On Polynomial Multiplication in Chebyshev Basis

In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's multiplication scheme to improve upon the naive method but without being able to get rid of its quadratic complexity. In this paper, we extend their result by providing a reduction scheme which allows to multiply polynomial in Chebyshev basis by using algorithms from the monomial basis case and therefore get the same asymptotic complexity estimate. Our reduction allows to use any of these algorithms without converting polynomials input to monomial basis which therefore provide a more direct reduction scheme then the one using conversions. We also demonstrate that our reduction is efficient in practice, and even outperform the performance of the best known algorithm for Chebyshev basis when polynomials have large degree. Finally, we demonstrate a linear time equivalence between the polynomial multiplication problem under monomial basis and under Chebyshev basis

A review of enhanced image techniques using chaos encryption

Secured multimedia data has grown in importance over the last few decades to safeguard multimedia content from unwanted users. Generally speaking, a number of methods have been employed to hide important visual data from eavesdroppers, one of which is chaotic encryption. This review article will examine chaotic encryption methods currently in use, highlighting their benefits and drawbacks in terms of their applicability for picture security

NTRU-KE: A Lattice-based Public Key Exchange Protocol

Public key exchange protocol is identified as an important application in the field of public-key cryptography. Most of the existing public key exchange schemes are Diffie-Hellman (DH)-type, whose security is based on DH problems over different groups. Note that there exists Shor\u27s polynomial-time algorithm to solve these DH problems when a quantum computer is available, we are therefore motivated to seek for a non-DH-type and quantum resistant key exchange protocol. To this end, we turn our attention to lattice-based cryptography. The higher methodology behind our roadmap is that in analogy to the link between ElGamal, DSA, and DH, one should expect a NTRU lattice-based key exchange primitive in related to NTRU-ENCRYPT and NTRU-SIGN. However, this excepted key exchange protocol is not presented yet and still missing. In this paper, this missing key exchange protocol is found, hereafter referred to as NTRU-KE, which is studied in aspects of security and key-mismatch failure. In comparison with ECDH (Elliptic Curve-based Diffie-Hellman), NTRU-KE features faster computation speed, resistance to quantum attack, and more communication overhead. Accordingly, we come to the conclusion that NTRU-KE is currently comparable with ECDH. However, decisive advantage of NTRU-KE will occur when quantum computers become a reality

Enhancing Electromagnetic Side-Channel Analysis in an Operational Environment

Side-channel attacks exploit the unintentional emissions from cryptographic devices to determine the secret encryption key. This research identifies methods to make attacks demonstrated in an academic environment more operationally relevant. Algebraic cryptanalysis is used to reconcile redundant information extracted from side-channel attacks on the AES key schedule. A novel thresholding technique is used to select key byte guesses for a satisfiability solver resulting in a 97.5% success rate despite failing for 100% of attacks using standard methods. Two techniques are developed to compensate for differences in emissions from training and test devices dramatically improving the effectiveness of cross device template attacks. Mean and variance normalization improves same part number attack success rates from 65.1% to 100%, and increases the number of locations an attack can be performed by 226%. When normalization is combined with a novel technique to identify and filter signals in collected traces not related to the encryption operation, the number of traces required to perform a successful attack is reduced by 85.8% on average. Finally, software-defined radios are shown to be an effective low-cost method for collecting side-channel emissions in real-time, eliminating the need to modify or profile the target encryption device to gain precise timing information

Enhancement of Nth degree truncated polynomial ring for improving decryption failure

Nth Degree Truncated Polynomial (NTRU) is a public key cryptosystem constructed in a polynomial ring with integer coefficients that is based on three main key integer parameters N; p and q. However, decryption failure of validly created ciphertexts may occur, at which point the encrypted message is discarded and the sender re-encrypts the messages using different parameters. This may leak information about the private key of the recipient thereby making it vulnerable to attacks. Due to this, the study focused on reduction or elimination of decryption failure through several solutions. The study began with an experimental evaluation of NTRU parameters and existing selection criteria by uniform quartile random sampling without replacement in order to identify the most influential parameter(s) for decryption failure, and thus developed a predictive parameter selection model with the aid of machine learning. Subsequently, an improved NTRU modular inverse algorithm was developed following an exploratory evaluation of alternative modular inverse algorithms in terms of probability of invertibility, speed of inversion and computational complexity. Finally, several alternative algebraic ring structures were evaluated in terms of simplification of multiplication, modular inversion, one-way function properties and security analysis for NTRU variant formulation. The study showed that the private key f and large prime q were the most influential parameters in decryption failure. Firstly, an extended parameter selection criteria specifying that the private polynomial f should be selected such that f(1) = 1, number of 1 coefficients should be one more or one less than -1 coefficients, which doubles the range of invertible polynomials thereby doubling the presented key space. Furthermore, selecting q 2:5754 f(1)+83:9038 gave an appropriate size q with the least size required for successful message decryption, resulting in a 33.05% reduction of the public key size. Secondly, an improved modular inverse algorithm was developed using the least squares method of finding a generalized inverse applying homomorphism of ring R and an (N x N) circulant matrix with integer coefficients. This ensured inversion for selected polynomial f except for binary polynomial having all 1 coefficients. This resulted in an increase of 48% to 51% whereby the number of invertible polynomials enlarged the key space and consequently improved security. Finally, an NTRU variant based on the ring of integers, Integer TRUncated ring (ITRU) was developed to address the invertiblity problem of key generation which causes decryption failure. Based on this analysis, inversion is guaranteed, and less pre-computation is required. Besides, a lower key generation computational complexity of O(N2) compared to O(N2(log2p+log2q)) for NTRU as well as a public key size that is 38% to 53% smaller, and a message expansion factor that is 2 to15 times larger than that of NTRU enhanced message security were obtained

Aggregating privatized medical data for secure querying applications

 This thesis analyses and examines the challenges of aggregation of sensitive data and data querying on aggregated data at cloud server. This thesis also delineates applications of aggregation of sensitive medical data in several application scenarios, and tests privatization techniques to assist in improving the strength of privacy and utility

A Survey of Cryptography and Key Management Schemes for Wireless Sensor Networks

Wireless sensor networks (WSNs) are made up of a large number of tiny sensors, which can sense, analyze, and communicate information about the outside world. These networks play a significant role in a broad range of fields, from crucial military surveillance applications to monitoring building security. Key management in WSNs is a critical task. While the security and integrity of messages communicated through these networks and the authenticity of the nodes are dependent on the robustness of the key management schemes, designing an efficient key generation, distribution, and revocation scheme is quite challenging. While resource-constrained sensor nodes should not be exposed to computationally demanding asymmetric key algorithms, the use of symmetric key-based systems leaves the entire network vulnerable to several attacks. This chapter provides a comprehensive survey of several well-known cryptographic mechanisms and key management schemes for WSNs

Mathematics Yearbook 2021

The Deakin University Mathematics Yearbook publishes student reports and articles in all areas of mathematics with an aim of promoting interest and engagement in mathematics and celebrating student achievements. The 2021 edition includes 7 coursework articles, where students have extended upon submissions in their mathematics units, as well as 4 articles based on student research projects conducted throughout 2020 and 2021