Description
Following the famous 1949 paper of Shannon, breaking a "good" cipher should require: "as much work as solving a system of simultaneous equations in a large number of unknowns of a complex type". For most practical cryptosystems, the problem of recovering the key can indeed can be seen as solving a huge system of binary nonlinear equations. In general, solving such a problem is known to be NP-hard, and chances to have a general and efficient method to break ciphers this way are extremely low. However, what makes this problem hard, is not the size of the system, and not the number of variables involved, but the difference between the number of equations and the number of monomials. In many interesting cases, even very big systems of multivariate equations may be solved efficiently. For example, systems that are overdefined, sparse, or both turn out to be solved much easier than expected, by the XL method [due to Shamir, Patarin, Courtois, Klimov, Eurocrypt'2000] and the recent XSL variant [Courtois, Pieprzyk, Asiacrypt'2002].<br/> We will explain that, the new encryption standard AES, designed to resist all previously known attacks on block ciphers, turns out to be an extremely weak cipher with regard to these new algebraic attacks (it is in fact difficult to imagine a worse cipher). One version of this attack, due to Courtois, Pieprzyk, Murphy and Robshaw, seems to be able to achieve an "academic" break of AES: recover the key a bit faster than trying all possible keys.<br/> These attacks are very new, based on some unproven heuristics, and evaluating their exact complexity remains an open problem. In fact, many people naively believe that they cannot break on AES. For example the American government NIST and the European consortium Nessie, still fully back up and recommend AES. Yet, to the best of our knowledge, there is nothing that allows to say they will not work. We will also explain how to design better ciphers, for which there will be no algebraic attacks.<br/> Another area of application of algebraic attacks are stream ciphers. For reasons that will be explained the situation is much worse here, and we will exhibit several general classes of stream ciphers that resist to all known attacks, and yet can be broken in polynomial time by an algebraic attack. Surprisingly, the resulting design criterion on Boolean functions and S-boxes to be used in stream ciphers in order to resist algebraic attacks, applies equally to the components of block ciphers, and can be seen as an application of the security criterion proposed by Courtois for multivariate trapdoor functions (motivated by the security of the multivariate public key cryptosystem HFE). Finally, it can also be seen as an interpretation of Shannon's prescription quoted above.
Next sessions
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Some applications of linear programming to Dilithium
Speaker : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…] -
Wagner’s Algorithm Provably Runs in Subexponential Time for SIS^∞
Speaker : Johanna Loyer - Inria Saclay
At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus q = poly(n) and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner’s algorithm (CRYPTO 2002), run[…]-
Cryptography
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CryptoVerif: a computationally-sound security protocol verifier
Speaker : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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Structured-Seed Local Pseudorandom Generators and their Applications
Speaker : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
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Predicting Module-Lattice Reduction
Speaker : Paola de Perthuis - CWI
Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as `Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens[…]-
Cryptography
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