Gaussian Integers
Cubic Root Extractors of Gaussian Integers and Their Application in Fast Encryption for Time Constrained Secure Communication
... [4] H. Elkamchouchi, K. Elshenawy and H. Shaban, “Ex- tended RSA Cryptosystem and Digital Signature Schemes in the Domain of Gaussian Integers,” The 8th Interna- tional Conference on Communication Systems, ...
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On the Line Graph of the Complement Graph for the Ring of Gaussian Integers Modulo n
... to 3 modulo 4. All rings in this paper are assumed to be commutative with unity. The zero divisor graph for the ring of Gaussian integers modulo n is studied in [1] and [2], the complement of this graph is ...
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Information Protection Based on Extraction of Square Roots of Gaussian Integers
... of Gaussian integers {Gaussians, for short} in PKC were extended to the RSA scheme [2], and to ElGamal cryptosystems ...real integers have cycles of order , groups based on Gaussians modulo prime p ...
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Gaussian integers with small prime factors
... Jordan’s estimate fixed the parameter t and our estimate had t bounded with The purpose of this note is to present an asymptotic estimate for.. respect to x..[r] ...
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Norm of Gaussian integers in arithmetical progressions and narrow sectors
... For the classical arithmetic functions τ (n) (the number of divisors for the positive integer n) and r(n) (the number of representations for the positive integer n as sum of two squares of integers) there were ...
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Quadratic residues of the norm group in sectorial domains
... of Gaussian integers is, evidently, a difficult problem by the virtue of the fact, that geometry of points of a plane is richer than geometry of points on a ...
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Vol 9, No 4 (2018)
... the Gaussian prime labelling of unicyclic ...introduce Gaussian integers and their ...to Gaussian prime labelling by using the first n Gaussian ...the Gaussian integers ...
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The order of the second group of units of the ring Z[i]/
... of Gaussian integers Z[i], where φ G (β ) represents the order of the group of units of the ring Z[i]/ < β > where β is a non zero Gaussian ...
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Complete residue systems in the quadratic domain Z(e2πi/3)
... A Minimum Problem Connected with Complete Residue Systems in the Gaussian Integers, Amer.. Complete Residue Systems in the Gaussian Integers, Math.[r] ...
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Codes over Quaternion Integers
... over Gaussian integers with respect to the Mannheim metric which are suitable for quadrature amplitude modulation (QAM)-type were introduced by Huber in [1, ...over Gaussian integers Z [i] ...
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Fast multiplication of multiple-precision integers
... functions to the simplified multiplication 3.3.3 modular modular multiplication particular already very decrease bits using num the ordinary according to the formula for the bit complexi[r] ...
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On the Weil étale Cohomology of S Integers
... In this thesis, we first briefly introduce the history of the Weil-´ etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the ...
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Idempotent Factorizations of Square-free Integers
... positive integers n that admit idempotent factorizations n = p ¯q ¯ such that λ(n) ∣ (p ¯ − 1)(q ¯ − 1), where λ is the Carmichael lambda ...idempotent integers, those n for which all bipartite ...
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SUBTRACTION OF INTEGERS IN MIXED RADIX SYSTEM
... In this paper, two integers with two radices are considered and represented the subtraction of the two integers with the mixed radix system. In the second part of the paper, more than two radices are taken ...
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ECM at Work
... of integers, which are constructed such that they can be computed using an addition-subtraction chain with a high doubling/addition ratio, are tested for smoothness and ...these integers using a greedy ...
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Partitioning the positive integers with higher order recurrences
... some choice positive integer for which 2.1 holds for For a given Stolarsky array, if k is the least determined, and identity 0, then these integers are uniquely of integers ck-, c_2,...,[r] ...
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SRC RR 145 pdf
... specialization specification IntSetSSpec f state field elements; // A mathematical set of integers state field cache; // Also a mathematical set of integers invariant cache ⊆ elements //[r] ...
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Finding the ring of integers and its algorithms in algebraic number theory
... of integers modulo n:the sum of the congruence classes of integers x and y is the congruence class of x+y, and the product of these congruence classes is the congruence class of ...
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Estimating the polygamma functions for negative integers
... Ozcag et al. [, ] applied the neutrix limit to extend the definition of incomplete beta function and its partial derivatives for negative integers. Also, the digamma function was generalized for negative ...
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New Multilinear Maps over the Integers
... Multilinear maps. Since the breakthrough construction of Garg, Gentry and Halevi [GGH13a], there has been a growing interest in cryptographic multilinear maps. They have spurred scores of new cryptographic applications. ...
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