On Elastic Block Ciphers and Their Differential and Linear Cryptanalyses

Motivated by applications such as databases with nonuniform field lengths, we introduce the concept of an elastic block cipher, a new approach to variable length block ciphers which incorporates fixed sized cipher components into a new network structure. Our scheme allows us to dynamically “stretch” the supported block size of a block cipher up to a length double the original block size, while increasing the computational workload proportionally to the block size. We show that traditional attacks against an elastic block cipher are impractical if the original cipher is secure. In this paper we focus on differential and linear attacks. Specifically, we employ an elastic version of Rijndael supporting block sizes of 128 to 256 bits as an example, and show it is resistant to both differential and linear attacks. In particular, employing a different method than what is employed in Rijndael design, we show that the probability of any differential characteristic for the elastic version of Rijndael is ≤ 2. We further prove that both linear and nonlinear attacks are computationally infeasible for any elastic block cipher if the original cipher is not subject to such an attack and involves a block size for which an exhaustive plaintext search is computationally infeasible (as is the case for Rijndael).