Algebraic Cryptography

2015 ◽  
pp. 173-228
Author(s):  
Richard Klima ◽  
Neil Sigmon ◽  
Ernest Stitzinger
Keyword(s):  
Algebraic Cryptography

scholarly journals Mixed signal testing system technique with algebraic signature analyzer without carry propagation

2021 ◽  
Author(s):  
Mohammed Faruque Ahmed
Keyword(s):  
Testing System ◽  
Signal System ◽  
High Complexity ◽  
Hardware Complexity ◽  
Mixed Signal ◽  
Algebraic Signature ◽  
Signature Analyzer ◽  
System Technique ◽  
Algebraic Cryptography ◽  
Mixed Signal Testing

Signature Analyzer is an analyzer which is widely used for mixed-signal system testing. But its hardware has high complexity in implementation as the application technique is a system with rules of an arithmetic finite field with arbitrary radix. It’s a challenging task. To avoid this complexity here the project is made based on Algebraic Signature Analyzer that can be used for mixed signal testing and the analyzer doesn’t contain carry propagation circuitry. It improves performance and fault tolerance. This technique is simple and applicable to systems of any size or radix. The hardware complexity is very low compared to the conventional one and can be used in arithmetic/ algebraic cryptography as well as coding

scholarly journals Algebraic cryptography: new constructions and their security against provable break

2009 ◽  
Vol 20 (6) ◽  
pp. 937-953 ◽  
Author(s):  
D. Grigoriev ◽  
A. Kojevnikov ◽  
S. J. Nikolenko
Keyword(s):  
Algebraic Cryptography

Involutory Matrices Over Finite Local Rings

1972 ◽  
Vol 24 (3) ◽  
pp. 369-378 ◽  
Author(s):  
B. R. McDonald
Keyword(s):  
Prime Power ◽  
Quotient Ring ◽  
Careful Analysis ◽  
Commutative Rings ◽  
Local Rings ◽  
Power Characteristic ◽  
Special Cases ◽  
Algebraic Cryptography ◽  
Characteristic 2 ◽  
Finite Commutative Rings

A square matrix A over a commutative ring R is said to be involutory if A2 = I (identity matrix). It has been recognized for some time that involutory matrices have important applications in algebraic cryptography and the special cases where R is either a finite field or a quotient ring of the rational integers have been extensively researched. However, there has been no detailed attempt to extend the theory to all finite commutative rings. In this paper we illustrate in detail the theory of involutory matrices over finite commutative rings with 1 having odd characteristic. The method is a careful analysis of finite local rings of odd prime power characteristic. The techniques might be also used in the examination of involutory matrices over local rings of characteristic 2λ; however, as illustrated by finite fields of characteristic 2 and Z/2λZ (Z the rational integers), the arguments are basically different. The reader will note the methods are not limited to only questions on involutory matrices.

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