Unbiased Random Sequences from Quasigroup String Transformations

Markovski, Smile; Gligoroski, Danilo; Kocarev, Ljupčo

doi:10.1007/11502760_11

Cited by 19 publications

(21 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…-improving the existing and defining new kinds of pseudo random number (and sequence) generators [11]; -defining primitives for hash functions [8], [9]; -defining primitives for stream cipher [7]; -design of random codes [10]; and many others.…”

Section: Resultsmentioning

confidence: 99%

Quasigroup String Processing: Part 4

Markovski¹,

Bakeva²

2017

Contributions

Self Cite

View full text Add to dashboard Cite

A b s t r a c t: Given a finite alphabet A and a quasigroup operation * on the set A, in earlier paper of ours we have defined the quasigroup transformation E :+ is the set of all finite strings with letters from A. Here we present several generalizations of the transformation E and we consider the conditions under which the transformed strings have uniform distributions of n-tuples of letters of A. The obtained results can be applied in cryptography, coding theory, defining and improving pseudo random generators, and so on.

show abstract

Section: Resultsmentioning

confidence: 99%

Quasigroup String Processing: Part 4

Markovski¹,

Bakeva²

2017

Contributions

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the first RO -one latch, in the second RO -two latches, and in the N th -N latches. Output bits from the combined TRNG may still be biased and correlated for small N [8], [9]. To overcome this problem it seems to be necessary to use post-processing [10].…”

Section: Trng With Sha-256 Hash Functionmentioning

confidence: 98%

A true random number generator using ring oscillators and SHA-256 as post-processing

Łoza

Matuszewski

2014

2014 International Conference on Signals and Electronic Systems (ICSES)

View full text Add to dashboard Cite

in cryptography, we often require sequences of numbers with unpredictable elements. Such sequences have to pass all known statistical tests for random sequences, e.g. NIST 800-22 test suite, Diehard, TestU01 or UC1. To hamper different attacks, random number generators should be implemented in the same chip as a cryptographic system using random numbers. It forces a designer to create a true random number generator purely digitally. The obtained sequences are biased and do not pass many statistical tests. Therefore an output of the random number generator should be subjected to a transformation called post-processing. In this paper a true random number generator consisted of several uniformly sampled ring oscillators and using hash function SHA-256 as post-processing, is presented. Both components are implemented in a single Field Programmable Gate Array (FPGA). We expect that the proposed solution, implemented in the same FPGA together with a cryptographic system, is more attack-resistant owing to many sources of randomness with significantly different nominal frequencies.Keywords-true random number generation, cryptography, hash functions, randomness and pseudo-randomness, fieldpgogrammable gate array.

show abstract

“…Keedwell [Dénes & Keedwell, 1992, Keedwell 1999 proclaimed the start of new era in cryptography by using the non-associative algebraic structures such as quasigroups and neofields. Since then there have been some attempts of designing quasigroup based pseudorandom number generators/cryptographic schemes [Kościelny, 1996, Kościelny & Mullen, 1999, Golomb et al 2001, Gligoroski, 2004, Gligoroski, 2005, Markovski et al, 2005, Satti and Kak, 2009, Battey and Parakh, 2013 but weaknesses have been found in them [Dichtl & Böffgen, 2012] and have seen relatively less success than chaos based systems. Some of the comprehensive and in-depth overviews of the recent developments and current state of the art in the field of applications of quasigrous in cryptology can be seen in [Shcherbacov, 2012, Mileva, 2014.…”

Section: Page4mentioning

confidence: 99%

A Novel Quasigroup Substitution Scheme for Chaos Based Image Encryption

Patidar¹,

Purohit²

2018

JAND

View full text Add to dashboard Cite

A novel quasigroup substitution scheme for chaos based image encryption During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the networks in a secure way. However, there have been some issues with the implementation of chaos based image ciphers in practice. One of them is reduced/small key space due to the fact that chaotic behavior is only observed for certain range of system parameters/initial conditions of the chaotic system used in such algorithms. To overcome this difficulty, we propose a simple, efficient and robust image encryption algorithm based on combined applications of quasigroups and chaotic standard map.The proposed image cipher is based on the Shannon's popular substitution-diffusion architecture where a quasigroup of order 256 and chaotic standard map have been used for the substitution and permutation of image pixels respectively. Due to the introduction of quasigroup as part of the secret key along with the parameter and initial conditions of the chaotic standard map, the key space has been increased significantly. The proposed image cipher is very fast due to the fact that the substitution based on the quasigroup operations is very simple and can be executed easily through the lookup table operations on Latin squares (which are Cayley operation tables of quasigroups) and the permutation is performed row-by-row as well as column-by-column using the pseudo random number sequences generated through the chaotic standard map. The security and performance have been analyzed through the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis etc. and the results prove the efficiency and robustness of the proposed image cipher against the possible security threats.

show abstract

Unbiased Random Sequences from Quasigroup String Transformations

Cited by 19 publications

References 6 publications

Quasigroup String Processing: Part 4

Quasigroup String Processing: Part 4

A true random number generator using ring oscillators and SHA-256 as post-processing

A Novel Quasigroup Substitution Scheme for Chaos Based Image Encryption

Contact Info

Product

Resources

About