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研究生:林志信
研究生(外文):Chin-Hsin Lin
論文名稱:布林函數在密碼標準上的頻譜分析
論文名稱(外文):Spectral Analysis of Boolean Functions for Cryptographic Criteria
指導教授:蔡錫鈞蔡錫鈞引用關係陳榮傑陳榮傑引用關係
指導教授(外文):Shi-Chun TsaiRong-Jay Chen
學位類別:碩士
校院名稱:國立交通大學
系所名稱:資訊工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:67
中文關鍵詞:布林函數華勒式-哈達瑪轉換頻譜分析非線性相關免疫函數遺傳特性標準等價類別
外文關鍵詞:Boolean functionsWalsh-Hadamard transformSpectral analysisNonlinearityCorrelation immune functionsPropagation criterionEquivalence classes
相關次數:
  • 被引用被引用:0
  • 點閱點閱:174
  • 評分評分:
  • 下載下載:17
  • 收藏至我的研究室書目清單書目收藏:0
對稱式加/解密演算法有對於訊息的加/解密效率高,製作成本低,及容易加解密的優點,而其核心元件通常是布林函數,
所以布林函數在密碼學上的特性一直為研究的範疇,在此之前已經有許多學者提出相關的標準,用來檢測布林函數的密碼特性,其中我們將針對下面的標準來討論:
(1)調和性、(2)代數冪級數、(3)非線性、 (4)遺傳特性、(5)相關免疫性.
在本篇論文中,我們首先簡介這些密碼檢測標準,利用布林函數經華勒式-哈達瑪轉換在頻譜上的結果來分析,並研究及回顧目前對於這些密碼檢測標準間的關係的研究,
透過了解其相對關係,
我們將提出兩個在同時考慮遺傳特性及相關免疫性標準下的布林函數建構方式。

Symmetric-key cryptography system has many advantages of high
performance, low cost of implementation, and easily encrypting or
decrypting messages. A core component of these systems is the
cryptographic boolean functions. Therefore, it is research topic
for boolean functions on the cryptographic properties. Many
researchers have provided many cryptographic criteria to verify
the cryptographic properties of boolean functions. We focus the
following criteria of the cryptographic boolean functions:
(1)balancedness,(2)algebraic degree,
(3)nonlinearity,(4))propagation criterion,(5)correlation immunity.
In this thesis, we first introduce these cryptographic criteria.
Using the Walsh-Hadamard transform of boolean function, we analyze
the boolean function on cryptographic properties. Moreover, we
study and review the relationship among these criteria. From this,
We present two new constructions of a strong boolean function
under of consideration of propagation criterion and correlation
immunity simultaneously.

Chinese Abstract
English Abstract
Acknowledgement
Contents
List of Tables
1. Introduction
2. Preliminaries
2.1 Boolean functions
2.2 Walsh-Hadamard Transform
2.3 Cryptographic Properties for Boolean Functions
2.3.1 Balanced functions
2.3.2 Nonlinearity
2.3.3 Correlation Immune and Resilient Boolean Functions
2.3.4 Propagation Criterion
2.4 Bent Functions
3 Relationship Among Cryptographic Propterties
3.1 Nonlinearity and Algebraic Degree
3.2 Nonlinearity and Correlation Immunity
3.3 Nonlinearity and Propagation Criterion
3.4 Propagation Criterion and Correlation Immunity
4 Constructions
4.1 Construction of A Boolean Function With important cryptographic properties
4.2 The Equivalence Classes of Boolean Functions
5 Conclusion

@ARTICLE{bib:ZeroOfPolynomial64,
author = {James Ax},
title = {\textbf{Zeros of polynomials over finite fields}},
journal = {American Journal of Mathematics 86},
year = {1964},
volume = {},
number = {},
pages = {255-261}
}
@ARTICLE{bib:PCM72,
author = {J. F. Dillon},
title = {\textbf{A survey of bent functions}},
journal = {The NSA Technical Journal},
year = {1972},
volume = {},
number = {},
pages = {191-215}
}
@ARTICLE{bib:Nf(5)74,
author = {E.R. Berlekamp and L. R. Welch},
title = {\textbf{Weight distribution of the cosets of the (32,6) Reed-Muller code}},
journal = {IEEE Transactions on Information Theorey},
year = {1974},
volume = {IT-18},
number = {1},
pages = {203-207}
}
@ARTICLE{bib:bent76,
author = {O. S. Rothaus},
title = {\textbf{On bent functions}},
journal = {Journal of Combinatorial Theory, Series A20},
year = {1976},
volume = {},
number = {},
pages = {300-305}
}
@BOOK{bib:Parsval78,
author = {F. J. MacWilliams and N. J. A. Sloane},
title = {The Theory of Error-Correcting Codes},
publisher = {Amsterdam, The Netherlands:North-Holland},
year = {1978}
}
@ARTICLE{bib:Nf(7)80,
author = {J. Mykkeltveit},
title = {\textbf{The covering radius of the (128,8) Reed-Muller code is 56}},
journal = {IEEE Transactions on Information Theorey},
year = {1980},
volume = {26},
number = {},
pages = {359-362}
}
@ARTICLE{bib:Nf(15)83,
author = {N. J. Patterson and D. H. Wiedemann},
title = {\textbf{The covering radius of the $[2^{15},16]$ Reed-Muller code is at least 16276}},
journal = {IEEE Transactions on Information Theorey},
year = {1983},
volume = {29},
number = {},
pages = {354-356}
}
@BOOK{bib:WKtheo84,
author = {K. Beauchamp},
title = {Applications of Walsh and Related Functions : With an Introduction to Sequency Theory},
publisher = {Academic Press; ISBN: 0120841800},
year = {1984}
}
@ARTICLE{bib:CI84,
author = {T.Siegenthaler},
title = {\textbf{Correlation-immunity of nonlinear combining functions for cryptographic applications}},
journal = {IEEE Transactions on Information Theorey},
year = {1984},
volume = {30},
number = {5},
pages = {776-780}
}
@ARTICLE{bib:designSbox85,
author = {A.F. Webster and S.E. Tavares},
title = {\textbf{On the design of S-Boxes}},
journal = {Advances in Cryptology -CRYPTO'85},
year = {1985},
volume = {},
number = {},
pages = {523-534}
}
@ARTICLE{bib:CorrelationAttack85,
author = {T.Siegenthaler},
title = {\textbf{Decrypting a class of stream ciphers using ciphertext only}},
journal = {IEEE Transactions on Computers},
year = {1985},
volume = {c-34},
number = {1},
pages = {81-85}
}
@ARTICLE{bib:bentanalysis89,
author = {Rao Yarlagadda and John E. Hershey},
title = {\textbf{Analysis and synthesis of bent sequences}},
journal = {IEE Proceedings},
year = {1987},
volume = {966},
number = {2},
pages = {112-123}
}
@ARTICLE{bib:spectralCI88,
author = {Xiao Guo-Zhen and James L. Massey},
title = {\textbf{A spectral characterization of correlation-immune combining functions}},
journal = {IEEE Transactions on Information Theory},
year = {1988},
volume = {34},
number = {3},
pages = {569-571}
}
@ARTICLE{bib:sacspectral88,
author = {Xiao Guo-Zhen and James L. Massey},
title = {\textbf{The Strict Avalanche Criterion: special properties of boolean functions and extended definition}},
journal = {Advances in Cryptology - CRYPTO'88},
year = {1988},
volume = {},
number = {},
pages = {450-468}
}
@ARTICLE{bib:FastCorrelatoinAttack88,
author = {Willi Meier and Othmar Staffelbach},
title = {\textbf{Fast correlation attack on stream cipher}},
journal = {Advances in Cryptology - EUROCRYPT'88},
year = {1988},
volume = {},
number = {},
pages = {301-315}
}
@ARTICLE{bib:nonlinearitycriteria89,
author = {Willi Meier and Othmar Staffelbach},
title = {\textbf{Nonlinearity criteria for cryptographic functions}},
journal = {Advances in Cryptology - EUROCRYPT'89},
year = {1989},
volume = {},
number = {},
pages = {549-562}
}
@ARTICLE{bib:propagation90,
author = {Bart Preneel and Wener Van Leekwijck and Luc Van Linden and Rene Govaerts and Joos Vandewalle},
title = {\textbf{Propagation characteristic of boolean functions}},
journal = {Advances in Cryptology -EUROCRYPT'90},
year = {1990},
volume = {},
number = {},
pages = {161-173}
}
@ARTICLE{bib:bentcounting90,
author = {Carlisle M. Adams and Stafford E. Tavares},
title = {\textbf{Generating and counting binary sequences}},
journal = {IEEE Transation on Information Theory},
year = {1990},
volume = {IT-36},
number = {5},
pages = {1170-1173}
}
@ARTICLE{bib:DifferentAttack91,
author = {Eli Biham and Adi Shamir},
title = {\textbf{Differential cryptanalysis for DES-like cryptosystem}},
journal = {Journal of Cryptology},
year = {1991},
volume = {4},
number = {1},
pages = {3-72}
}
@ARTICLE{bib:partiallybent93,
author = {Claude Carlet},
title = {\textbf{Partially-bent functions}},
journal = {Designs, Codes and Cryptography},
year = {1993},
volume = {3},
number = {},
pages = {135-145}
}
@ARTICLE{bib:ConstructCI93,
author = {Jennifer Seberry and Xian-Mo Zang and Yuliang Zeng},
title = {\textbf{On constructions and nonlinearity of correlation immune functions}},
journal = {Advances in Cryptology - EUROCRYPTO'93},
year = {1993},
volume = {},
number = {},
pages = {181-199}
}
@ARTICLE{bib:linearAttack93,
author = {Mitsuru Matsui},
title = {\textbf{Linear cryptanalysis method for DES cipher}},
journal = {Advances in Cryptology - EUROCRYPTO'93},
year = {1993},
volume = {},
number = {},
pages = {386-397}
}
@ARTICLE{bib:relationPN95,
author = {Jennifer Seberry and Xian-Mo Zang and Yuliang Zeng},
title = {\textbf{The relationship between propagation characteristic and nonlinearity of cryptographic functions}},
journal = {Journal of Universal Computer Science},
year = {1995},
volume = {1},
number = {2},
pages = {136-150}
}
@ARTICLE{bib:GAC95,
author = {Xian-Mo Zang and Yuliang Zeng},
title = {\textbf{GAC-the criterion of global alvanche characterics of cryptographic function}},
journal = {Journal of Universal Computer Science},
year = {1995},
volume = {1},
number = {5},
pages = {320-337}
}
@ARTICLE{bib:constructCI96,
author = {Seongtaek Chee and Sangjin Lee and Daiki Lee and Soo Hak Sung},
title = {\textbf{On the correlation immune functions and their nonlinearity}},
journal = {Advances in Cryptology -ASIACRYPT'96},
year = {1996},
volume = {},
number = {},
pages = {232-243}
}
@ARTICLE{bib:designsac97,
author = {Kaoru Kurosawa and Takashi},
title = {\textbf{Design of SAC/PC($l$) of order $k$ boolean functions and three other cryptographic criteria}},
journal = {Advances in Cryptology - EUROCRYPTO'97},
year = {1997},
volume = {},
number = {},
pages = {434-449}
}
@ARTICLE{bib:PClk98,
author = {C. Carlet and P. Codes},
title = {\textbf{On the propagation criterion of degree $l$ and order $k$}},
journal = {Advances in Cryptology -EUROCRYPT'98},
year = {1998},
volume = {},
number = {},
pages = {462-474}
}
@ARTICLE{bib:withimportant00,
author = {P. Sarkar and S. Maitra},
title = {\textbf{Construction of nonlinear Boolean functions with important cryptographic properties}},
journal = {Advances in Cryptology -EUROCRYPT2000},
year = {2000},
volume = {},
number = {},
pages = {485-506}
}
@ARTICLE{bib:relationANC00,
author = {Yuliang Zeng and Xian-Mo Zang},
title = {\textbf{On relationships among avalance, nonlinearity and correlation immunity}},
journal = {Advances in Cryptology -ASIACRYPT2000},
year = {2000},
volume = {},
number = {},
pages = {460-480}
}
@TECHREPORT{bib:spectralCIR00,
author = {Palash Sarkar},
title = {\textbf{Spectral domain analysis of correlation immune and resilient boolean functions}},
institution = {Centre for Applied Cryptographic Research},
year = {2000}
}
@ARTICLE{bib:plateau01,
author = {Yuliang Zeng and Xian-Mo Zang},
title = {\textbf{On plateaued functions}},
journal = {IEEE Transation on Information Theory},
year = {2001},
volume = {IT-47},
number = {3},
pages = {1215-1223}
}
@ARTICLE{bib:OptimalCosetOf1stRM01,
author = {Anne Canteaut},
title = {\textbf{On the weight distributions of optimal cosets of the first-order Reed-Muller codes}},
journal = {IEEE Transation on Information Theory},
year = {2001},
volume = {IT-47},
number = {1},
pages = {407-413}
}
@TECHREPORT{bib:HighOfAu00,
author = {Subhamoy Maitra},
title = {\textbf{Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property}},
institution = {Cryptology ePrint Archive, Report 2000/047},
year = {2000}
}
@ARTICLE{bib:newBoundNfofR00,
author = {Palash Sarkar and Subhamony Maitra},
title = {\textbf{Nonlinearity bounds and constructions of resilient boolean functions}},
journal = {Advances in Cryptology -CRYPT2000},
year = {2000},
volume = {},
number = {},
pages = {515-532}
}

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