Imprimitive permutations groups generated by the round functions of key-alternating block ciphers and truncated differential cryptanalysis

On some block ciphers and imprimitive groups

The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the SERPENT.

Constructive Non-Linear Polynomial Cryptanalysis of a Historical Block Cipher

One of the major open problems in symmetric cryptanalysis is to discover new specif i c types of invariant properties which can hold for a larger number of rounds of a block cipher. We have Generalised Linear Cryptanalysis (GLC) and Partitioning Cryptanalysis (PC). Due to double-exponential combinatorial explosion of the number of possible invariant properties systematic exploration is not possible and extremely few positive working examples of GLC are known. Our answer is to work with polynomial algebraic invariants which makes partitions more intelligible. We have developed a constructive al…

The role of Boolean functions in hiding sums as trapdoors for some block ciphers

Most modern block ciphers are built using components whose cryptographic strength is evaluated in terms of their resistance to attacks on the whole cipher. In particular, differential properties of vectorial Boolean functions are studied for the S-Boxes to thwart differential cryptanalysis. Little is known on similar properties to avoid trapdoors in the design of the block cipher. In this paper we present a form of trapdoors coming from alternative vector space structures, which we call hidden sums, and give a characterization on the Boolean function S-Box to avoid any such hidden sum. We also…

Wave-Shaped Round Functions and Primitive Groups

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. The bijectivity of any encryption function, crucial in order to make the decryption possible, is guaranteed by the use of invertible layers or by the Feistel structure. In this work a new family of ciphers, called wave ciphers, is introduced. In wave ciphers, round functions feature wave functions, which are vectorial Boolean functions ob…

使用并行替代运算的差分实验

Differential experiments using parallel alternative operations

本文将基于替代差分运算的攻击扩展至作用于分组每个s-box的并行替代运算，通过数学框架回顾与玩具密码实验，验证了其相较于XOR-差分攻击的有效性。