Modern Cryptography with Proof Techniques and Applications

2021 ◽  
Author(s):  
Seong Oun Hwang ◽  
Intae Kim ◽  
Wai Kong Lee
Keyword(s):  
Proof Techniques ◽  
Modern Cryptography

INTRODUCING PROOF TECHNIQUES USING THE LOGICAL GAMEMINE HUNTER

PRIMUS ◽  
1995 ◽  
Vol 5 (2) ◽  
pp. 108-112 ◽  
Author(s):  
Allan Alexander Struthers
Keyword(s):  
Proof Techniques

scholarly journals Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lize Gu ◽  
Shihui Zheng
Keyword(s):  
Performance Analysis ◽  
Quantum Algorithm ◽  
Integer Factorization ◽  
Algebraic Structures ◽  
Cryptographic Primitives ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Modern Cryptography ◽  
Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

PARITY RESULTS FOR PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER OF TIMES

2018 ◽  
Vol 99 (1) ◽  
pp. 51-55
Author(s):  
MICHAEL D. HIRSCHHORN ◽  
JAMES A. SELLERS
Keyword(s):  
Generating Function ◽  
Proof Techniques ◽  
One To One

We consider the function $f(n)$ that enumerates partitions of weight $n$ wherein each part appears an odd number of times. Chern [‘Unlimited parity alternating partitions’, Quaest. Math. (to appear)] noted that such partitions can be placed in one-to-one correspondence with the partitions of $n$ which he calls unlimited parity alternating partitions with smallest part odd. Our goal is to study the parity of $f(n)$ in detail. In particular, we prove a characterisation of $f(2n)$ modulo 2 which implies that there are infinitely many Ramanujan-like congruences modulo 2 satisfied by the function $f.$ The proof techniques are elementary and involve classical generating function dissection tools.

Proof Techniques

Proofs 101 ◽  
2020 ◽  
pp. 15-36
Author(s):  
Joseph Kirtland
Keyword(s):  
Proof Techniques

Modern Cryptography

2020 ◽  
pp. 106-122
Author(s):  
Wayne Patterson ◽  
Cynthia E. Winston-Proctor
Keyword(s):  
Modern Cryptography

scholarly journals Discrete Mathematics into K-11 and K-12 Grade Education

2021 ◽  
Vol 23 (05) ◽  
pp. 319-324
Author(s):  
Mr. Balaji. N ◽  
◽  
Dr. Karthik Pai B H ◽  
Keyword(s):  
Set Theory ◽  
Mathematical Reasoning ◽  
Mathematical Induction ◽  
Discrete Mathematics ◽  
College Classrooms ◽  
Underlying Principle ◽  
Education Study ◽  
Strongly Connected ◽  
Proof Techniques ◽  
K 12

Discrete mathematics is one of the significant part of K-11 and K-12 grade college classrooms. In this contribution, we discuss the usefulness of basic elementary, some of the intermediate discrete mathematics for K-11 and K-12 grade colleges. Then we formulate the targets and objectives of this education study. We introduced the discrete mathematics topics such as set theory and their representation, relations, functions, mathematical induction and proof techniques, counting and its underlying principle, probability and its theory and mathematical reasoning. Core of this contribution is proof techniques, counting and mathematical reasoning. Since all these three concepts of discrete mathematics is strongly connected and creates greater impact on students. Moreover, it is potentially useful in their life also out of the college study. We explain the importance, applications in computer science and the comments regarding introduction of such topics in discrete mathematics. Last part of this article provides the theoretical knowledge and practical usability will strengthen the made them understand easily.

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