In cryptology, secure channels enable the exchange of messages in a confidential and authenticated manner. The literature of cryptology is rich with proposals and analysis that address the secure communication over public (insecure) channels. In this work, we propose an information theoretically secure direction for the construction of secure channels. First, we propose a method of achieving un...

We propose constructions of fully homomorphic encryption completely different from the previous work, using special kinds of non-commutative finite groups. Unlike the existing schemes, our ciphertexts involve no “noise” terms, hence the inefficient “bootstrapping” procedures are not necessary. Our first scheme is based on improved results on embeddings of logic gates into (almost) simple groups...

A new technique for combinational circuit optimization is described in the context of S-boxes. The technique is a two-step process. In the first step, the non-linearity of the circuit – as measured by the number of non-linear gates it contains – is reduced. The second step reduces the number of gates in the linear components of the already reduced circuit. The technique can be applied to arbitr...

We describe aspects of computational thinking as covered in the course Codes and Ciphers (CSC 233). 1 Cryptology and Computational Thinking Cryptology consists of cryptography and cryptanalysis, or, in other words, the making and the breaking of ciphers. History suggests that one cannot successfully do one without the other: too many ciphers were designed by enthusiasts without any knowledge of...

In this work, we are interested in non-trivial upper bounds on the spectral norm of binary matrices M from {−1, 1}N×N . It is known that the distributed Boolean function represented by M is hard to compute in various restricted models of computation if the spectral norm is bounded from above by N1−ε, where ε > 0 denotes a fixed constant. For instance, the size of a two-layer threshold circuit (...

Constructing a Pseudo Random Function (PRF) is fundamental problem in cryptology. Such construction, implemented by truncating the last m bits of permutations { 0 , 1 } n was suggested Hall et al. (1998). They conjectured that distinguishing advantage an adversary with q queries, Adv ( ) small if = o 2 + ∕ established upper bound on confirms conjecture for < 7 and also declared general lower Ω ...

In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing systems (LNECS) are introduced. Then, numerical map (LCLS), Logistic Sine map, given. Through analysis bifurcation diagram, Lyapunov exponent (LE), Sample entropy (SE), we can see that CLS has overcome shortcomings lo...

INTRODUCTION Traditional government structures are sometimes regarded as overly bulky. However, with the rapid expansion of interconnected computer networks and the progressive development of Information Technology (IT), it is now possible to exchange massive amounts of data at light speed over great distances. These infrastructure and technology provide the opportunity for governments to trans...