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.

This paper investigates the feasibility of employing artificial neural network techniques for solving fundamental cryptography problems, taking quadratic residue detection as an example. The problem of quadratic residue detection is one which is well known in both number theory and cryptography. While it garners less attention than problems such as factoring or discrete logarithms, it is similar in both difficulty and importance. No polynomial-time algorithm is currently known to the public by which the quadratic residue status of one number modulo another may be determined. This work leverages machine learning algorithms in an attempt to create a detector capable of solving instances of the problem more efficiently. A variety of neural networks, currently at the forefront of machine learning methodologies, were compared to see if any were capable of consistently outperforming random guessing as a mechanism for detection. Surprisingly, neural networks were repeatably able to achieve accuracies well in excess of random guessing on numbers up to 20 bits in length. Unfortunately, this performance was only achieved after a super-polynomial amount of network training, and therefore we do not believe that the system as implemented could scale to cryptographically relevant inputs of 500 to 1000 bits. This nonetheless suggests a new avenue of attack in the search for solutions to the quadratic residues problem, where future work focused on feature set refinement could potentially reveal the components necessary to construct a true closed-form solution.

With the continuous growth of cyberinfrastructure throughout modern society, the need for secure computing and communication is more important than ever before. As a result, there is also an increasing need for entry-level developers who are capable of designing and building practical solutions for systems with stringent security requirements. This calls for careful attention to algorithm choice and implementation method, as well as trade-offs between hardware and software implementations. This article describes motivation and efforts taken by three departments at Rochester Institute of Technology (Computer Engineering, Computer Science, and Software Engineering) that were focused on creating a multidisciplinary course that integrates the algorithmic, engineering, and practical aspects of security as exemplified by applied cryptography. In particular, the article presents the structure of this new course, topics covered, lab tools and results from the first two spring quarter offerings in 2011 and 2012.

In this paper, we study Shannon capacity of channels in the context of classical Ramsey numbers. We overview some of the results on capacity of noisy channels modeled by graphs, and how some constructions may contribute to our knowledge of this capacity. We present an improvement to the constructions by Abbott and Song and thus establish new lower bounds for a special type of multicolor Ramsey numbers. We prove that our construction implies that the supremum of the Shannon capacity over all graphs with independence number 2 cannot be achieved by any finite graph power. This can be generalized to graphs with bounded independence number.

The Ramsey number $R(G_1, G_2, G_3)$ is the smallest positive integer $n$ such that for all 3-colorings of the edges of $K_n$ there is a monochromatic $G_1$ in the first color, $G_2$ in the second color, or $G_3$ in the third color. We study the bounds on various 3-color Ramsey numbers $R(G_1, G_2, G_3)$, where $G_i \in \{K_3, K_3+e, K_4-e, K_4\}$. The minimal and maximal combinations of $G_i$'s correspond to the classical Ramsey numbers $R_3(K_3)$ and $R_3(K_4)$, respectively, where $R_3(G) = R(G, G, G)$. Here, we focus on the much less studied combinations between these two cases. Through computational and theoretical means we establish that $R(K_3, K_3, K_4-e)=17$, and by construction we raise the lower bounds on $R(K_3, K_4-e, K_4-e)$ and $R(K_4, K_4-e, K_4-e)$. For some $G$ and $H$ it was known that $R(K_3, G, H)=R(K_3+e, G, H)$; we prove this is true for several more cases including $R(K_3, K_3, K_4-e) = R(K_3+e, K_3+e, K_4-e)$. Ramsey numbers generalize to more colors, such as in the famous 4-color case of $R_4(K_3)$, where monochromatic triangles are avoided. It is known that $51 \leq R_4(K_3) \leq 62$. We prove a surprising theorem stating that if $R_4(K_3)=51$, then $R_4(K_3+e)=52$, otherwise $R_4(K_3+e)=R_4(K_3)$.

We present several new constructive lower bounds for classical Ramsey numbers. In particular, the inequality $R(k,s+1) \geq R(k,s)+2k-2$ is proved for $k \geq 5$. The general construction permits us to prove that, for all integers k, l, with $k \geq 5$ and $l \geq 3$, the connectivity of any Ramsey-critical $(k,l)$-graph is at least k, and if $k \geq l-1 \geq 1$, $k \geq 3$ and $(k,l) \neq (3,2)$, then such graphs are Hamiltonian. New concrete lower bounds for Ramsey numbers are obtained, some with the help of computer algorithms, including: $R(5,17) \geq 388$, $R(5,19) \geq 411$, $R(5,20) \geq 424$, $R(6,8) \geq 132$, $R(6,12) \geq 263$, $R(7,8) \geq 217$, $R(7,9) \geq 241$, $R(7,12) \geq 417$, $R(8,17) \geq 961$, $R(9,10) \geq 581$, $R(12,12) \geq 1639$, and also one three-color case $R(8,8,8) \geq 6079$.

Implantable medical devices (IMDs) have played an important role in many medical fields. Any failure in IMDs operations could cause serious consequences and it is important to protect the IMDs access from unauthenticated access. This study investigates secure IMD data collection within a telehealthcare [mobile health (m-health)] network. We use medical sensors carried by patients to securely access IMD data and perform secure sensor-to-sensor communications between patients to relay the IMD data to a remote doctor's server. To meet the requirements on low computational complexity, we choose N-th degree truncated polynomial ring (NTRU)-based encryption/decryption to secure IMD-sensor and sensor-sensor communications. An extended matryoshkas model is developed to estimate direct/indirect trust relationship among sensors. An NTRU hardware implementation in very large integrated circuit hardware description language is studied based on industry Standard IEEE 1363 to increase the speed of key generation. The performance analysis results demonstrate the security robustness of the proposed IMD data access trust model.

Abstract Wireless sensor network security requires the cryptography software extremely low complex and energy efficient due to the limited memory and CPU capacity in a sensor. The NTRU (Nth degree truncated polynomial ring) encrypt algorithm has been shown to provide certain advantages when designing low power and resource constrained systems, while still providing comparable security levels to higher complexity algorithms. Unlike the current works that build NTRU software in a chip, this research focuses on the hardware implementation of NTRU algorithms because hardware implementation has much higher execution speed than software implementation. In contrast to previous research, the focus is shifted away from specific optimizations but rather provides a study of many of the recommended practices and suggested optimizations with particular emphasis on polynomial arithmetic and parameter selection. Recommendations for algorithm and parameter selection are made regarding implementation in hardware with respect to the resources available. Copyright © 2008 John Wiley & Sons, Ltd.