Modular exponentiation methods in cryptography

Download

index.pdf

Date

2017

Author

Yünüak, Hasan Bartu

Metadata

Show full item record

Item Usage Stats

325
views

444
downloads

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.

Subject Keywords

Cryptography., Computer algorithms., Exponential functions., Data encryption (Computer science).

URI

http://etd.lib.metu.edu.tr/upload/12621489/index.pdf
https://hdl.handle.net/11511/26778

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

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...
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...
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...
Mutual correlation of randomness test and analysis of test outputs of transformed and biased sequences Akcengiz, Ziya; Doğanaksoy, Ali; Department of Cryptography (2014) Randomness is one of the most important parts of the cryptography because key generation and key itself depend on random values. In literature, there exist statistical randomness tests and test suites to evaluate randomness of the cryptographic algorithm. Although there exist randomness tests, there is no mathematical evidence to prove that a sequence or a number is random. Therefore, it is vital to choose tests in the test suites due to independency and coverage of the tests used in the suites. Sensitivity...

Citation Formats

H. B. Yünüak, “Modular exponentiation methods in cryptography,” M.S. - Master of Science, Middle East Technical University, 2017.