Protecting Against Multidimensional Linear and Truncated Differential Cryptanalysis by Decorrelation

The decorrelation theory provides a different point of view on the security of block cipher primitives. Results on some statistical attacks obtained in this context can support or provide new insight on the security of symmetric cryptographic primitives. In this paper, we study, for the first time, the multidimensional linear attacks as well as the truncated differential attacks in this context. We show that the cipher should be decorrelated of order two to be resistant against some multidimensional linear and truncated differential attacks. Previous results obtained with this theory for linear, differential, differential-linear and boomerang attacks are also resumed and improved in this paper.

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

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

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

[4]  Serge Vaudenay,et al.  Resistance against Iterated Attacks by Decorrelation Revisited, , 2012, CRYPTO.

[5]  Larry Carter,et al.  New Hash Functions and Their Use in Authentication and Set Equality , 1981, J. Comput. Syst. Sci..

[6]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[7]  Serge Vaudenay,et al.  Decorrelation: A Theory for Block Cipher Security , 2003, Journal of Cryptology.

[8]  Serge Vaudenay,et al.  Adaptive-Attack Norm for Decorrelation and Super-Pseudorandomness , 1999, Selected Areas in Cryptography.

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

[10]  Lars R. Knudsen,et al.  Truncated and Higher Order Differentials , 1994, FSE.

[11]  Serge Vaudenay,et al.  Resistance against Adaptive Plaintext-Ciphertext Iterated Distinguishers , 2012, INDOCRYPT.

[12]  Serge Vaudenay,et al.  Provable Security for Block Ciphers by Decorrelation , 1998, STACS.

[13]  Serge Vaudenay,et al.  Revisiting iterated attacks in the context of decorrelation theory , 2014, Cryptography and Communications.

[14]  David A. Wagner,et al.  The Boomerang Attack , 1999, FSE.

[15]  Eli Biham,et al.  Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials , 1999 .

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

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

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

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

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

[21]  Aslı Bay.  Provable Security of Block Ciphers and Cryptanalysis , 2014 .

[22]  Jakub Töpfer.  Links Between Differential and Linear Cryptanalysis , 2015 .

[23]  Serge Vaudenay,et al.  Resistance Against General Iterated Attacks , 1999, EUROCRYPT.