With recent progress in the development of large-scale, general-purpose, fault-tolerant quantum computing (QC), significant effort is being made in the cybersecurity community to create viable long-term solutions mitigating the threat of quantum computers breaking classical public-key based security schemes. The current post-quantum cryptography (PQC) standardization process led by the National Institute of Standards and Technology (NIST) has standardized cryptographic protocols designed to be resistant to QC. PQC education is still in its early stages, with limited curricular materials available for broad distribution in an appropriate academic format. Another challenge is developing curricula for students with different levels of computing and cryptographic preparedness. The modular approach to curriculum development has been proven to be an effective method for introducing new concepts. The authors of this work have several years of experience teaching cryptography and PQC courses at two academic institutions. We introduce two types of PQC instruction modules at varying levels of complexity: Awareness and Proficiency. The suggested contents, learning outcomes, and duration for each module are presented.

With recent progress in the development of cryptographically relevant Quantum Computing (QC), significant effort is being made in the cryptography community to create viable long-term solutions against the threat of QC breaking classical public-key security schemes. The current Post-Quantum Cryptography (PQC) standardization process led by the NIST has made some selections and is about to recommend new cryptographic protocols resistant to QC. This work reports our experiences teaching a first-in-kind module- based course in Quantum-Resistant Cryptography (QRC) at two universities.

The security of many commonly used cryptographic protocols, especially public-key cryptosystems, would be compromised if general-purpose, large-scale, fault-tolerant quantum computers become a reality. In this paper we present our experience developing and launching a course in Post-Quantum Cryptography (PQC). PQC refers to cryptographic systems that are secure against both quantum and classical computers. Such systems may be achieved through classical (i.e. non-quantum) means.

On December 20th, 2016, the National Institute of Standards and Technology (NIST) formally initiated a competition to solicit, evaluate, and standardize one or more quantumresistant cryptographic algorithms.Among the current candidates is a cryptographic primitive which has shown much promise in the post-quantum age, Multivariate Cryptography.These schemes compose two affine bijections S and T with a system of multivariate polynomials.However, this composition of S and T becomes costly as the data encrypted grows in size.Here we present Constructive Affine Stream (CAS) Transformations, a set of algorithms which enable specialized, large-scale, affine transformations in O(n) space and O(n log n) time, without compromising security.The goal of this paper is to address the practical problems related to affine transformations common among almost all multivariate cryptographic schemes.

The main purpose of this paper is to introduce stream ciphers with the nonbijective encryption function of multivariate nature constructed in terms of algebraic graph theory. More precisely, we describe the two main symmetric algorithms for creation of multivariate encryption transformations based on three families of bipartite graphs with partition sets isomorphic to Kn , where K is selected as the finite commutative ring. The plainspace of the algorithm is Ω={x∣∑xi∈K⁎, x∈Kn}⊂Kn, Ω≅K⁎×Kn-1. The second algorithm is a generalization of the first one with using the jump operator, where generalized encryption map has an essentially higher degree in comparison with the previous version. Moreover, the degree of this generalized map is not bounded by some constant. This property guarantees resistance of the cipher to linearization attacks.

Certain families of graphs can be used to obtain multivariate polynomials for cryptographic algorithms.In particular, in this paper, we introduce stream ciphers based on nonbijective multivariate maps.The presented symmetric encryption algorithms are based on three families of bipartite graphs with partition sets isomorphic to K n , where K is selected as the finite commutative ring.The plainspace of the algorithm isWe describe the algorithm for the case K = Z2m , m ≥ 2. In fact, we use the relation d * d dec ≡ 1(mod 2 m-1 ), d, d dec ∈ Z