New insights on linear cryptanalysis

Linear cryptanalysis is one of the most important cryptanalytic tools against block ciphers, thus modern block ciphers are always deliberately devised to avoid good long linear characteristics so as to resist linear cryptanalysis and its extensions. Differential-linear cryptanalysis, a powerful extension of linear cryptanalysis, has drawn much attention due to its applicability even in certain case that there is no good long linear characteristic of block ciphers. To further refine differential-linear cryptanalysis, we investigate the correlation distribution of differential-linear hull over random permutation and derive a concrete and concise correlation distribution accordingly. Theoretically, this could make differential-linear cryptanalysis more reasonable and precise. Moreover, the newly-proposed correlation distribution could lead to an interesting potential for improving the effectiveness of differential-linear cryptanalysis.

[1]  Andrey Bogdanov,et al.  On the (In)Equivalence of Impossible Differential and Zero-Correlation Distinguishers for Feistel- and Skipjack-Type Ciphers , 2014, ACNS.

[2]  Serge Vaudenay,et al.  How Far Can We Go Beyond Linear Cryptanalysis? , 2004, ASIACRYPT.

[3]  Jing Zhang,et al.  Differential-Multiple Linear Cryptanalysis , 2009, Inscrypt.

[4]  Andrey Bogdanov,et al.  Zero Correlation Linear Cryptanalysis with Reduced Data Complexity , 2012, FSE.

[5]  Kaisa Nyberg,et al.  Multidimensional Extension of Matsui's Algorithm 2 , 2009, FSE.

[6]  Susan K. Langford,et al.  Differential-Linear Cryptanalysis , 1994, CRYPTO.

[7]  Matthew J. B. Robshaw,et al.  Non-Linear Approximations in Linear Cryptanalysis , 1996, EUROCRYPT.

[8]  Kaisa Nyberg,et al.  New Links Between Differential and Linear Cryptanalysis , 2015, IACR Cryptol. ePrint Arch..

[9]  Kaisa Nyberg,et al.  Joint data and key distribution of simple, multiple, and multidimensional linear cryptanalysis test statistic and its impact to data complexity , 2017, Des. Codes Cryptogr..

[10]  Jason Smith,et al.  The SIMON and SPECK Families of Lightweight Block Ciphers , 2013, IACR Cryptol. ePrint Arch..

[11]  Kaisa Nyberg,et al.  Improved Parameter Estimates for Correlation and Capacity Deviates in Linear Cryptanalysis , 2017, IACR Trans. Symmetric Cryptol..

[12]  Vincent Rijmen,et al.  Cryptanalysis of Reduced-Round SIMON32 and SIMON48 , 2014, INDOCRYPT.

[13]  Vincent Rijmen,et al.  Links Among Impossible Differential, Integral and Zero Correlation Linear Cryptanalysis , 2015, CRYPTO.

[14]  Serge Vaudenay,et al.  Links Between Differential and Linear Cryptanalysis , 1994, EUROCRYPT.

[15]  Kaisa Nyberg,et al.  A New Technique for Multidimensional Linear Cryptanalysis with Applications on Reduced Round Serpent , 2008, ICISC.

[16]  Jiqiang Lu.  A methodology for differential-linear cryptanalysis and its applications , 2015, Des. Codes Cryptogr..

[17]  Alex Biryukov,et al.  Differential Analysis of Block Ciphers SIMON and SPECK , 2014, FSE.

[18]  Gaëtan Leurent,et al.  Improved Differential-Linear Cryptanalysis of 7-Round Chaskey with Partitioning , 2016, EUROCRYPT.

[19]  Andrey Bogdanov,et al.  Multidimensional zero-correlation attacks on lightweight block cipher HIGHT: Improved cryptanalysis of an ISO standard , 2014, Inf. Process. Lett..

[20]  Kaisa Nyberg,et al.  Links Between Truncated Differential and Multidimensional Linear Properties of Block Ciphers and Underlying Attack Complexities , 2014, IACR Cryptol. ePrint Arch..

[21]  Kaisa Nyberg,et al.  Statistical Tests for Key Recovery Using Multidimensional Extension of Matsui's Algorithm 1 , 2009, Symmetric Cryptography.

[22]  Kaisa Nyberg,et al.  Multidimensional Linear Cryptanalysis of Reduced Round Serpent , 2008, ACISP.

[23]  Amr M. Youssef,et al.  Multidimensional Zero-Correlation Linear Cryptanalysis of Reduced Round SPARX-128 , 2017, SAC.

[24]  Alex Biryukov,et al.  On Multiple Linear Approximations , 2004, IACR Cryptol. ePrint Arch..

[25]  Eli Biham,et al.  Enhancing Differential-Linear Cryptanalysis , 2002, ASIACRYPT.

[26]  Vincent Rijmen,et al.  Probability distributions of correlation and differentials in block ciphers , 2007, J. Math. Cryptol..

[27]  Gregor Leander,et al.  On Linear Hulls, Statistical Saturation Attacks, PRESENT and a Cryptanalysis of PUFFIN , 2011, EUROCRYPT.

[28]  Matthew J. B. Robshaw,et al.  Linear Cryptanalysis Using Multiple Approximations , 1994, CRYPTO.

[29]  Carlo Harpes,et al.  A Generalization of Linear Cryptanalysis and the Applicability of Matsui's Piling-Up Lemma , 1995, EUROCRYPT.

[30]  Shaozhen Chen,et al.  Multidimensional zero-correlation linear cryptanalysis of the block cipher KASUMI , 2016, IET Inf. Secur..

[31]  Vincent Rijmen,et al.  Linear hulls with correlation zero and linear cryptanalysis of block ciphers , 2014, Des. Codes Cryptogr..

[32]  Nicolas Courtois.  Feistel Schemes and Bi-linear Cryptanalysis , 2004, CRYPTO.

[33]  Jiqiang Lu.  A Methodology for Differential-Linear Cryptanalysis and Its Applications - (Extended Abstract) , 2012, FSE.

[34]  Andrey Bogdanov,et al.  Integral and Multidimensional Linear Distinguishers with Correlation Zero , 2012, ASIACRYPT.

[35]  Gregor Leander,et al.  Differential-Linear Cryptanalysis Revisited , 2014, FSE.

[36]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[37]  Eli Biham,et al.  An Improvement of Linear Cryptanalysis with Addition Operations with Applications to FEAL-8X , 2014, Selected Areas in Cryptography.

[38]  Wenling Wu,et al.  Improved Multidimensional Zero-Correlation Linear Cryptanalysis and Applications to LBlock and TWINE , 2014, ACISP.