carlos cid

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Jennifer Seberry

University of Wollongong

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Jolanta Tamosaitiene

Vilnius Gediminas Technical University

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Papers by carlos cid

An Analysis of the XSL Algorithm

The XSL “algorithm” is a method for solving systems of multivariate polynomial equations based on... more The XSL “algorithm” is a method for solving systems of multivariate polynomial equations based on the linearization method. It was proposed in 2002 as a dedicated method for exploiting the structure of some types of block ciphers, for example the AES and Serpent. Since its proposal, the potential for algebraic attacks against the AES has been the source of much speculation. Although it has attracted a lot of attention from the cryptographic community, currently very little is known about the effectiveness of the XSL algorithm. In this paper we present an analysis of the XSL algorithm, by giving a more concise description of the method and studying it from a more systematic point of view. We present strong evidence that, in its current form, the XSL algorithm does not provide an efficient method for solving the AES system of equations.

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Some Algebraic Aspects of the Advanced Encryption Standard

Since being officially selected as the new Advanced Encryption Standard (AES), Rijndael has conti... more Since being officially selected as the new Advanced Encryption Standard (AES), Rijndael has continued to receive great attention and has had its security continuously evaluated by the cryptographic community. Rijndael is a cipher with a simple, elegant and highly algebraic structure. Its selection as the AES has led to a growing interest in the study of algebraic properties of block ciphers, and in particular algebraic techniques that can be used in their cryptanalysis. In these notes we will examine some algebraic aspects of the AES and consider a number of algebraic techniques that could be used in the analysis of the cipher. In particular, we will focus on the large, though surprisingly simple, systems of multivariate quadratic equations derived from the encryption operation, and consider some approaches that could be used when attempting to solve these systems. These notes refer to an invited talk given at the Fourth Conference on the Advanced Encryption Standard (AES4) in May 2004, and are largely based on[4].

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An Algebraic Framework for Cipher Embeddings

In this paper we discuss the idea of block cipher embeddings and consider a natural algebraic fra... more In this paper we discuss the idea of block cipher embeddings and consider a natural algebraic framework for such constructions. In this approach we regard block cipher state spaces as algebras and study some properties of cipher extensions on larger algebras. We apply this framework to some well-known examples of AES embeddings.

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The eSTREAM Portfolio (rev. 1

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Small Scale Variants of the AES

In this paper we define small scale variants of the AES. These variants inherit the design featur... more In this paper we define small scale variants of the AES. These variants inherit the design features of the AES and provide a suitable framework for comparing different cryptanalytic methods. In particular, we provide some preliminary results and insights when using off-the-shelf computational algebra techniques to solve the systems of equations arising from these small scale variants.

Computational and Algebraic Aspects of the Advanced Encryption Standard

The new Advanced Encryption Standard (AES) has been recently selected by the US government to rep... more The new Advanced Encryption Standard (AES) has been recently selected by the US government to replace the old Data Encryption Standard (DES) for protecting sensitive official information. Due to its simplicity and elegant algebraic structure, the choice of the AES algorithm has motivated the study of a new approach to the analysis of block ciphers. While conventional methods of cryptanalysis (e.g. differential and linear cryptanalysis) are usually based on a "statistical" approach, where an attacker attempts to construct statistical patterns through many interactions of the cipher, the so-called algebraic attacks exploit the intrinsic algebraic structure of a cipher. More specifically, the attacker expresses the encryption transformation as a set of multivariate polynomial equations and attempts to recover the encryption key by solving the system. In this paper we consider a number of algebraic aspects of the AES, and examine a few computational and algebraic techniques that could be used in the cryptanalysis of cipher. We show how one can express the cipher as a very large, though surprisingly simple, system of multivariate quadratic equations over the finite field F 2 8 , and consider some approaches that can be used to solve this system.

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Ongoing Research Areas in Symmetric Cryptography

... RUB), H˚akan Englund (LUND), Henri Gilbert (FTRD), Louis Granboulan (ENS), Helena Handschuh (... more

The eSTREAM Portfolio 2009 Annual Update

... Carlos Cid1 and Matthew Robshaw2 1 Royal Holloway, United Kingdom 2 Orange Labs, France July ... more

Algebraic aspects of the advanced encryption standard

A Note on Static Solutions of a Lorentz Invariant Equation in Dimension 3

Letters in Mathematical Physics, 2000

The aim of this Letter is to prove the existence of a static solution to the Lorentz invariant eq... more

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Orbital Stability of Standing Waves for the Nonlinear Schrödinger Equation with Potential

Reviews in Mathematical Physics, 2001

We prove existence and orbital stability of standing waves for the nonlinear Schrödinger equation... more We prove existence and orbital stability of standing waves for the nonlinear Schrödinger equation <DF> <TEX ID="S0129055X01001095E001">\[ i \ep \psi_t = \ep^2 \Delta \psi - V(x) \psi + f(|\psi|) \psi\quad \mbox{in}\quad \R^N \times (0,\infty)\,, \]</TEX> </DF> concentrating near a possibly degenerate local minimum of the potential V, when the Plank's constant ℎ is small enough. Our method applies to general nonlinearities, including f(s)=sp - 1 with p ∈ (1,1 + 4/N), but does not require uniqueness nor non-degeneracy of the limiting equation.

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography b... more

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An Analysis of the XSL Algorithm

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Some Algebraic Aspects of the Advanced Encryption Standard

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An Algebraic Framework for Cipher Embeddings

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The eSTREAM Portfolio (rev. 1

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Small Scale Variants of the AES

Computational and Algebraic Aspects of the Advanced Encryption Standard

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Ongoing Research Areas in Symmetric Cryptography

... RUB), H˚akan Englund (LUND), Henri Gilbert (FTRD), Louis Granboulan (ENS), Helena Handschuh (... more

The eSTREAM Portfolio 2009 Annual Update

... Carlos Cid1 and Matthew Robshaw2 1 Royal Holloway, United Kingdom 2 Orange Labs, France July ... more

Algebraic aspects of the advanced encryption standard

A Note on Static Solutions of a Lorentz Invariant Equation in Dimension 3

Letters in Mathematical Physics, 2000

The aim of this Letter is to prove the existence of a static solution to the Lorentz invariant eq... more

Download

Orbital Stability of Standing Waves for the Nonlinear Schrödinger Equation with Potential

Reviews in Mathematical Physics, 2001

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography b... more

Download

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