Using Local Reduction for the Experimental Evaluation of the Cipher Security

Evaluating the strength of block ciphers against algebraic attacks can be difficult. The attack methods often use different metrics, and experiments do not scale well in practice. We propose a methodology that splits the algebraic attack into a polynomial part (local reduction), and an exponential part (guessing), respectively. The evaluator uses instances with known solutions to estimate the complexity of the attacks, and the response to changing parameters of the problem (e.g. the number of rounds). Although the methodology does not provide a positive answer ("the cipher is secure"), it can be used to construct a negative test (reject weak ciphers), or as a tool of qualitative comparison of cipher designs. Potential applications in other areas of computer science are discussed in the concluding parts of the article

Selected Topics in Cryptanalysis of Symmetric Ciphers

It is well established that a symmetric cipher may be described as a system of Boolean polynomials, and that the security of the cipher cannot be better than the difficulty of solving said system. Compressed Right-Hand Side (CRHS) Equations is but one way of describing a symmetric cipher in terms of Boolean polynomials. The first paper of this thesis provides a comprehensive treatment firstly of the relationship between Boolean functions in algebraic normal form, Binary Decision Diagrams and CRHS equations. Secondly, of how CRHS equations may be used to describe certain kinds of symmetric ciphers and how this model may be used to attempt a key-recovery attack. This technique is not left as a theoretical exercise, as the process have been implemented as an open-source project named CryptaPath. To ensure accessibility for researchers unfamiliar with algebraic cryptanalysis, CryptaPath can convert a reference implementation of the target cipher, as specified by a Rust trait, into the CRHS equations model automatically. CRHS equations are not limited to key-recovery attacks, and Paper II explores one such avenue of CRHS equations flexibility. Linear and differential cryptanalysis have long since established their position as two of the most important cryptanalytical attacks, and every new design since must show resistance to both. For some ciphers, like the AES, this resistance can be mathematically proven, but many others are left to heuristic arguments and computer aided proofs. This work is tedious, and most of the tools require good background knowledge of a tool/technique to transform a design to the right input format, with a notable exception in CryptaGraph. CryptaGraph is written in Rust and transforms a reference implementation into CryptaGraphs underlying data structure automatically. Paper II introduces a new way to use CRHS equations to model a symmetric cipher, this time in such a way that linear and differential trail searches are possible. In addition, a new set of operations allowing us to count the number of active S-boxes in a path is presented. Due to CRHS equations effective initial data compression, all possible trails are captured in the initial system description. As is the case with CRHS equations, the crux is the memory consumption. However, this approach also enables the graph of a CRHS equation to be pruned, allowing the memory consumption to be kept at manageable levels. Unfortunately, pruning nodes also means that we will lose valid, incomplete paths, meaning that the hulls found are probably incomplete. On the flip side, all paths, and their corresponding probabilities, found by the tool are guaranteed to be valid trails for the cipher. This theory is also implemented in an extension of CryptaPath, and the name is PathFinder. PathFinder is also able to automatically turn a reference implementation of a cipher into its CRHS equations-based model. As an additional bonus, PathFinder supports the reference implementation specifications specified by CryptaGraph, meaning that the same reference implementation can be used for both CryptaGraph and PathFinder. Paper III shifts focus onto symmetric ciphers designed to be used in conjunction with FHE schemes. Symmetric ciphers designed for this purpose are relatively new and have naturally had a strong focus on reducing the number of multiplications performed. A multiplication is considered expensive on the noise budget of the FHE scheme, while linear operations are viewed as cheap. These ciphers are all assuming that it is possible to find parameters in the various FHE schemes which allow these ciphers to work well in symbiosis with the FHE scheme. Unfortunately, this is not always possible, with the consequence that the decryption process becomes more costly than necessary. Paper III therefore proposes Fasta, a stream cipher which has its parameters and linear layer especially chosen to allow efficient implementation over the BGV scheme, particularly as implemented in the HElib library. The linear layers are drawn from a family of rotation-based linear transformations, as cyclic rotations are cheap to do in FHE schemes that allow packing of multiple plaintext elements in one FHE ciphertext. Fasta follows the same design philosophy as Rasta, and will never use the same linear layer twice under the same key. The result is a stream cipher tailor-made for fast evaluation in HElib. Fasta shows an improvement in throughput of a factor more than 7 when compared to the most efficient implementation of Rasta.Doktorgradsavhandlin

Roadmap on optical security

Postprint (author's final draft

C-DIFFERENTIALS AND GENERALIZED CRYPTOGRAPHIC PROPERTIES OF VECTORIAL BOOLEAN AND P-ARY FUNCTIONS

This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.Commander, United States NavyApproved for public release. Distribution is unlimited

The Quasigroup Block Cipher and its Analysis

This thesis discusses the Quasigroup Block Cipher (QGBC) and its analysis. We first present the basic form of the QGBC and then follow with improvements in memory consumption and security. As a means of analyzing the system, we utilize tools such as the NIST Statistical Test Suite, auto and crosscorrelation, then linear and algebraic cryptanalysis. Finally, as we review the results of these analyses, we propose improvements and suggest an algorithm suitable for low-cost FPGA implementation