Improvements of Algebraic Attacks Based on Structured Gaussian Elimination

Algebraic attacks are studied as a potential cryptanalytic procedure for various types of ciphers. The XL_SGE algorithm has been recently proposed to improve the complexity of the XL attack. XL_SGE uses structured Gaussian elimination (SGE) during the expansion phase of XL. In this paper, we establish that XL_SGE suffers from some serious drawbacks that impair the effectiveness of SGE-based reduction at all multiplication stages except the first. In order to avoid this problem, we propose several improvements of XL_SGE. Our modifications are based upon partial monomial multiplication and handling of columns of weight two. Our modified algorithms have been experimentally verified to be substantially superior to XL_SGE

A tight security reduction in the quantum random oracle model for code-based signature schemes

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes

Generic Decoding of Restricted Errors

Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem from a restricted set. In this paper, we propose new generic decoders, that are inspired by subset sum solvers and tailored to the new setting. The introduced algorithms take the restricted structure of the error set into account in order to utilize the representation technique efficiently. This leads to a considerable decrease in the security levels of recently published code-based cryptosystems

D.STVL.7 - Algebraic cryptanalysis of symmetric primitives

The recent development of algebraic attacks can be considered an important breakthrough in the analysis of symmetric primitives; these are powerful techniques that apply to both block and stream ciphers (and potentially hash functions). The basic principle of these techniques goes back to Shannon's work: they consist in expressing the whole cryptographic algorithm as a large system of multivariate algebraic equations (typically over F2), which can be solved to recover the secret key. Efficient algorithms for solving such algebraic systems are therefore the essential ingredients of algebraic attacks. Algebraic cryptanalysis against symmetric primitives has recently received much attention from the cryptographic community, particularly after it was proposed against some LFSR- based stream ciphers and against the AES and Serpent block ciphers. This is currently a very active area of research. In this report we discuss the basic principles of algebraic cryptanalysis of stream ciphers and block ciphers, and review the latest developments in the field. We give an overview of the construction of such attacks against both types of primitives, and recall the main algorithms for solving algebraic systems. Finally we discuss future research directions

The geometry of syntax and semantics for directed file transformations

We introduce a conceptual framework that associates syntax and semantics with vertical and horizontal directions in principal bundles and related constructions. This notion of geometry corresponds to a mechanism for performing goal-directed file transformations such as "eliminate unsafe syntax" and suggests various engineering practices