D.STVL.7 - Algebraic cryptanalysis of symmetric primitives

Carlos Cid (1) , Martin Albrecht (1) , Daniel Augot (2) , Anne Canteaut (2) , Ralf-Philipp Weinmann (3)

1 RHUL - Royal Holloway [University of London]
2 CODES - Coding and cryptography
3 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt

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.

Domaines: Cryptographie et sécurité [cs.CR]

Carlos Cid, Martin Albrecht, Daniel Augot, Anne Canteaut, Ralf-Philipp Weinmann. D.STVL.7 - Algebraic cryptanalysis of symmetric primitives. 2008. ⟨hal-00328626⟩