Department of Mathematics
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Periodic template tests: A family of statistical randomness tests for a collection of binary sequences
SULAK, FATİH; Doğanaksoy, Ali; Uğuz, Muhiddin; Koçak, Onur Ozan (Elsevier BV, 2019-12-01)
In this work, we classify all templates according to their periods and for each template we evaluate the exact probabilities using generating functions. Afterwards, we propose a new family of statistical randomness tests, ...
R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences
Uğuz, Muhiddin; Doğanaksoy, Ali (Springer Science and Business Media LLC, 2019-09-01)
In this article a family of statistical randomness tests for binary strings are introduced, based on Golomb's pseudorandomness postulate R-2 on the number of runs. The basic idea is to construct recursive formulae with com...
Koçak, Onur Ozan; SULAK, FATİH; Doğanaksoy, Ali; Uğuz, Muhiddin (2018-01-01)
Generating random numbers and random sequences that are indistinguishable from truly random sequences is an important task for cryptography. To measure the randomness, statistical randomness tests are applied to the genera...
Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences
Doğanaksoy, Ali; Uğuz, Muhiddin; Akcengiz, Ziya (2017-01-01)
Random sequences are widely used in many cryptographic applications and hence their generation is one of the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses or nonr...
On the independence of statistical randomness tests included in the NIST test suite
SULAK, FATİH; Uğuz, Muhiddin; Koçak, Onur Ozan; Doğanaksoy, Ali (2017-01-01)
Random numbers and random sequences are used to produce vital parts of cryptographic algorithms such as encryption keys and therefore the generation and evaluation of random sequences in terms of randomness are vital. Test...
On Differential Factors
Tezcan, Cihangir; Doğanaksoy, Ali; Doğan, Erol; Yücebaş, Furkan; Baykal, Nazife (2016-10-24)
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappi...
Counting Boolean functions with specified values in their Walsh spectrum
Uyan, Erdener; Calik, Cagdas; Doğanaksoy, Ali (Elsevier BV, 2014-03-15)
The problem of counting Boolean functions with specified number s of Walsh coefficients omega in their Walsh spectrum is discussed in this paper. Strategies to solve this problem shall help solving many more problems relat...
Doğanaksoy, Ali (2011-07-15)
The paper is on using jokes to introduce certain mathematical concepts. The main point is attracting the student to a discussion which is initiated with an anecdote. On the one hand some very common and familiar concepts a...
Evaluation of Randomness Test Results for Short Sequences
Sulak, Fatih; Doğanaksoy, Ali; Ege, Baris; Koçak, Onur Ozan (2010-09-17)
Randomness testing of cryptographic algorithms are of crucial importance to both designer and the attacker. When block ciphers and hash functions are considered, the sequences subject to randomness testing are of at most 5...
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