Abstract. We propose a new cryptographic primitive, the “tweakable block cipher. ” Such a cipher has not only the usual inputs—message and cryptographic key—but also a third input, the “tweak. ” The tweak serves much the same purpose that an initialization vector does for CBC mode or that a nonce does for OCB mode. Our proposal thus brings this feature down to the primitive block-cipher level, instead of incorporating it only at the higher modes-of-operation levels. We suggest that (1) tweakable block ciphers are easy to design, (2) the extra cost of making a block cipher “tweakable ” is small, and (3) it is easier to design and prove modes of operation based on tweakable block ciphers.

In this paper we introduce a new method of attacks on block ciphers, the interpolation attack. This new method is useful for attacking ciphers using simple algebraic functions (in particular quadratic functions) as S-boxes. Also, ciphers of low non-linear order are vulnerable to attacks based on higher order differentials. Recently, Knudsen and Nyberg presented a 6-round prototype cipher which is provably secure against ordinary differential cryptanalysis. We show how to attack the cipher by using higher order differentials and a variant of the cipher by the interpolation attack. It is possible to successfully cryptanalyse up to 32 rounds of the variant using about 2 32 chosen plaintexts with a running time less than 2 64 . Using higher order differentials, a new design concept for block ciphers by Kiefer is also shown to be insecure. Rijmen et al presented a design strategy for block ciphers and the cipher SHARK. We show that there exist ciphers constructed according to this des...

Twofish is a 128-bit block cipher that accepts a variable-length key up to 256 bits. The cipher is a 16-round Feistel network with a bijective F function made up of four key-dependent 8-by-8-bit S-boxes, a fixed 4-by-4 maximum distance separable matrix over GF(2 8 ), a pseudo-Hadamard transform, bitwise rotations, and a carefully designed key schedule. A fully optimized implementation of Twofish encrypts on a Pentium Pro at 17.8 clock cycles per byte, and an 8-bit smart card implementation encrypts at 1660 clock cycles per byte. Twofish can be implemented in hardware in 14000 gates. The design of both the round function and the key schedule permits a wide variety of tradeoffs between speed, software size, key setup time, gate count, and memory. We have extensively cryptanalyzed Twofish; our best attack breaks 5 rounds with 2 22.5 chosen plaintexts and 2 51 effort.

Choosing the most storage- and energy-e#cient block cipher specifically for wireless sensor networks (WSNs) is not as straightforward as it seems. To our knowledge so far, there is no systematic evaluation framework for the purpose. In this paper, we have identified the candidates of block ciphers suitable for WSNs based on existing literature.

We study [2m −1, 2m]-binary linear codes whose weights lie between w0 and 2m −w0, where w0 takes the highest possible value. Primitive cyclic codes with two zeros whose dual satisfies this property actually correspond to almost bent power functions and to pairs of maximum-length sequences with preferred crosscorrelation. We prove that, for odd m, these codes are completely characterized by their dual distance and by their weight divisibility. Using McEliece’s theorem we give some general results on the weight divisibility of duals of cyclic codes with two zeros; specifically, we exhibit some infinite families of pairs of maximum-length sequences which are not preferred.

Abstract. In the SPN (Substitution-Permutation Network) structure, it is very important to design a diffusion layer to construct a secure block cipher against differential cryptanalysis and linear cryptanalysis. The purpose of this work is to prove that the SPN structure with a maximal diffusion layer provides a provable security against differential cryptanalysis and linear cryptanalysis in the sense that the probability of each differential (respectively linear hull) is bounded by p n (respectively q n), where p (respectively q) is the maximum differential (respectively liner hull) probability of nS-boxes used in the substitution layer. We will also give a provable security for the SPN structure with a semi-maximal diffusion layer against differential cryptanalysis and linear cryptanalysis. 1

Abstract. We present a new algorithm for upper bounding the maximum average linear hull probability for SPNs, a value required to determine provable security against linear cryptanalysis. The best previous result (Hong et al. [9]) applies only when the linear transformation branch number (B) is M or (M + 1) (maximal case), where M is the number of s-boxes per round. In contrast, our upper bound can be computed for any value of B. Moreover, the new upper bound is a function of the number of rounds (other upper bounds known to the authors are not). When B = M, our upper bound is consistently superior to [9]. When B = (M + 1), our upper bound does not appear to improve on [9]. On application to Rijndael (128-bit block size, 10 rounds), we obtain the upper bound UB = 2 −75, corresponding to a lower bound on the data 8 complexity of UB = 278 (for 96.7 % success rate). Note that this does not demonstrate the existence of a such an attack, but is, to our knowledge, the first such lower bound.

: In this paper, we present a detailed tutorial on linear cryptanalysis and differential cryptanalysis, the two most significant attacks applicable to symmetric-key block ciphers. The intent of the paper is to present a lucid explanation of the attacks, detailing the practical application of the attacks to a cipher in a simple, conceptually revealing manner for the novice cryptanalyst. The tutorial is based on the analysis of a simple, yet realistically structured, basic Substitution-Permutation Network cipher. Understanding the attacks as they apply to this structure is useful, as the Rijndael cipher, recently selected for the Advanced Encryption Standard (AES), has been derived from the basic SPN architecture. As well, experimental data from the attacks is presented as confirmation of the applicability of the concepts as outlined.

In [15], Keliher et al. present a new method for upper bounding the maximum average linear hull probability (MALHP) for SPNs, a value which is required to make claims about provable security against linear cryptanalysis. Application of this method to Rijndael (AES) yields an upper bound of UB = 2 \Gamma75 when 7 or more rounds are approximated, corresponding to a lower bound on the data complexity of 32 UB = 2 80 (for a 96.7% success rate). In the current paper, we improve this upper bound for Rijndael by taking into consideration the distribution of linear probability values for the (unique) Rijndael 8 \Theta 8 s-box. Our new upper bound on the MALHP when 9 rounds are approximated is 2 \Gamma92 , corresponding to a lower bound on the data complexity of 2 97 (again for a 96.7% success rate). [This is after completing 43% of the computation; however, we believe that values have stabilized---see Section 7.] Keywords: linear cryptanalysis, maximum average linear hull probability, provable security, Rijndael, AES 1

Abstract. We study the functions from F m 2 into F m 2 for odd m which oppose an optimal resistance to linear cryptanalysis. These functions are called almost bent. It is known that almost bent functions are also almost perfect nonlinear, i.e. they also ensure an optimal resistance to differential cryptanalysis but the converse is not true. We here give a necessary and sufficient condition for an almost perfect nonlinear function to be almost bent. This notably enables us to exhibit some infinite families of power functions which are not almost bent. 1