Cryptanalysis of the Two-Dimensional Circulation Encryption Algorithm

In symmetric-key cryptography, two parties share a secret key K to encrypt messages using a cipher. Symmetric encryption techniques are used to efficiently encrypt data. Two common types of ciphers are commonly used nowadays: block ciphers and stream ciphers. Block ciphers encrypt blocks of data (typically 64 or 128 bits) in a fixed key-dependent way. The design of block ciphers is a well-studied area of research. The best known block ciphers are the Data Encryption Standard (DES) [2] and the Advanced Encryption Standard (AES) [3]. In the past decade, many new attacks on block ciphers have emerged, the most important ones being differential [4] and linear [5] cryptanalysis. Differential cryptanalysis is an example of a chosen-plaintext attack, while linear cryptanalysis is a known-plaintext attack. A good design should at least be resistant to these attacks. Stream ciphers, on the other hand, generate a pseudorandom key stream independent of the plaintext. This key stream is then used to encrypt the plaintext character per character in a time-varying way. In this paper, we will study the security of the recently published two-dimensional circulation encryption algorithm (TDCEA) [1]. This design can be seen as a block cipher, but it also has some properties of a stream cipher. It encrypts blocks of 64 bits at a time by combining each block with the secret key. The outline of this paper is as follows. In Section 2, we briefly describe TDCEA. In Section 3, we study the security of TDCEA. We show several flaws in the algorithm and describe a known-plaintext attack that breaks the cipher in less than 10 seconds on a 1.5GHz PC. We also explain why we believe that it will not be possible to improve the design to be cryptographically sound, as TDCEA lacks many of the desirable properties of a state-of-the-art symmetric encryption algorithm. In Section 4, we address the tradeoffs that need to be made between performance and security of a design. We then discuss the use of concepts from chaos theory in cryptography in Section 5, and conclude in Section 6.