Hash Functions Based on Ramanujan Graphs

2017 ◽  
pp. 63-79
Author(s):  
Hyungrok Jo
Keyword(s):  
Hash Functions ◽  
Ramanujan Graphs

scholarly journals Ramanujan Graphs for Post-Quantum Cryptography

2020 ◽  
pp. 231-250
Author(s):  
Hyungrok Jo ◽  
Shingo Sugiyama ◽  
Yoshinori Yamasaki
Keyword(s):  
Group Theory ◽  
Quantum Cryptography ◽  
Hash Function ◽  
Hash Functions ◽  
Optimal Structure ◽  
Expander Graphs ◽  
Ramanujan Graphs ◽  
Hard Problems ◽  
Post Quantum Cryptography ◽  
The Relationship

Abstract We introduce a cryptographic hash function based on expander graphs, suggested by Charles et al. ’09, as one prominent candidate in post-quantum cryptography. We propose a generalized version of explicit constructions of Ramanujan graphs, which are seen as an optimal structure of expander graphs in a spectral sense, from the previous works of Lubotzky, Phillips, Sarnak ’88 and Chiu ’92. We also describe the relationship between the security of Cayley hash functions and word problems for group theory. We also give a brief comparison of LPS-type graphs and Pizer’s graphs to draw attention to the underlying hard problems in cryptography.

scholarly journals Generalized Group–Subgroup Pair Graphs

2020 ◽  
pp. 169-185
Author(s):  
Kazufumi Kimoto
Keyword(s):  
Zeta Function ◽  
Riemann Hypothesis ◽  
Cayley Graphs ◽  
Hash Functions ◽  
Finite Graph ◽  
Ramanujan Graphs ◽  
Basic Properties ◽  
Ramanujan Graph ◽  
Second Eigenvalue ◽  
Cryptographic Hash Functions

Abstract A regular finite graph is called a Ramanujan graph if its zeta function satisfies an analog of the Riemann Hypothesis. Such a graph has a small second eigenvalue so that it is used to construct cryptographic hash functions. Typically, explicit family of Ramanujan graphs are constructed by using Cayley graphs. In the paper, we introduce a generalization of Cayley graphs called generalized group–subgroup pair graphs, which are a generalization of group–subgroup pair graphs defined by Reyes-Bustos. We study basic properties, especially spectra of them.

Hash Functions Based on Block Ciphers

2009 ◽  
Vol 20 (3) ◽  
pp. 682-691
Author(s):  
Pin LIN ◽  
Wen-Ling WU ◽  
Chuan-Kun WU
Keyword(s):  
Hash Functions ◽  
Block Ciphers

Data Integrity

2017 ◽  
Author(s):  
Keith M. Martin
Keyword(s):  
Hash Function ◽  
Hash Functions ◽  
Data Integrity ◽  
Message Authentication ◽  
Authenticated Encryption ◽  
Authentication Codes ◽  
Basic Model ◽  
Function Design ◽  
Security Properties ◽  
Different Levels

This chapter discusses cryptographic mechanisms for providing data integrity. We begin by identifying different levels of data integrity that can be provided. We then look in detail at hash functions, explaining the different security properties that they have, as well as presenting several different applications of a hash function. We then look at hash function design and illustrate this by discussing the hash function SHA-3. Next, we discuss message authentication codes (MACs), presenting a basic model and discussing basic properties. We compare two different MAC constructions, CBC-MAC and HMAC. Finally, we consider different ways of using MACs together with encryption. We focus on authenticated encryption modes, and illustrate these by describing Galois Counter mode.

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