Evolutionary block cipher against multidimensional linear and differential cryptanalysis

Cryptology is one of the most important techniques in the field of information security, which provides an abundance of services including privacy, data integrity, authentication, access control, anonymity, non-repudiation. The high level of security, efficiency and ease of implementation of a cryptosystem are the main design aims of cryptographers. Prof. ZHANG Huanguo and his group from Key Laboratory of Aerospace Information Security and Trusted Computing of Ministry of Education, Wuhan University, have been undertaking research on a entirely new cryptography—Evolutionary Cryptography—during the past 10 years, and have achieved a series of impressive research results on the design, hardware/software implementation and cryptanalysis of the evolutionary cryptography. Their latest work, titled "Capability of evolutionary cryptosystems against differential cryptanalysis" and "Evolutionary cryptography against multidimensional linear cryptanalysis", were published in Refs.[2] and [1] respectively.

In modern times, the term cryptosystem refers to the ordered list of elements of finite possible plaintexts (P), finite possible ciphertexts (C), finite possible keys (K), and algorithms for encryption (E) and decryption (D). Encryption is the process of converting plaintext into unintelligible ciphertext, whereas decryption is the reverse process to encryption that reveals the plaintext from the unintelligible ciphertext. From a mathematical point of view, a cryptosystem can be precisely expressed as a five-tuple (P, C, K, E, D). Up to now, all known cryptosystems have been designed to encrypt and decrypt the data with fixed algorithms and randomly-changed key. More specifically, suppose E is an encryption algorithm and K=K0K1…Kt-1 is the key, the process of encrypting plaintexts P=P0P1…Pt-1 is as below:

C0=E(P0, K0), C1=E(P1, K1), …, Ct-1=E(Pt-1, Kt-1),
where P, C, K belong to the plaintexts set P, the ciphertexts set C and the keys set K respectively.

Inspired by the fact that frequent replacement of the key contributes to a cryptosystem's high secrecy level and the success of evolutionary computing, which applies biological evolution into computer science, Prof. ZHANG Huanguo concentrated on replacing both encryption algorithms and keys, and introduced a novel encryption scheme Evolutionary Cryptography. This scheme is distinguished from known cryptographies by two features: the encryption/decryption algorithms are alterable instead of being fixed and the encryption algorithms are replaced with increasingly cryptographically-strong ones from time to time. It can be roughly described in the following way: suppose E-r is an initial encryption algorithm with low level of security, the encryption scheme starting from E-r, evolves through E-r+1, … , E0, E1,…, Et-1 with increasingly higher levels of security. The evolving phase from E-r to E0 acts like an embryonic stage. In this embryonic stage, the encryption algorithm E-i does not in practice meet security requirements until it evolves into E0, but afterwards it is secure enough to be used in practical applications and its security level becomes increasingly higher as the process evolves. The evolution process of the encryption algorithms is characterized as follows:

E-r → E-r+1→E-r+2→… →E-1→E0→E1→… →Et-1
S(E-r) END