Abstract. Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4 × 4 words diffusion layer. The proposed diffusion layers only require word-level XORs, rotations, and they have simple inverses. They can be replaced in the diffusion layer of the block ciphers MMB and Hierocrypt to increase their security and performance, respectively. Finally, we try to extend our results for up to 8 × 8 words diffusion layers.

Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduce a method for the construction of an MDS matrix from two Vandermonde matrices in the finite field. In this paper, we first suggest a method that makes an involutory MDS matrix from the Vandermonde matrices. Then we propose another method for the construction of 2 n × 2 n Hadamard MDS matrices in the finite field G F(2 q ). In addition to introducing this method, we present a direct method for the inversion of a special class of 2 n × 2 n Vandermonde matrices.Keywords MDS matrix · Vandermonde matrix · Hadamard matrix · Blockcipher Mathematics Subject Classification (2000) 11T71 · 14G50 · 51E22 · 94B05 · 20H30 · 15A09 Communicated by J. Jedwab. M. Sajadieh (B) · M. Dakhilalian

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Security against differential and linear cryptanalysis is an essential requirement for modern block ciphers. This measure is usually evaluated by finding a lower bound for the minimum number of active S-boxes. The 128-bit block cipher AES which was adopted by National Institute of Standards and Technology (NIST) as a symmetric encryption standard in 2001 is a member of Rijndael family of block ciphers. For Rijndael, the block length and the key length can be independently specified to 128, 192 or 256 bits. It has been proved that for all variants of Rijndael the lower bound of the number of active S-boxes for any 4-round differential or linear trail is 25, and for 4r (r ≥ 1) rounds 25r active S-boxes is a tight bound only for Rijndael with block length 128. In this paper, a new counting method is introduced to find tighter lower bounds for the minimum number of active S-boxes for several consecutive rounds of Rijndael with larger block lengths. The new method shows that 12 and 14 rounds of Rijndael with 192-bit block length have at least 87 and 103 active S-boxes, respectively. Also the corresponding bounds for Rijndael with 256-bit block are Communicated by C. Cid. 123 M. Sajadieh et al.105 and 120, respectively. Additionally, a modified version of Rijndael-192 is proposed for which the minimum number of active S-boxes is more than that of . Moreover, we extend the method to obtain a better lower bound for the number of active S-boxes for the block cipher 3D. Our counting method shows that, for example, 20 and 22 rounds of 3D have at least 185 and 205 active S-boxes, respectively.

Abstract. Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a very efficient new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4 × 4 words diffusion layer, which is an indication of highest level of security with respect to linear and differential attacks. We try to extend our results for up to 8 × 8 words diffusion layers. The proposed diffusion layers only require simple operations such as word-level XORs, rotations, and they have simple inverses. They can replace the diffusion layer of several block ciphers and hash functions in the literature to increase their security, and performance. Furthermore, it can be deployed in the design of new efficient lightweight block ciphers and hash functions in future.

In mobile ad hoc networks, a single certificate authority (CA) node could be a security bottleneck. Multiple replica of CA is fault tolerant, but the network is as vulnerable as single CA or even worse since breaking one of the CAs means breaking all of them. In this paper a distributed CA system is proposed which is based on the secret sharing scheme. It is assumed that the network is partitioned into clusters and responsibility of the CA is distributed among the cluster-heads (CHs). Therefore, a valid certificate is produced by a quorum of CHs. Also, based on the proposed distributed CA, an efficient key establishment protocol for intra-cluster and inter-cluster communications is proposed.

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