Browsing by Author "Rahma, Mohammed Kadhim"

Now showing 1 - 3 of 3

Computing square roots and solve equations of ECC over galois fields
(Видавництво Львівської політехніки, 2017-12-23) Rahma, Mohammed Kadhim; Hlukhov, Valeriy; Lviv Polytechnic National University
Computing square roots in finite fields are important computational problems with significant applications to cryptography. Therefore, in this paper, we introduced some methods for finding square roots. Our proposed method calculates the Square root using multiplier over. The proposed method is competitive compared with other existing methods. It is introduced development to decrease of complexity of arithmetic units. In addition, we approach a novel technique for Computation square roots presented using Half_even_odd unit mixed with multiplier and adder. One approach of Square Root presented using the same multiplier for arithmetic units of ECC. Thus, we goes to gets on reduced complexity for arithmetic units.
Galois field operational unit for Elliptic Curve Cryptography Digital Signature
(Lviv Polytechnic Publishing House, 2015) Rahma, Mohammed Kadhim; Lviv Polytechnic National University
Cryptography is the most standard and efficient way to protect the security of data transactions. An efficient cryptosystem must be one that is strong enough to ensure a high level of security for reliable transmission of information. Elliptic curve cryptography is one such type of public key and private key cryptosystem based on small key size with high efficient speed up of cryptography process. Elliptic curve cryptography is an alternative to traditional techniques for public key cryptography. It can be called the future generation of public key systems since it involves less number of bits suitable for resource constrained and wireless applications without compromising on the security level. The proposed architecture for elliptic curve scalar is based on Point multiplication algorithm. It was also generated (Extension Field) assimilation by EF(387) where GF(2173)& EF(387) fields have approximately the same number of elements, and results were compared and implemented.
Time complexity of multipliers for Galois fields
(Lviv Polytechnic Publishing House, 2016) Rahma, Mohammed Kadhim; Hlukhov, Valeriy S.; Lviv Polytechnic National University
Multipliers for binary Galois field GF (2n) hardware complexity allows to implement in FPGA an operational device with multiple multipliers. But because of large structural complexity for some combinations of large degrees n of field and the multipliers number to make it is practically impossible. One of the possible choices of this problem solving is the move to using Galois fields with the base d, greater than 2. Multipliers for such extended Galois field GF (dm) with approximately the same number of elements dm  2n are estimated in the article in terms of their time complexity to determine the fields in which the multiplier will have the least time complexity.