Semirings As An Algebraic Structure Have Been Known Since 1934, But Remained Unapplied For Mathematical Purposes For A Long Time. It Has Only Been In The Past Decade That They Have Been Used In Cryptography. The Advantage Of (additively) Idempotent Semirings Is That The Additive Operation Does Not Have An Inverse, Which Can Help In Preventing The Breakage Of A Cryptosystem. This Book Describes A Number Of Cryptographic Protocols, As Well As The Hard Mathematical Problems On Which Their Security Is Based. It Will Appeal To Cryptographers And Specialists In Applied Algebra.

lgrsnf/Semirings As Building.pdf

zlib/Computers/Cryptography/Mariana Durcheva/Semirings as Building Blocks in Cryptography_5524834.pdf

Durcheva M

Cambridge Scholars Publishing, Newcastle-upon-Tyne, 1920

United Kingdom and Ireland, United Kingdom

Newcastle upon Tyne, 2020

lg2525394

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Contents
Acknowledgements
Preface
Chapter One
Chapter Two
2.1 Discrete Logarithms in Finite Fields
2.1.1 Definitions
2.1.2 Public key Cryptosystems based on the Discrete Logarithm Problem
2.1.3 Generic algorithms for solving the Discrete Logarithm Problem
2.1.4 Index Calculus algorithms for finite fields
2.2 Group Based Cryptography
2.2.1 The Discrete Logarithm Problem in abelian groups
2.2.2 The Discrete Logarithm Problem in nonabelian groups
2.2.3 Groups used as platforms for cryptosystems
2.3 The Discrete Logarithm Problem in Rings and Semirings
2.3.1 The Diffie-Hellman protocol in terms of formal algebra –a parallel between groups and rings
2.3.2 The Discrete Logarithm Problem in noncommutative rings
2.3.3 The Discrete Logarithm Problem and cryptography using semirings
2.3.4 Semirings and cryptography
Bibliography to Chapters One and Two
Chapter Three
3.1 Idempotent Algebra
3.1.1 Dioids as lattices
3.1.2 Residuated maps
3.1.3 Semimodules over idempotent semirings
3.1.4 Residuated lattices
3.1.5 Construction of complete dioid
3.1.6 Matrices defined over idempotent semifields
3.1.7 Residuated operations over matrix semimodules
3.1.8 Max-plus algebra
3.1.9 Min-plus algebra
3.1.10 Max-time algebra
3.1.11 Min-time algebra
3.2 Linear Equations
3.3 Applications of Idempotent Algebra in Cryptography
Bibliography to Chapter Three
Chapter Four
4.1 Definitions and Motivation to Study
4.2 Distributed Secure Multicast Protocol
Bibliography to Chapter Four
Chapter Five
5.1 Endomorphism Semirings
5.2 Simplices and Simplicial Complexes
5.3 Cryptography Based on Endomorphism Semirings
5.3.1 Motivation, basic definitions and notations
5.3.2 Three key-exchange protocols based on endomorphism semirings
5.3.3 Four key exchange protocols using right identities of the simplex
Bibliography to Chapter Five

2020-05-21