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2023
In "Non-Field Structure of the Reals, Projective System Preferred," it wasdemonstrated using standard variable algebra how the so called, "Real Num-bers," are actually a projective scheme, and do not truly form a, "field," asexceptions have to made for the multiplicative inverse when a variable equalszero, which is possible.
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In "Non-Field Structure of the Reals, Projective System Preferred," it wasdemonstrated using standard variable algebra how the so called, "Real Num-bers," are actually a projective scheme, and do not truly form a, "field," asexceptions have to made for the multiplicative inverse when a variable equalszero, which is possible.
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International Conference on Theory and Practice of Public Key Cryptography, 2017
Taechan Kim, Jinhyuck Jeong
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Taechan Kim, Jinhyuck Jeong
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New Complexity Trade-Offs for the (Multiple) Number Field Sieve Algorithm in Non-Prime Fields
IACR Cryptology ePrint Archive, 2016P. Sarkar, Shashank Singh
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2012
This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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The Special Number Field Sieve in 𝔽pn - Application to Pairing-Friendly Constructions
Pairing-Based Cryptography, 2013A. Joux, Cécile Pierrot
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1989
For the benefit of less experienced readers, we repeat some basic definitions of abstract algebra. A group is a pair (G, + G ) in which G is a set and + G is a closed associative binary operation on G for which the following hold: a) there exists an element 1 G of G, called the identity, which has the property that for any element a in G, we ...
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For the benefit of less experienced readers, we repeat some basic definitions of abstract algebra. A group is a pair (G, + G ) in which G is a set and + G is a closed associative binary operation on G for which the following hold: a) there exists an element 1 G of G, called the identity, which has the property that for any element a in G, we ...
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Cancer treatment and survivorship statistics, 2022
Ca-A Cancer Journal for Clinicians, 2022Kimberly D Miller +2 more
exaly