Journal ArticleDOI
Hybrid approach for solving multivariate systems over finite fields
TLDR
This work presents a new general algorithm to solve multivariate polynomial systems over finite fields and gives theoretical evidences that this method brings a significant improvement in a very large context and clearly defines its limitations.Abstract:
In this paper, we present an improved approach to solve multivariate systems over finite fields. Our approach is a tradeoff between exhaustive search and Grobner bases techniques. We give theoretical evidences that our method brings a significant improvement in a very large context and we clearly define its limitations. The efficiency depends on the choice of the tradeoff. Our analysis gives an explicit way to choose the best tradeoff as well as an approximation. From our analysis, we present a new general algorithm to solve multivariate polynomial systems. Our theoretical results are experimentally supported by successful cryptanalysis of several multivariate schemes (TRMS, UOV, . . . ). As a proof of concept, we were able to break the proposed parameters assumed to be secure until now. Parameters that resists to our method are also explicitly given. Our work permits to refine the parameters to be chosen for multivariate schemes.read more
Citations
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Book
Advances in Cryptology - CRYPTO 2006
TL;DR: A new construction for private intersection sum with cardinality is presented that provides malicious security with abort and guarantees that both parties receive the output upon successful completion of the protocol.
Book ChapterDOI
Public-key identification schemes based on multivariate quadratic polynomials
TL;DR: This paper proposes public-key identification schemes based on the conjectured intractability of the MQ problem under the assumption of the existence of a non-interactive commitment scheme, and they consist of an identification protocol which is zeroknowledge argument of knowledge for the Mq problem.
Journal Article
Comparison between XL and Gröbner basis algorithms
TL;DR: It is shown that to solve a system of algebraic equations via the XL algorithm is equivalent to calculate the reduced Grobner basis of the ideal associated with the system.
Book ChapterDOI
Design Principles for HFEv- Based Multivariate Signature Schemes
TL;DR: The new HFEv- based signature scheme Gui is proposed, which is more than 100 times faster than QUARTZ and therefore highly comparable with classical signature schemes such as RSA and ECDSA.
Journal ArticleDOI
A Survey of Public-Key Cryptographic Primitives in Wireless Sensor Networks
TL;DR: This survey provides invaluable insights on public-key cryptographic primitives on WSN platforms, and solutions to find tradeoffs between cost, performance and security for designing security protocols in WSNs.
References
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BookDOI
Ideals, Varieties, and Algorithms
TL;DR: In the Groebner package, the most commonly used commands are NormalForm, for doing the division algorithm, and Basis, for computing a Groebners basis as mentioned in this paper. But these commands require a large number of variables.
Book ChapterDOI
Finding collisions in the full SHA-1
TL;DR: This is the first attack on the full 80-step SHA-1 with complexity less than the 280 theoretical bound, and it is shown that collisions ofSHA-1 can be found with complexityLess than 269 hash operations.
Journal ArticleDOI
A new efficient algorithm for computing Gröbner bases (F4)
TL;DR: In this paper, the Buchberger algorithm is replaced by the simultaneous reduction of several polynomials, which is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods.
Journal Article
Advances in Cryptology - EUROCRYPT 2005: 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques
TL;DR: This paper discusses Cryptography in High Dimensional Tori, a Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers, and reducing Complexity Assumptions for Statistically-Hiding Commitment.
Book ChapterDOI
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
TL;DR: It is provided strong evidence that relinearization and XL can solve randomly generated systems of polynomial equations in subexponential time when m exceeds n by a number that increases slowly with n.