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Просмотр по автору "Ishmukhametov S."

Просмотр по автору "Ishmukhametov S."

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  • An algorithm for counting smooth integers 
    Ishmukhametov S.; Sharifullina F. (2016)
    © 2016, Pleiades Publishing, Ltd.An integer number n > 0 is called y-smooth for y > 0 if any prime factor p of n satisfies p ≤ y. Let ψ(x, y) be the number of all y-smooth integers less or equal to x. In this paper we ...
  • An approximating k-ary GCD algorithm 
    Ishmukhametov S. (2016)
    © 2016, Pleiades Publishing, Ltd.In our paper we elaborate a new version of the k-ary GCD algorithm. Our algorithm is based on the Farey Series and surpasses all existing realizations of the k-ary algorithm. It can have ...
  • Analysis of the k-ary Euclid for tuples of integers 
    Amer I.; Ishmukhametov S. (2019)
    © Published under licence by IOP Publishing Ltd. In our paper we discuss the k-ary Euclid Algorithm for counting the great common divisor (GCD) of two or more integers and suggest some improvements. This gives us a possibility ...
  • Archain: A Novel Blockchain Based Archival System 
    Galiev A.; Prokopyev N.; Ishmukhametov S.; Stolov E.; Latypov R.; Vlasov I. (2019)
    © 2018 IEEE. In this paper, we present a novel archival system called ARCHAIN, developed for the State Archive-keeping Committee of the Republic of Tatarstan (Russia). Blockchain is the principal part of the system, which ...
  • Calculation of Bezout’s coefficients for the k-ary algorithm of finding GCD 
    Ishmukhametov S.; Mubarakov B.; Maad K. (2017)
    © 2017, Allerton Press, Inc. Bezout’s equation is a representation of the greatest common divisor d of integers A and B as a linear combination Ax + By = d, where x and y are integers called Bezout’s coefficients. The task ...
  • On acceleration of the k-ary GCD algorithm 
    Amer I.; Ishmukhametov S. (2019)
    © 2019, Kazan Federal University. All rights reserved. In this paper, methods of acceleration of GCD algorithms for natural numbers based on the k-ary GCD algorithm have been studied. The k-ary algorithm was elaborated by ...
  • On distribution of semiprime numbers 
    Ishmukhametov S.; Sharifullina F. (2014)
    A semiprime is a natural number which is the product of two (possibly equal) prime numbers. Let y be a natural number and g(y) be the probability for a number y to be semiprime. In this paper we derive an asymptotic formula ...
  • One approach to factorization of positive integers 
    Boiko A.; Ziyatdinov D.; Ishmukhametov S. (2011)
    Factorization of positive integers into primes is a hard computational task. Its complexity lies in the base of the most popular method of cryptography, the RSA method. In this paper we propose a new technique in a ...
  • The Error Probability of the Miller–Rabin Primality Test 
    Ishmukhametov S.; Rubtsova R.; Savelyev N. (2018)
    © 2018, Pleiades Publishing, Ltd. In our paper we give theoretical and practical estimations of the error probability in the well-known Miller–Rabin probabilistic primality test. We show that a theoretical probability of ...

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