This book is about relations between three di? erent areas of mathematics and
theoreticalcomputer science: combinatorialgroup theory, cryptography, and c-plexity theory …

We introduce a method for obtaining provable polynomial time solutions of problems in
nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and …

The enciphering schemes based on medium transformations by following the strict
guidelines are almost used everywhere. We have developed the structure to simulate the …

The goalofthisbookis toshowcasenewdirectionsingroup theorymotivated bycomputer
science. The subtitle (GAGTA book) reflects the fact that the book follows the courseoftheGeometricandAsymptoticGroup …

The area of cybersecurity problems has reached the stage of becoming a science. This
raises questions about the connection between the mathematical theories used in …

As special types of factorization of finite groups, logarithmic signatures and covers have
been used as the main components of cryptographic keys for secret key cryptosystems such …

The concept of directionally unbiased optical multiports is introduced, in which photons may
reflect back out the input direction. A linear-optical implementation is described, and the …

This paper is a guide for the pure mathematician who would like to know more about
cryptography based on group theory. The paper gives a brief overview of the subject, and …

We propose a generalization of the learning parity with noise (LPN) and learning with errors
(LWE) problems to an abstract class of group-theoretic learning problems that we term …

Public-key solutions based on number theory, including RSA, ECC, and Diffie-Hellman, are
subject to various quantum attacks, which makes such solutions less attractive long term …