :정보보호대학원, | - |
dc.contributor.alternativeauthor | Lee, Jooyoung | - |
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