The algebraic immunity of nonlinear nodes symmetric ciphers
Keywords:
symmetric ciphers, algebraic immunity, nonlinear replacement nodes
Abstract
Researched methods for computing algebraic immunity cryptographic Boolean functions and nonlinear knots of replacements (substitutions) of symmetric ciphers. The presented results of a comparative analysis algebraic immunity of non-linear nodes of symmetric ciphers.
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References
Menezes A. J. Handbook of Applied Cryptography / Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. – CRC Press, 1997. – 794 р.
Gorbenko I.D. Prykladna kryptologija. Teorija. Praktyka. Zastosuvannja: pidruchnyk dlja vyshhyh navch. zakladiv / I.D. Gorbenko, Ju.I. Gorbenko. – Kharkiv: Vyd-vo «Fort», 2013. – 880 s.
Preneel B. Analysis and Design of Cryptographic Hash Functions [Electronic resource]. – Way of access: homes.esat.kuleuven.be/~preneel/phd_preneel_feb1993.pdf.
Carlet C. Vectorial boolean functions for cryptography. – Cambridge: Cambridge Univ. Press. – 95 p. [Electronic resource]. – Way of access: www.math.univ-paris13.fr/~carlet/chap-vectorial-fcts-corr.pdf.
Carlet C. Boolean functions for cryptography and error correcting codes. – Cambridge : Cambridge Univ. Press, 2007. – 148 p. [Electronic resource]. – Access mode: www1.spms.ntu.edu.sg/~kkhoongm/chap-fcts-Bool.pdf.
Zepeng Z. On correlation properties of Boolean functions / Zhuo Zepeng, Zhang Weiguo // Chinese Journal of Electronics. –2011. – Vol.20. – №1. – Р.143-146.
O’Connor L. An analysis of a class of algorithms for S-box construction / L. O’Connor // J. Cryptology. – 1994. – Р. 133-151.
Clark J.A., Jacob J.L., Stepney S. The Design of S-Boxes by Simulated Annealing / J.A. Clark, J.L. Jacob, S. Stepney // New Generation Computing. – 2005. – Issue 23(3). – Р.219–231.
Kuznetsov A.A. Analiz i sravnitel'nye issledovaniya nelineinykh uzlov zameny sovremennykh blochnykh simmetrichnykh shifrov / A.A. Kuznetsov, I.N. Belozertsev, A.V. Andrushkevich // Prikladnaya radioelektronika. – 2015. – T.14. – №4. – S. 343 – 350.
Courtois N. Algebraic Attacks on Stream Ciphers with Linear Feedback / N. Courtois, W. Meier // Eurocrypt 2003: LNCS. – 2003. – Vol.2656. – Р. 345-359.
Meier W. Algebraic Attacks and Decomposition of Boolean Functions / W. Meier, E. Pasalic, C. Carlet // Eurocrypt 2004: LNCS. – 2004. – Vol.3027. – Р. 474-491.
Courtois N. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations / Nicolas Courtois, Josef Pieprzyk // LNCS. – 2002. – Vol.2501. – Р.267–287.
Ars G. Algebraic Immunities of functions over finite fields / Gw´enol´e Ars, Jean-Charles Faug`ere // RR-5532: [Research Report]. – INRIA, 2005. – Р.17.
Baev V. V. Effektivnye algoritmy polucheniya otsenok algebraicheskoi immunnosti bulevykh funktsii: dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk : 01.01.09 / Baev Vladimir Valer'evich; [Mesto zashchity: Mosk. gos. un-t im. M.V. Lomonosova. Fak. vychislit. matematiki i kibernetiki]. – Moskva, 2008. – 101 s.
Arzhantsev I.V. Bazisy Grebnera i sistemy algebraicheskikh uravnenii / I.V. Arzhantsev. // Sovremennaya matematika: Letnyaya shkola (Dubna, iyul' 2002). – Moskva: MTsNMO, 2003. – 68 s.
Zlobin A.I. Komp'yuternaya algebra v sisteme Sage: uchebnoe posobie / A.I. Zlobin, O.V. Sokolova. – Moskva: MGTU im. Baumana, 2011. – 55 s.
Faugère J.-C. A new efficient algorithm for computing Gröbner bases / J.-C. Faugère // Journal of Pure and Applied Algebra: [F4]. –1999. – Issue 139 (1). – Р.61–88.
Faugère J.-C. A new efficient algorithm for computing Gröbner bases without reduction to zero / J.-C. Faugère // Proceedings of the International Symposium on Symbolic and algebraic computation (ISSAC, 2002, July): [F5]. – 2002. – Р.75–83.
Gröbner Bases, Coding, and Cryptography / Massimiliano Sala, Teo Mora, Ludovic Perret, Shojiro Sakata, Carlo Traverso. – Berlin: Springer-Verlag Heidelberg. – 426 p.
FIPS 197. National Institute of Standards and Technology: Advanced Encryption Standard. – 2001 [Electronic resource]. – Way of access: http://www.nist.gov/aes. – Title from the screen.
ISO/IEC 18033-3. Information technology – Security techniques – Encryption algorithms, Part 3: Block ciphers. – 80 p.
DSTU 7624:2014. Informacijni tehnologii'. Kryptografichnyj zahyst informacii'. Algorytm symetrychnogo blokovogo pe-retvorennja. – Kyi'v: Minekonomrozvytku Ukrai'ny, 2015. – 238 s.
GOST R 34.12-2015. Informatsionnaya tekhnologiya. Kriptograficheskaya zashchita informatsii. Blochnye shifry. – Moskva: Standartinform, 2015. – 25 s.
STB 34.101.31-2011. Informatsionnye tekhnologii i bezopasnost'. Kriptograficheskie algoritmy shifrovaniya i kontrolya tselostnosti. – Minsk: Gosstandart, 2011. – 32 s.
ISO/IEC 10118-3:2004. Information technology – Security techniques – Hash-functions – Part 3: Dedicated hash-functions. – 94 p.
Magma Computational Algebra System [Electronic resource]. – Way of access: http://magma.maths.usyd.edu.au/magma. – Title from the screen.
Courtois N. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations / Nicolas Courtois, Alexander Klimov, Jacques Patarin, Adi Shamir // Proceedings of the 19th international conference on Theory and application of cryptographic techniques EUROCRYPT'00. – 2000. – P. 392 – 407.
Courtois N. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations / Nicolas Courtois, Josef Pieprzyk // Advances in cryptology (ASIACRYPT, 2002). – 2002. – Р. 267-287.
Pyshkin A. Algebraic Cryptanalysis of Block Ciphers Using Grobner Bases: Dissertation zur Erlangung des Grades Doktor rerum naturalium / Andrey Pyshkin; [Technischen Universitat Darmstadt]. – Darmstadt, 2008. – 118 р.
Gorbenko I.D. Prykladna kryptologija. Teorija. Praktyka. Zastosuvannja: pidruchnyk dlja vyshhyh navch. zakladiv / I.D. Gorbenko, Ju.I. Gorbenko. – Kharkiv: Vyd-vo «Fort», 2013. – 880 s.
Preneel B. Analysis and Design of Cryptographic Hash Functions [Electronic resource]. – Way of access: homes.esat.kuleuven.be/~preneel/phd_preneel_feb1993.pdf.
Carlet C. Vectorial boolean functions for cryptography. – Cambridge: Cambridge Univ. Press. – 95 p. [Electronic resource]. – Way of access: www.math.univ-paris13.fr/~carlet/chap-vectorial-fcts-corr.pdf.
Carlet C. Boolean functions for cryptography and error correcting codes. – Cambridge : Cambridge Univ. Press, 2007. – 148 p. [Electronic resource]. – Access mode: www1.spms.ntu.edu.sg/~kkhoongm/chap-fcts-Bool.pdf.
Zepeng Z. On correlation properties of Boolean functions / Zhuo Zepeng, Zhang Weiguo // Chinese Journal of Electronics. –2011. – Vol.20. – №1. – Р.143-146.
O’Connor L. An analysis of a class of algorithms for S-box construction / L. O’Connor // J. Cryptology. – 1994. – Р. 133-151.
Clark J.A., Jacob J.L., Stepney S. The Design of S-Boxes by Simulated Annealing / J.A. Clark, J.L. Jacob, S. Stepney // New Generation Computing. – 2005. – Issue 23(3). – Р.219–231.
Kuznetsov A.A. Analiz i sravnitel'nye issledovaniya nelineinykh uzlov zameny sovremennykh blochnykh simmetrichnykh shifrov / A.A. Kuznetsov, I.N. Belozertsev, A.V. Andrushkevich // Prikladnaya radioelektronika. – 2015. – T.14. – №4. – S. 343 – 350.
Courtois N. Algebraic Attacks on Stream Ciphers with Linear Feedback / N. Courtois, W. Meier // Eurocrypt 2003: LNCS. – 2003. – Vol.2656. – Р. 345-359.
Meier W. Algebraic Attacks and Decomposition of Boolean Functions / W. Meier, E. Pasalic, C. Carlet // Eurocrypt 2004: LNCS. – 2004. – Vol.3027. – Р. 474-491.
Courtois N. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations / Nicolas Courtois, Josef Pieprzyk // LNCS. – 2002. – Vol.2501. – Р.267–287.
Ars G. Algebraic Immunities of functions over finite fields / Gw´enol´e Ars, Jean-Charles Faug`ere // RR-5532: [Research Report]. – INRIA, 2005. – Р.17.
Baev V. V. Effektivnye algoritmy polucheniya otsenok algebraicheskoi immunnosti bulevykh funktsii: dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk : 01.01.09 / Baev Vladimir Valer'evich; [Mesto zashchity: Mosk. gos. un-t im. M.V. Lomonosova. Fak. vychislit. matematiki i kibernetiki]. – Moskva, 2008. – 101 s.
Arzhantsev I.V. Bazisy Grebnera i sistemy algebraicheskikh uravnenii / I.V. Arzhantsev. // Sovremennaya matematika: Letnyaya shkola (Dubna, iyul' 2002). – Moskva: MTsNMO, 2003. – 68 s.
Zlobin A.I. Komp'yuternaya algebra v sisteme Sage: uchebnoe posobie / A.I. Zlobin, O.V. Sokolova. – Moskva: MGTU im. Baumana, 2011. – 55 s.
Faugère J.-C. A new efficient algorithm for computing Gröbner bases / J.-C. Faugère // Journal of Pure and Applied Algebra: [F4]. –1999. – Issue 139 (1). – Р.61–88.
Faugère J.-C. A new efficient algorithm for computing Gröbner bases without reduction to zero / J.-C. Faugère // Proceedings of the International Symposium on Symbolic and algebraic computation (ISSAC, 2002, July): [F5]. – 2002. – Р.75–83.
Gröbner Bases, Coding, and Cryptography / Massimiliano Sala, Teo Mora, Ludovic Perret, Shojiro Sakata, Carlo Traverso. – Berlin: Springer-Verlag Heidelberg. – 426 p.
FIPS 197. National Institute of Standards and Technology: Advanced Encryption Standard. – 2001 [Electronic resource]. – Way of access: http://www.nist.gov/aes. – Title from the screen.
ISO/IEC 18033-3. Information technology – Security techniques – Encryption algorithms, Part 3: Block ciphers. – 80 p.
DSTU 7624:2014. Informacijni tehnologii'. Kryptografichnyj zahyst informacii'. Algorytm symetrychnogo blokovogo pe-retvorennja. – Kyi'v: Minekonomrozvytku Ukrai'ny, 2015. – 238 s.
GOST R 34.12-2015. Informatsionnaya tekhnologiya. Kriptograficheskaya zashchita informatsii. Blochnye shifry. – Moskva: Standartinform, 2015. – 25 s.
STB 34.101.31-2011. Informatsionnye tekhnologii i bezopasnost'. Kriptograficheskie algoritmy shifrovaniya i kontrolya tselostnosti. – Minsk: Gosstandart, 2011. – 32 s.
ISO/IEC 10118-3:2004. Information technology – Security techniques – Hash-functions – Part 3: Dedicated hash-functions. – 94 p.
Magma Computational Algebra System [Electronic resource]. – Way of access: http://magma.maths.usyd.edu.au/magma. – Title from the screen.
Courtois N. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations / Nicolas Courtois, Alexander Klimov, Jacques Patarin, Adi Shamir // Proceedings of the 19th international conference on Theory and application of cryptographic techniques EUROCRYPT'00. – 2000. – P. 392 – 407.
Courtois N. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations / Nicolas Courtois, Josef Pieprzyk // Advances in cryptology (ASIACRYPT, 2002). – 2002. – Р. 267-287.
Pyshkin A. Algebraic Cryptanalysis of Block Ciphers Using Grobner Bases: Dissertation zur Erlangung des Grades Doktor rerum naturalium / Andrey Pyshkin; [Technischen Universitat Darmstadt]. – Darmstadt, 2008. – 118 р.
Published
2017-03-26
Cited
How to Cite
Kuznetsov, A., Gorbenko, Y., Belozertsev, I., Andrushkevich, A., & Naregniy, A. (2017). The algebraic immunity of nonlinear nodes symmetric ciphers. Computer Science and Cybersecurity, (4), 42-55. Retrieved from https://periodicals.karazin.ua/cscs/article/view/8267
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