Average case completeness

Gurevich, Yuri

doi:10.1016/0022-0000(91)90007-r

Cited by 134 publications

(111 citation statements)

References 14 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…This phase transition is particularly interesting because it turns out that the really difficult instances, from the algorithmic point of view, are those where α is close to α c . The study of this phase transition is thus one step in the elaboration of a theory of typical case complexity, [19,33,35] and it has attracted a lot of interest [15,6,9,32].…”

Section: Introductionmentioning

confidence: 99%

Threshold values of random K‐SAT from the cavity method

Mertens

Mézard

Zecchina

2005

Random Struct Algorithms

212

280

View full text Add to dashboard Cite

Using the cavity equations of [23,24], we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K. The stability of the solution is also computed. For any K, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.

show abstract

Section: Introductionmentioning

confidence: 99%

Threshold values of random K‐SAT from the cavity method

Mertens

Mézard

Zecchina

2005

Random Struct Algorithms

212

280

View full text Add to dashboard Cite

show abstract

“…However, following Gurevich and Levin [7,9] discussion for syndrome decoding, we believe that both these problems are difficult on average.…”

Section: Security Reductionmentioning

confidence: 94%

A Family of Fast Syndrome Based Cryptographic Hash Functions

Augot

Finiasz

Sendrier

2005

Lecture Notes in Computer Science

110

View full text Add to dashboard Cite

Abstract. Recently, some collisions have been exposed for a variety of cryptographic hash functions [20,21] including some of the most widely used today. Many other hash functions using similar constructions can however still be considered secure. Nevertheless, this has drawn attention on the need for new hash function designs. In this article is presented a family of secure hash functions, whose security is directly related to the syndrome decoding problem from the theory of error-correcting codes. Taking into account the analysis by Coron and Joux [4] based on Wagner's generalized birthday algorithm [19] we study the asymptotical security of our functions. We demonstrate that this attack is always exponential in terms of the length of the hash value. We also study the work-factor of this attack, along with other attacks from coding theory, for non asymptotic range, i.e. for practical values. Accordingly, we propose a few sets of parameters giving a good security and either a faster hashing or a shorter description for the function.

show abstract

“…Indeed, this is only a worst-case complexity result. But, though no formal reduction is known [17], [14], decoding in a random linear code is believed to be hard in the average case. In practice, decoding a general linear code has recieved a lot attention, both in cryptology and in coding theory (see [2] for a state of the art).…”

Section: A Syndrome Decodingmentioning

confidence: 99%

SYND: a Fast Code-Based Stream Cipher with a Security Reduction

Gaborit

Lauradoux

Sendrier

2007

2007 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

Abstract-In this note we reconsider the code-based pseudorandom generator proposed by Fischer and Stern. This generator is proven as secure as the syndrome decoding problem but has two main drawbacks: it is slow (3000 bits/s) and a large size of memory is needed (88 kiloBytes). We propose a variation on the scheme which avoid them: the use of regular words speeds the system up and the use of quasi-cyclic codes allows a decrease of the memory requirements. We eventually obtain a generator as fast as AES in counter mode using only about 8000 bits of memory. We also give a more precise security reduction.

show abstract

Average case completeness

Abstract: We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions.

Cited by 134 publications

References 14 publications

Threshold values of random K‐SAT from the cavity method

Threshold values of random K‐SAT from the cavity method

A Family of Fast Syndrome Based Cryptographic Hash Functions

SYND: a Fast Code-Based Stream Cipher with a Security Reduction

Contact Info

Product

Resources

About