Flexible Quasi-Dyadic Code-Based Public-Key Encryption and Signature

Drawback of code-based public-key cryptosystems is that their public-key size is lage. It takes some hundreds KB to some MB for typical parameters. While several attempts have been conducted to reduce it, most of them have failed except one, which is Quasi-Dyadic (QD) public-key (for large extention degrees). While an attack has been proposed on QD public-key (for small extension degrees), it can be prevented by making the extension degree $m$ larger, specifically by making $q^(m (m-1))$ large enough where $q$ is the base filed and for a binary code, $q=2$. The drawback of QD is, however, it must hold $n << 2^m - t$ (at least $n \leq 2^{m-1}$) where $n$ and $t$ are the code lenght and the error correction capability of the underlying code. If it is not satisfied, its key generation fails since it is performed by trial and error. This condition also prevents QD from generating parameters for code-based digital signatures since without making $n$ close to $2^m - t$, $2^{mt}/{n \choose t}$ cannot be small. To overcome these problems, we propose ``Flexible\u27\u27 Quasi-Dyadic (FQD) public-key that can even achieve $n=2^m - t$ with one shot. Advantages of FQD include 1) it can reduce the publi-key size further, 2) it can be applied to code-based digital signatures, too

Compact McEliece keys based on Quasi-Dyadic Srivastava codes

The McEliece cryptosystem is one of the few systems to be considered secure against Quantum attacks. The original scheme is built upon Goppa codes and produces very large keys, hence latest research has focused mainly on trying to reduce the public key size. Previous proposals tried to replace the class of Goppa codes with other families of codes, but this revealed to be an insecure choice. In this paper we introduce a construction based on Generalized Srivastava codes, a large class which include Goppa codes as a special case, that allows relatively short public keys without being vulnerable to known structural attacks

Research on digital image watermark encryption based on hyperchaos

The digital watermarking technique embeds meaningful information into one or more watermark images hidden in one image, in which it is known as a secret carrier. It is difficult for a hacker to extract or remove any hidden watermark from an image, and especially to crack so called digital watermark. The combination of digital watermarking technique and traditional image encryption technique is able to greatly improve anti-hacking capability, which suggests it is a good method for keeping the integrity of the original image. The research works contained in this thesis include: (1)A literature review the hyperchaotic watermarking technique is relatively more advantageous, and becomes the main subject in this programme. (2)The theoretical foundation of watermarking technologies, including the human visual system (HVS), the colour space transform, discrete wavelet transform (DWT), the main watermark embedding algorithms, and the mainstream methods for improving watermark robustness and for evaluating watermark embedding performance. (3) The devised hyperchaotic scrambling technique it has been applied to colour image watermark that helps to improve the image encryption and anti-cracking capabilities. The experiments in this research prove the robustness and some other advantages of the invented technique. This thesis focuses on combining the chaotic scrambling and wavelet watermark embedding to achieve a hyperchaotic digital watermark to encrypt digital products, with the human visual system (HVS) and other factors taken into account. This research is of significant importance and has industrial application value

Recent Application in Biometrics

In the recent years, a number of recognition and authentication systems based on biometric measurements have been proposed. Algorithms and sensors have been developed to acquire and process many different biometric traits. Moreover, the biometric technology is being used in novel ways, with potential commercial and practical implications to our daily activities. The key objective of the book is to provide a collection of comprehensive references on some recent theoretical development as well as novel applications in biometrics. The topics covered in this book reflect well both aspects of development. They include biometric sample quality, privacy preserving and cancellable biometrics, contactless biometrics, novel and unconventional biometrics, and the technical challenges in implementing the technology in portable devices. The book consists of 15 chapters. It is divided into four sections, namely, biometric applications on mobile platforms, cancelable biometrics, biometric encryption, and other applications. The book was reviewed by editors Dr. Jucheng Yang and Dr. Norman Poh. We deeply appreciate the efforts of our guest editors: Dr. Girija Chetty, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park and Dr. Sook Yoon, as well as a number of anonymous reviewers

More Than Error Correction: Cryptography from Codes

The first code-based cryptosystem, McEliece, was invented in the very early development of public-key cryptography, yet code-based cryptosystems received little attention for decades due to their relatively large key-sizes. But recently they are re-discovered for their potentials to provide efficient post-quantum cryptographic tools and homomorphic encryption schemes, and the development of large storage and fast Internet have made these schemes closer to practice than ever. Through our review of the revolution of code-based cryptography, we will demonstrate the usage of codes in cryptographic applicaitons. We will follow the path of the development, from the design, analysis, and implementation of McEliece cryptosystem and the quantum attack resistance to the latest fully homomorphic encryption scheme based on Learning with Errors, a code-related problem, designed by Brakerski et al. We will also cover algebraic manipulation detection codes, a newly proposed extension of error-correcting codes and a lightweight alternative to MACs as an authentication component embedded in security protocols

Peer Tutoring in Middle School: How it Changes Student Achievement and Attitudes

Research literature shows that mathematics is a gatekeeper to success. Providing alternative opportunities for students to strengthen mathematical reasoning over algorithmic computations while problem-solving in a collaborative environment helps to prepare students to compete locally and globally. The purpose of this qualitative case study was to investigate how an afterschool Peer Tutoring Club (PTC) affected academic performances and attitudes of Grade 6, at-risk or “at-promise,” (Samuels, 2020), middle school mathematics students. The gap found in literature revealed a need for additional research involving rigorous multistep problem-solving within peer tutoring programs. This study collected data from 46, 1-hour, afterschool peer tutoring sessions between December 2017 and May 2018. Six PTC tutees were selected as participants. The participants received cross-age and same age peer tutoring while utilizing a district aligned curriculum that consisted of multistep problem-solving. This dissertation addressed the gap found in literature by collecting qualitative and quantitative data from four instruments: (a) district’s math pre/posttest, (b) Attitudes Toward Math Inventory (ATMI), (c) participants’ work, and (d) participants’ exit interviews. Descriptive statistics were used to analyze both qualitative and quantitative data. The data was triangulated to answer the two research questions. The findings from the PTC study supported theory and empirical study evidence that peer tutoring improved academic achievement and attitudes toward math

Curves, codes, and cryptography

This thesis deals with two topics: elliptic-curve cryptography and code-based cryptography. In 2007 elliptic-curve cryptography received a boost from the introduction of a new way of representing elliptic curves. Edwards, generalizing an example from Euler and Gauss, presented an addition law for the curves x2 + y2 = c2(1 + x2y2) over non-binary fields. Edwards showed that every elliptic curve can be expressed in this form as long as the underlying field is algebraically closed. Bernstein and Lange found fast explicit formulas for addition and doubling in coordinates (X : Y : Z) representing (x, y) = (X/Z, Y/Z) on these curves, and showed that these explicit formulas save time in elliptic-curve cryptography. It is easy to see that all of these curves are isomorphic to curves x2 + y2 = 1 + dx2y2 which now are called "Edwards curves" and whose shape covers considerably more elliptic curves over a finite field than x2 + y2 = c2(1 + x2y2). In this thesis the Edwards addition law is generalized to cover all curves ax2 +y2 = 1+dx2y2 which now are called "twisted Edwards curves." The fast explicit formulas for addition and doubling presented here are almost as fast in the general case as they are for the special case a = 1. This generalization brings the speed of the Edwards addition law to every Montgomery curve. Tripling formulas for Edwards curves can be used for double-base scalar multiplication where a multiple of a point is computed using a series of additions, doublings, and triplings. The use of double-base chains for elliptic-curve scalar multiplication for elliptic curves in various shapes is investigated in this thesis. It turns out that not only are Edwards curves among the fastest curve shapes, but also that the speed of doublings on Edwards curves renders double bases obsolete for this curve shape. Elliptic curves in Edwards form and twisted Edwards form can be used to speed up the Elliptic-Curve Method for integer factorization (ECM). We show how to construct elliptic curves in Edwards form and twisted Edwards form with large torsion groups which are used by the EECM-MPFQ implementation of ECM. Code-based cryptography was invented by McEliece in 1978. The McEliece public-key cryptosystem uses as public key a hidden Goppa code over a finite field. Encryption in McEliece’s system is remarkably fast (a matrix-vector multiplication). This system is rarely used in implementations. The main complaint is that the public key is too large. The McEliece cryptosystem recently regained attention with the advent of post-quantum cryptography, a new field in cryptography which deals with public-key systems without (known) vulnerabilities to attacks by quantum computers. The McEliece cryptosystem is one of them. In this thesis we underline the strength of the McEliece cryptosystem by improving attacks against it and by coming up with smaller-key variants. McEliece proposed to use binary Goppa codes. For these codes the most effective attacks rely on information-set decoding. In this thesis we present an attack developed together with Daniel J. Bernstein and Tanja Lange which uses and improves Stern’s idea of collision decoding. This attack is faster by a factor of more than 150 than previous attacks, bringing it within reach of a moderate computer cluster. We were able to extract a plaintext from a ciphertext by decoding 50 errors in a [1024, 524] binary code. The attack should not be interpreted as destroying the McEliece cryptosystem. However, the attack demonstrates that the original parameters were chosen too small. Building on this work the collision-decoding algorithm is generalized in two directions. First, we generalize the improved collision-decoding algorithm for codes over arbitrary fields and give a precise analysis of the running time. We use the analysis to propose parameters for the McEliece cryptosystem with Goppa codes over fields such as F31. Second, collision decoding is generalized to ball-collision decoding in the case of binary linear codes. Ball-collision decoding is asymptotically faster than any previous attack against the McEliece cryptosystem. Another way to strengthen the system is to use codes with a larger error-correction capability. This thesis presents "wild Goppa codes" which contain the classical binary Goppa codes as a special case. We explain how to encrypt and decrypt messages in the McEliece cryptosystem when using wild Goppa codes. The size of the public key can be reduced by using wild Goppa codes over moderate fields which is explained by evaluating the security of the "Wild McEliece" cryptosystem against our generalized collision attack for codes over finite fields. Code-based cryptography not only deals with public-key cryptography: a code-based hash function "FSB"was submitted to NIST’s SHA-3 competition, a competition to establish a new standard for cryptographic hashing. Wagner’s generalized birthday attack is a generic attack which can be used to find collisions in the compression function of FSB. However, applying Wagner’s algorithm is a challenge in storage-restricted environments. The FSBday project showed how to successfully mount the generalized birthday attack on 8 nodes of the Coding and Cryptography Computer Cluster (CCCC) at Technische Universiteit Eindhoven to find collisions in the toy version FSB48 which is contained in the submission to NIST