Evaluating Coppersmith’s Criteria by way of SAT Solving

S-boxes are the non-linear part of DES cryptosystem. Along the years it has became clear that any kind of edit to the structure of DES S-boxes increases the probability of success of breaking the algorithm, which was very carefully designed. The reason why the S-boxes were built in this way was clarified by Coppersmith, years after the publication of the encryption algorithm. The aim of this thesis is to investigate on Coppersmith’s DES S-boxes design criteria and to evaluate them by way of SAT Solving, in order to analyze the performance of SAT-Solvers for different versions of DES algorithm, in which S-boxes respect only a sample of Coppersmith’s design criteria. This aim is achieved thanks to the implementation of a Python tool: DESBoxGen. The main challenge in the design of DESBoxGen is the one of finding a way to efficiently generating S-boxes satisfying certain criteria

Design implementation and analysis of a dynamic cryptography algorithm with applications

Cryptographers need to provide the world with a new encryption standard. DES, the major encryption algorithm for the past fifteen years, is nearing the end of its useful life. Its 56-bit key size is vulnerable to a brute-force attack on powerful microprocessors and recent advances in linear cryptanalysis and differential cryptanalysis indicate that DES is vulnerable to other attacks as well. A more recent attack called XSL, proposes a new attack against AES and Serpent. The attack depends much more critically on the complexity of the nonlinear components than on the number of rounds. Ciphers with small S-boxes and simple structures are particularly vulnerable. Serpent has small S-boxes and a simple structure. AES has larger S-boxes, but a very simple algebraic description. If the attack is proven to be correct, cryptographers predict it to break AES with a 2; 80 complexity, over the coming years; Many of the other unbroken algorithms---Khufu, REDOC II, and IDEA---are protected by patents. RC2 is broken. The U.S. government has declassified the Skipjack algorithm in the Clipper and Capstone chips

Plaintext Recovery in DES-like Cryptosystems Based on S-boxes with Embedded Parity Check

We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively low entropy. Our investigations demonstrate once again that modifications resulting to S-boxes which still satisfy some design criteria may lead to very weak ciphers. ACM Computing Classification System (1998): E.3, I.2.7, I.2.8.This work was presented in part at the 1-st International Conference Bulgarian Cryptography Days 2012, Sofia, Bulgaria, 20–21 September 2012

Exercice de style

We present the construction and implementation of an 8-bit S-box with a differential and linear branch number of 3. We show an application by designing FLY, a simple block cipher based on bitsliced evaluations of the S-box and bit rotations that targets the same platforms as PRIDE, and which can be seen as a variant of PRESENT with 8-bit S-boxes. It achieves the same performance as PRIDE on 8-bit microcontrollers (in terms of number of instructions per round) while having 1.5 times more equivalent active S-boxes. The S-box also has an efficient implementation with SIMD instructions, a low implementation cost in hardware and it can be masked efficiently thanks to its sparing use of non-linear gates.Cette note présente la construction et l'implémentation d'une boîte S sur 8 bits qui a un branchement linéaire et différentiel de 3.Nous montrons une application en construisant un chiffre par bloc sur 64 bits dont la structure est très simple et est basée sur l'évaluationen tranches (bitsliced) de la boîte S et des rotations sur mots de 8 bits et qui peut être vu comme une variante de PRESENT avec une boîte S de 8 bits. La fonction de tour de ce chiffre peut s'implémenter avec le même nombred'instructions que celle de PRIDE sur micro-controleurs 8-bits, tout en ayant 1,5 fois plus de boîtes S actives (relativement).Cette boîte S peut aussi s'implémenter efficacement avec des instructions SIMD, a un coût faible en matériel etpeut se masquer efficacement grâce au peu de portes non-linéaires nécessaires

Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions

Infinitesimal Liouville currents, cross-ratios and intersection numbers

Many classical objects on a surface S can be interpreted as cross-ratio functions on the circle at infinity of the universal covering. This includes closed curves considered up to homotopy, metrics of negative curvature considered up to isotopy and, in the case of interest here, tangent vectors to the Teichm\"uller space of complex structures on S. When two cross-ratio functions are sufficiently regular, they have a geometric intersection number, which generalizes the intersection number of two closed curves. In the case of the cross-ratio functions associated to tangent vectors to the Teichm\"uller space, we show that two such cross-ratio functions have a well-defined geometric intersection number, and that this intersection number is equal to the Weil-Petersson scalar product of the corresponding vectors.Comment: 17 page

The peak algebra and the Hecke-Clifford algebras at q=0q=0

Using the formalism of noncommutative symmetric functions, we derive the basic theory of the peak algebra of symmetric groups and of its graded Hopf dual. Our main result is to provide a representation theoretical interpretation of the peak algebra and its graded dual as Grothendieck rings of the tower of Hecke-Clifford algebras at $q=0$.Comment: Final version, 17 pages, LaTex, 1 PDF figure, graphic