Marios Georgiou

Nicolas T. Courtois, Marios Georgiou

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 algebraic approach which is about making sure that a certain combination of polynomial equations is zero. We work with an old block cipher from 1980s which has particularly large hardware complexity compared to modern ciphers e.g. AES. However all this complexity is not that useful if we are able to construct powerful non-linear invariants which work for any number of rounds. A key feature of our invariant attacks is that we are able to completely eliminate numerous state and key bits. We also construct invariants for the (presumably stronger) KT1 keys. Some of these lead to powerful ciphertext-only correlation attacks.

Marios Georgiou

T-310 is a cipher that was used for encryption of governmental communications in East Germany during the final years of the Cold War. Due to its complexity and the encryption process,there was no published attack for a period of more than 40 years until 2018 by Nicolas T. Courtois et al. in [10]. In this thesis we study the so called 'long term keys' that were used in the cipher, in order to expose weaknesses which will assist the design of various attacks on T-310.