Rubik’s for Cryptographers

Petit, Christophe; Quisquater, Jean-Jacques

doi:10.1090/noti1001

Cited by 17 publications

(14 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other instances of factorization problems in non-abelian groups have been solved previously, in both cryptographic contexts [15,16,17] and in mathematical literature [18]. The algorithms we develop in this paper for factorization in GL N (F q ) belongs to the family of subgroup attacks [19].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A Practical Cryptanalysis of WalnutDSA$$^{\text {TM}}$$

Hart

Kim

Micheli

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version. Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

show abstract

Section: Related Workmentioning

confidence: 99%

“…Over cyclic groups, this problem is known to be equivalent to the discrete logarithm problem when removing the constraint on L [39]. We refer to [19] for a more extensive discussion of the factorization problem and its connection with Babai's conjecture.…”

Section: Factorization Problem In Non-abelian Groupsmentioning

confidence: 99%

A Practical Cryptanalysis of WalnutDSA$$^{\text {TM}}$$

Hart

Kim

Micheli

et al. 2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Rubik's cube, perhaps one of the best-selling iconic puzzle tools, is also well known to us, even in our childhood. Recently, very interesting progress has been made by researchers trying to bridge these subjects: many cryptographic schemes, such as Cayley hash functions [PQ11], [PQ13], key agreement protocols [NM13], image encryption schemes [LCB12], [DPTS18], digital watermarking schemes [YL10], and zero-knowledge protocols [VPN13], were proposed based on Rubik's groups. However, most of them lack provable security reductions, and some even lay their security basis on a taken-for-granted hardness assumption: recovering of a Rubik's cube with random configuration (RRC for short).…”

Section: Introductionmentioning

confidence: 99%

Provably Secure Encryption Schemes With Zero Setup and Linear Speed by Using Rubik’s Cubes

Pan

Wang

et al. 2020

IEEE Access

View full text Add to dashboard Cite

and Telecommunications) (SKLNST-2020-2-16). ABSTRACT Recently, new paradigms for designing modern cryptographic schemes were proposed based on Rubik's rotations. However, most of them lack rigorous provable security reductions. Enlightened by this interesting progress, we present a novel method for designing encryption schemes by using Rubik's groups. Different from most naive designs of permutation ciphers based on Rubik's cubes, our proposals are probabilistic encryption schemes that combine some of the newest cryptographic primitives with modern coding theory. More specifically, under the intractability assumption of the conjugacy decision problem over Rubik's groups, the proposed schemes have provable security reductions (in the random oracle model). Furthermore, the proposed schemes have two remarkable performance advantages: zero setup and linear encryption/decryption speed. In addition, the processes of encoding/encryption and decryption/decoding are demonstrated graphically.

show abstract

“…most popular implementation of this idea so far is the Tillich-Zémor hash function [15]. We refer to [10] and [12] for a more detailed survey on Cayley hash functions.…”

Section: Introductionmentioning

confidence: 99%

Compositions of linear functions and applications to hashing

Shpilrain

Sosnovski

2016

Groups Complexity Cryptology

View full text Add to dashboard Cite

ABSTRACT. Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, A and B, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with linear functions of one variable over F p . The corresponding hash functions are very efficient. In particular, we show that hashing a bit string of length n with our method requires, in general, at most 2n multiplications in F p , but with particular pairs of linear functions that we suggest, one does not need to perform any multiplications at all. We also give explicit lower bounds on the length of collisions for hash functions corresponding to these particular pairs of linear functions over F p .

show abstract

Rubik’s for Cryptographers

Cited by 17 publications

References 69 publications

A Practical Cryptanalysis of WalnutDSA$$^{\text {TM}}$$

A Practical Cryptanalysis of WalnutDSA$$^{\text {TM}}$$

Provably Secure Encryption Schemes With Zero Setup and Linear Speed by Using Rubik’s Cubes

Compositions of linear functions and applications to hashing

Contact Info

Product

Resources

About