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Montgomery Algorithm over a Prime Field
Chinese Journal of Electronics, 2019New formulae for point addition and point doubling on elliptic curves over prime fields are presented. Based on these formulae, an improved Montgomery algorithm is proposed. The theoretical analysis indicates that it is about 13.4% faster than Brier and Joye's Montgomery algorithm.
Wei Yu, Kunpeng Wang, Bao Li, Song Tian
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International journal of circuit theory and applications, 2023
Elliptic curve point multiplication is the main primitive required in almost all security schemes using elliptic curve cryptography (ECC). It is the leading computationally intensive operation that sets the overall performance of the associated ...
Khalid Javeed, Ali A. El-Moursy
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Elliptic curve point multiplication is the main primitive required in almost all security schemes using elliptic curve cryptography (ECC). It is the leading computationally intensive operation that sets the overall performance of the associated ...
Khalid Javeed, Ali A. El-Moursy
semanticscholar +1 more source
ECC Coprocessor Over a NIST Prime Field Using Fast Partial Montgomery Reduction
IEEE Transactions on Circuits and Systems Part 1: Regular Papers, 2021Montgomery reduction is a well-known optimization technique for modular reduction over prime fields. However, it has rarely been used for national institute of standards and technology (NIST) prime fields, because the special structure of NIST primes ...
Piljoo Choi, Mun-Kyu Lee, Dong Kyue Kim
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2022
This paper presents evidence of a recursive fractal structure in the distribution of prime numbers,revealed through triplet decomposition and recursive extraction of strings based on the position of primeswithin triplets. Each level of recursion yields three new strings (X, Y, Z), forming a tree-like topology ofprime-derived sequences.
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This paper presents evidence of a recursive fractal structure in the distribution of prime numbers,revealed through triplet decomposition and recursive extraction of strings based on the position of primeswithin triplets. Each level of recursion yields three new strings (X, Y, Z), forming a tree-like topology ofprime-derived sequences.
+4 more sources
International journal of circuit theory and applications, 2020
Elliptic curve cryptography (ECC) schemes are widely adopted for the digital signature applications due to their key sizes, hardware resources, and higher security per bit than Rivest‐Shamir‐Adleman (RSA).
Thirumalesu Kudithi, Sakthivel R
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Elliptic curve cryptography (ECC) schemes are widely adopted for the digital signature applications due to their key sizes, hardware resources, and higher security per bit than Rivest‐Shamir‐Adleman (RSA).
Thirumalesu Kudithi, Sakthivel R
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Canadian Journal of Mathematics, 1995
AbstractAn additive subgroupPof a skew fieldFis called aprimeofFifPdoes not contain the identity, but if the productxyof two elementsxandyinFis contained inP, thenxoryis inP. A prime segment ofFis given by two neighbouring primesP1⊃P2; such a segment is invariant, simple, or exceptional depending on whetherA(P1) = {a∈P1|P1aP1⊂P1} equalsP1,P2or lies ...
Brungs, H. H., Schröder, M.
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AbstractAn additive subgroupPof a skew fieldFis called aprimeofFifPdoes not contain the identity, but if the productxyof two elementsxandyinFis contained inP, thenxoryis inP. A prime segment ofFis given by two neighbouring primesP1⊃P2; such a segment is invariant, simple, or exceptional depending on whetherA(P1) = {a∈P1|P1aP1⊂P1} equalsP1,P2or lies ...
Brungs, H. H., Schröder, M.
openaire +1 more source

