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This paper presents a variety of plaintext-recovering attacks against SSH. We implemented a proof of concept of our attacks against OpenSSH, where we can verifiably recover 14 bits of plaintext from an arbitrary block of ciphertext with probability 2 −14 and 32 bits of plaintext from an arbitrary block of ciphertext with probability 2 −18. These attacks… (More)

The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as… (More)

Designing an efficient cipher was always a delicate balance between linear and non-linear operations. This goes back to the design of DES, and in fact all the way back to the seminal work of Shannon. Here we focus, for the first time, on an extreme corner of the design space and initiate a study of symmetric-key primitives that minimize the multiplicative… (More)

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)

The subfield attack exploits the presence of a subfield to solve overstretched versions of the NTRU assumption: norming the public key h down to a subfield may lead to an easier lattice problem and any sufficiently good solution may be lifted to a short vector in the full NTRU-lattice. This approach was originally sketched in a paper of Gentry and Szydlo at… (More)

Bellare and Kohno introduced a formal framework for the study of related-key attacks against blockci-phers. They established sufficient conditions (output-unpredictability and collision-resistance) on the set of related-key-deriving (RKD) functions under which an ideal cipher is secure against related-key attacks, and suggested this could be used to derive… (More)

Block ciphers are fundamental building block of modern cryptography. Recently, a new technique to attack block ciphers has emerged called " algebraic attacks ". These attacks work by expressing block ciphers as quadratic equation systems and solving those systems of equations. In May 2006 Nicolas Courtois – author of many influential research papers on… (More)

We analyse the complexity of algebraic algorithms for solving systems of linear equations with noise. Such systems arise naturally in the theory of error-correcting codes as well as in computational learning theory. More recently, linear systems with noise have found application in cryptography. The Learning with Errors (LWE) problem has proven to be a rich… (More)

In this paper we propose a new cryptanalytic method against block ciphers, which combines both algebraic and statistical techniques. More specifically, we show how to use algebraic relations arising from differential characteristics to speed up and improve key-recovery differential attacks against block ciphers in some situations. To illustrate the new… (More)

The linear layer is a core component in any substitution-permutation network block cipher. Its design significantly influences both the security and the efficiency of the resulting block cipher. Surprisingly, not many general constructions are known that allow to choose trade-offs between security and efficiency. Especially, when compared to Sboxes, it… (More)