Modular exponentiation methods in cryptography

Yünüak, Hasan Bartu
Modular exponentiation has an important role in many cryptographic algorithms. These exponentiation methods differ in the bases used and their representations, the repeating aspect, and for which algorithms they are used for: fixed or variable base. Our research aims to compare the efficiencies and implementation timings for some selected algorithms. Also, we look at the options for using a dedicated cubing algorithm, and compare them with the current algorithms.


On the efficient implementation of RSA
Güner, Hatice Kübra; Cenk, Murat; Department of Cryptography (2015)
Modular exponentiation is an essential operation for many asymmetric key cryptosystems such as RSA in which encryption and decryption are based on modular exponentiation. Therefore, efficiency of the system is effected with running time of the modular exponentiation algorithm. At the same time, key sizes also influence the efficiency of the algorithm. Over the years key sizes had to be increased to provide security. To make RSA practical, one of usable choices is acceleration of the modular exponentiation a...
Secure password generation through statistical randomness tests
Uslu, Aycan; Doğanaksoy, Ali; Department of Cryptography (2017)
Both symmetric and asymmetric cryptographic algorithms must firstly be robust against brute force. The key needs to be choosen uniformly and randomly from the key space. It is possible to assure randomness by using statistical randomness tests which are also critical for other cryptographic issues as well. There is still an issue to be elaborated: the most well-known tool for attacking againts passwords namely dictionary attacks. These attacks are based on trying all keys from a particular subspace of the k...
Some characterizations of generalized s-plateaued functions
Çelik, Emircan; Özbudak, Ferruh; Department of Cryptography (2017)
Plateaued functions play important role in cryptography because of their various desirable cryptographic features. Due to this characteristics they have been widely studied in the literature. This studies include p-ary functions and some generalizations of the boolean functions. In this thesis, we present some of this important work and show that plateaued functions can be generalized much more general framework naturally. Characterizations of generalized plateaued functions using Walsh power moments are al...
Efficient subquadratic space complexity binary polynomial multipliers based on block recombination
Cenk, Murat; Negre, Christophe (2014-09-01)
Some applications like cryptography involve a large number of multiplications of binary polynomial. In this paper we consider two, three and four-way methods for parallel implementation of binary polynomial multiplication. We propose optimized three and four-way split formulas which reduce the space and time complexity of the best known methods. Moreover, we present a block recombination method which provides some further reduction in the space complexity of the considered two, three and four-way split mult...
Joint linear complexity of multisequences consisting of linear recurring sequences
Fu, Fang-Wei; Niederreiter, Harald; Özbudak, Ferruh (Springer Science and Business Media LLC, 2009-04-01)
The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, we study the joint linear complexity of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random multisequences consisting of linear recurring sequences are determined. These results extend the ...
Citation Formats
H. B. Yünüak, “Modular exponentiation methods in cryptography,” M.S. - Master of Science, Middle East Technical University, 2017.