ZHUO Zepeng, CHONG Jinfeng. On Algebraic Immunity of Boolean Functions by Concatenation[J]. Chinese Journal of Electronics, 2013, 22(2): 273-276.
Citation: ZHUO Zepeng, CHONG Jinfeng. On Algebraic Immunity of Boolean Functions by Concatenation[J]. Chinese Journal of Electronics, 2013, 22(2): 273-276.

On Algebraic Immunity of Boolean Functions by Concatenation

Funds:  This work is supported by the Anhui Provincial Natural Science Foundation (No.1208085QF119), the Natural Science Foundation of Anhui Higher Education Institutions of China (No.KJ2012z353).
  • Received Date: 2012-04-01
  • Rev Recd Date: 2012-06-01
  • Publish Date: 2013-04-25
  • Algebraic immunity measures the resistance of a Boolean function against algebraic attack. To resist algebraic attack, a Boolean function should possess high algebraic immunity. Concatenation is an important method by which we can construct Boolean functions with good cryptographic properties. In this paper, we investigate certain classes of Boolean functions g=f1||f2||f3||f4 for their algebraic immunity. When n is even, we obtain two special classes (n+2)-variable Boolean functions with maximum algebraic immunity. Last, for an odd integer n, we get the divisibility result on the weights of Boolean functions with maximum possible algebraic immunity.
  • loading
  • N. Courtois and J. Pieprzyk, "Cryptanalysis of block ciphers with overdefined systems of equations", Advances in Cryptology-ASIACRYPT 2002, Lecture Notes in Computer Science, Berlin: Springer-Verlag, pp.267-287, 2002.
    N. Courtois and W. Meier, "Algebraic attacks on stream ciphers with linear feedback", Advances in Cryptology-EUROCRYPT 2003, Lecture Notes in Computer Science, Berlin: Springer- Verlag, pp.346-359, 2003.
    N. Courtois, "Fast algebraic attacks on stream ciphers with linear feedback", Advances in Cryptology-CRYPTO 2003, Lecture Notes in Computer Science, Berlin: Springer-Verlag, pp.176- 194, 2003.
    F. Armknecht and M. Krause, "Algebraic attacks on stream combiners with memory", Advances in Cryptology-CRYPTO 2003, Lecture Notes in Computer Science, Berlin: Springer- Verlag, pp.162-176, 2003.
    F. Armknecht, "Improving fast algebraic attacks", Advances in FSE 2004, Lecture Notes in Computer Science, Berlin: Springer-Verlag, pp.65-82, 2004.
    W. Meier, E. Pasalic and C. Carlet, "Algebraic attacks and decomposition of Boolean functions", Advances in Cryptology- EUROCRYPT 2004, Lecture Notes in Computer Science, Berlin: Springer-Verlag, pp.474-491, 2004.
    C. Carlet, D.K. Dalai, K.C. Gupa and S. Maitra, "Algebraic immunity for cryptographically significant Boolean functions: Analysis and construction", IEEE Transactions on Information Theory, Vol.52, No.7, pp.3105-3121, 2006.
    C.E. Shannon, "Communication theory of secrecy systems", Bell System Technical Journal, Vol.28-4, pp.656-715, 1949.
    S. Maitra and E. Pasalic, "Further constructions of resilient Boolean functions with very high nonlinearity", IEEE Transactions on Information Theory, Vol.48, No.7, pp.1825-1834, 2002.
    C. Carlet, "A method of construction of balanced functions with the optimum algebraic immunity", http://eprint. iacr.org/2006/149.pdf.
    Longjiang Qu, Guozhen Feng, Chao Li, "On the Boolean functions with maximum possible algebraic immunity: Construction and a lower bound of the count", http://eprint. iacr.org/2005/449.pdf.
    Na Li, Wenfeng Qi, "Construction and count of Boolean functions of an odd number of variables with maximum algebraic immunity", http:// arxiv.org/abs/cs.CR/0605139.
    Na Li, Wenfeng Qi, "Boolean functions of an odd number of variables with maximum algebraic immunity", Science in China Series F: Information Sciences, Vol.50, No.3, pp.307-317, 2007.
    Yusong Du, Dingyi Pei, "Constructions of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree", Science in China Series F: Information Sciences, Vol.53, No.4, pp.780-787, 2010.
    Guanghong Sun, Chuankun Wu, "Some cryptographic properties of Boolean functions by concatenation", Acta Electronica Sinica, Vol.37, No.4, pp.884-888, 2009. (in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (326) PDF downloads(1132) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return