TL;DR: In this article, the security of S-boxes in block ciphers was studied under an additional hypothesis that the S-box can be described by an overdefined system of algebraic equations.
Abstract: Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds Nr.In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt'00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure.The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in Nr, with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.
TL;DR: It is confirmed that Camellia provides strong security against differential and linear cryptanalyses and at least comparable encryption speed in software and hardware.
Abstract: We present a new 128-bit block cipher called Camellia. Camellia supports 128-bit block size and 128-, 192-, and 256-bit keys, i.e., the same interface specifications as the Advanced Encryption Standard (AES). Efficiency on both software and hardware platforms is a remarkable characteristic of Camellia in addition to its high level of security. It is confirmed that Camellia provides strong security against differential and linear cryptanalyses. Compared to the AES finalists, i.e., MARS, RC6, Rijndael, Serpent, and Twofish, Camellia offers at least comparable encryption speed in software and hardware. An optimized implementation of Camellia in assembly language can encrypt on a Pentium III (800MHz) at the rate of more than 276 Mbits per second, which is much faster than the speed of an optimized DES implementation. In addition, a distinguishing feature is its small hardware design. The hardware design, which includes encryption and decryption and key schedule, occupies approximately 11K gates, which is the smallest among all existing 128-bit block ciphers as far as we know.
TL;DR: Having reviewed further public analysis of the finalists, NIST has decided to propose Rijndael as the Advanced Encryption Standard (AES).
Abstract: In 1997, the National Institute of Standards and Technology (NIST) initiated a process to select a symmetric-key encryption algorithm to be used to protect sensitive (unclassified) Federal information in furtherance of NIST’s statutory responsibilities. In 1998, NIST announced the acceptance of fifteen candidate algorithms and requested the assistance of the cryptographic research community in analyzing the candidates. This analysis included an initial examination of the security and efficiency characteristics for each algorithm. NIST reviewed the results of this preliminary research and selected MARS, RC6™, Rijndael, Serpent and Twofish as finalists. Having reviewed further public analysis of the finalists, NIST has decided to propose Rijndael as the Advanced Encryption Standard (AES). The research results and rationale for this selection are documented in this report.
TL;DR: In this paper, the DES S-boxes are used in a new structure that simultaneously allows a more rapid avalanche, a more efficient bitslice implementation, and an easy analysis that enables them to demonstrate its security against all known types of attack.
Abstract: We propose a new block cipher as a candidate for the Advanced Encryption Standard. Its design is highly conservative, yet still allows a very efficient implementation. It uses the well-understood DES S-boxes in a new structure that simultaneously allows a more rapid avalanche, a more efficient bitslice implementation, and an easy analysis that enables us to demonstrate its security against all known types of attack. With a 128-bit block size and a 256-bit key, it is almost as fast as DES on a wide range of platforms, yet conjectured to be at least as secure as three-key triple-DES.
TL;DR: A new cryptanalytic technique based on Wagner's boomerang and inside-out attacks is introduced, and its use on reduced-round variants of the MARS core and Serpent is demonstrated.
Abstract: We introduce a new cryptanalytic technique based on Wagner's boomerang and inside-out attacks. We first describe this new attack in terms of the original boomerang attack, and then demonstrate its use on reduced-round variants of the MARS core and Serpent. Our attack breaks eleven rounds of the MARS core with 265 chosen plaintexts, 270 memory, and 2229 partial decryptions. Our attack breaks eight rounds of Serpent with 2114 chosen plaintexts, 2119 memory, and 2179 partial decryptions.