All in the XL Family: Theory and Practice

Yang, Bo‐Yin; Chen, Jiun-Ming

doi:10.1007/11496618_7

Cited by 55 publications

(44 citation statements)

References 40 publications

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“…4 becomes non-positive. This is the meaning of "no extraneous dependencies" in [28,40], and semi-regularity in [2]: the XL-equations constructed according to an extension of the Buchberger criteria ( [19]) have no extraneous interdependencies. Bardet et al (nor anyone else) give no general properties implying semi-regularity.…”

Section: Basic Combinatorial Results Concerning XLmentioning

confidence: 99%

“…[3,27,35,40]). If the system matrix can be blocked efficiently via coloring analysis ( [16]), only the dominant block counts for T and R. When m, n → ∞ so does R/T .…”

Section: A Framework For Estimating Security Levelsmentioning

confidence: 99%

“…We shall use an optimistic c 0 = 16, c 1 = 1 4 for a complexity estimate in CPU cycles, which we should divide by 2 8 to get a rough estimate in 3DES blocks ( [40] and simulations); the E B estimate above is in contrast in field multiplications which is 2 −6 of a 3DES block (the NESSIE unit, cf.…”

Section: A Framework For Estimating Security Levelsmentioning

confidence: 99%

“…For applications to stream ciphers, see [7,8]; to PKC's especially about its variant types, see [9,12]; for block ciphers and the somewhat contentious related method of XSL, see [13], and also [29,30]. We will build on recent theoretical developments in XL ( [15,36,40,42]) for better security estimates under XL and related methods, including Gröbner Bases. More details can also be found in [9,12,13].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis

Yang

Chen²,

Courtois³

2004

Information and Communications Security

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Abstract. "Algebraic Cryptanalysis" against a cryptosystem often comprises finding enough relations that are generally or probabilistically valid, then solving the resultant system. The security of many schemes (most important being AES) thus depends on the difficulty of solving multivariate polynomial equations. Generically, this is NP-hard. The related methods of XL (eXtended Linearization), Gröbner Bases, and their variants (of which a large number has been proposed) form a unified approach to solving equations and thus affect our assessment and understanding of many cryptosystems. Building on prior theory, we analyze these XL variants and derive asymptotic formulas giving better security estimates under XL-related algebraic attacks; through this examination we have hopefully improved our understanding of such variants. In particular, guessing a portion of variables is a good idea for both XL and Gröbner Bases methods.

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Section: Basic Combinatorial Results Concerning XLmentioning

confidence: 99%

“…[3,27,35,40]). If the system matrix can be blocked efficiently via coloring analysis ( [16]), only the dominant block counts for T and R. When m, n → ∞ so does R/T .…”

Section: A Framework For Estimating Security Levelsmentioning

confidence: 99%

Section: A Framework For Estimating Security Levelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis

Yang

Chen²,

Courtois³

2004

Information and Communications Security

Self Cite

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“…[3] for an overview of the idea. Although it has been shown that techniques from the XL-family are strictly less efficient than from the F-family [40,39,5,17], XL does have its merits as it is easier to adapt to different settings. Hence we have used a specialized version of XL in our solver to improve its efficiency, cf.…”

Section: Related Workmentioning

confidence: 99%

Advanced Algebraic Attack on Trivium

Quedenfeld

Wolf

2016

Mathematical Aspects of Computer and Information Sciences

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Abstract. This paper presents an algebraic attack against Trivium that breaks 625 rounds using only 4096 bits of output in an overall time complexity of 2 42.2 Trivium computations. While other attacks can do better in terms of rounds (799), this is a practical attack with a very low data usage (down from 2 40 output bits) and low computation time (down from 2 62 ). From another angle, our attack can be seen as a proof of concept: how far can algebraic attacks can be pushed when several known techniques are combined into one implementation? All attacks have been fully implemented and tested; our figures are therefore not the result of any potentially error-prone extrapolation, but results of practical experiments.

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Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS

Yang

Chen²

2005

Lecture Notes in Computer Science

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Abstract. Multivariate public-key cryptosystems (sometimes polynomial-based PKC's or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The "tame-like" or "sparse" class of multivariates are distinguished by the relatively few terms that they have per central equation. We explain how they differ from the "big-field" type of multivariates, represented by derivatives of C * and HFE, how they are better, and give basic security criteria for them. The last is shown to be satisfied by efficient schemes called "Enhanced TTS" which is built on a combination of the Oil-and-Vinegar and Triangular ideas. Their security levels are estimated. In this process we summarize and in some cases, improve rank-based attacks, which seek linear combinations of certain matrices at given ranks. These attacks are responsible for breaking many prior multivariate designs.

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All in the XL Family: Theory and Practice

Cited by 55 publications

References 40 publications

On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis

On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis

Advanced Algebraic Attack on Trivium

Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS

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