Cryptanalysis of a digital signature scheme of W. He.

Wong, Chun Kuen.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 43-45).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Origin of The First Digital Signature Scheme --- p.2Chapter 1.2 --- On the security of digital signature schemes --- p.3Chapter 1.3 --- Organization of the Thesis --- p.4Chapter 2 --- Mathematical Background --- p.6Chapter 2.1 --- Divisibility --- p.6Chapter 2.2 --- Prime --- p.7Chapter 2.3 --- Modular arithmetic --- p.7Chapter 2.4 --- Congruence --- p.7Chapter 2.5 --- Greatest Common Divisor --- p.7Chapter 2.6 --- Integers modulo n --- p.8Chapter 2.7 --- Inverse --- p.8Chapter 2.8 --- Division in Zn --- p.8Chapter 2.9 --- Order of element --- p.8Chapter 2.10 --- Euclidean Algorithm --- p.9Chapter 2.11 --- Extended Euclidean Algorithm --- p.9Chapter 2.12 --- Chinese Remainder Theorem --- p.10Chapter 2.13 --- Relatively Prime --- p.10Chapter 2.14 --- Euler Totient Function --- p.10Chapter 2.15 --- Fermat's Little Theorem --- p.11Chapter 2.16 --- Euler's Theorem --- p.11Chapter 2.17 --- Square root --- p.12Chapter 2.18 --- Quadratic residue --- p.12Chapter 2.19 --- Legendre Symbol --- p.13Chapter 2.20 --- Jacobi Symbol --- p.14Chapter 2.21 --- Blum Integer --- p.15Chapter 2.22 --- The Factoring Problem --- p.16Chapter 2.23 --- The Discrete Logarithm Problem --- p.17Chapter 2.24 --- One-way Hash Function --- p.17Chapter 3 --- Survey of digital signature schemes --- p.19Chapter 3.1 --- The RSA signature scheme --- p.19Chapter 3.1.1 --- Key generation in the RSA signature scheme --- p.20Chapter 3.1.2 --- Signature generation in the RSA signature scheme --- p.20Chapter 3.1.3 --- Signature verification in the RSA signature scheme --- p.20Chapter 3.1.4 --- On the security of the RSA signature scheme --- p.21Chapter 3.2 --- The ElGamal signature scheme --- p.22Chapter 3.2.1 --- Key generation in the ElGamal signature scheme --- p.23Chapter 3.2.2 --- Signature generation in the ElGamal signature scheme --- p.23Chapter 3.2.3 --- Signature verification in the ElGamal signature scheme --- p.23Chapter 3.2.4 --- On the security of the ElGamal signature scheme --- p.24Chapter 3.3 --- The Schnorr signature scheme --- p.26Chapter 3.3.1 --- Key generation in the Schnorr signature scheme --- p.26Chapter 3.3.2 --- Signature generation in the Schnorr signature scheme --- p.26Chapter 3.3.3 --- Signature verification in the Schnorr signature scheme --- p.27Chapter 3.3.4 --- Discussion --- p.27Chapter 3.4 --- Digital signature schemes based on both the factoring and discrete logarithm problems --- p.27Chapter 3.4.1 --- The Brickell-McCurley signature scheme --- p.28Chapter 3.4.2 --- The Okamoto signature scheme --- p.29Chapter 3.4.3 --- The Harn signature scheme --- p.30Chapter 3.4.4 --- The Shao signature scheme --- p.30Chapter 3.4.5 --- The W. He signature scheme --- p.31Chapter 4 --- Cryptanalysis of the digital signature scheme of W. He --- p.32Chapter 4.1 --- The Digital Signature Scheme of W. He --- p.33Chapter 4.1.1 --- System setup in the W. He Digital Signature Scheme --- p.33Chapter 4.1.2 --- Key generation in the W. He Digital Signature Scheme --- p.34Chapter 4.1.3 --- Signature generation in the W. He Digital Signature Scheme --- p.34Chapter 4.1.4 --- Signature verification in the W. He Digital Signature Scheme --- p.34Chapter 4.2 --- Cryptanalysis of the digital signature scheme of W. He --- p.35Chapter 4.2.1 --- Theorems on the security of the digital signature scheme of W. He --- p.35Chapter 4.2.2 --- Signature Forgery in the digital signature scheme of W. He --- p.37Chapter 4.2.3 --- Remedy --- p.40Chapter 5 --- Conclusions --- p.41Bibliography --- p.4

A Thesis: A CRYPTOGRAPHIC STUDY OF SOME DIGITAL SIGNATURE SCHEMES.

In this thesis, we propose some directed signature schemes. In addition, we have discussed their applications in different situations. In this thesis, we would like to discuss the security aspects during the design process of the proposed directed digital signature schemes. The security of the most digital signature schemes widely use in practice is based on the two difficult problems, viz; the problem of factoring integers (The RSA scheme) and the problem of finding discrete logarithms over finite fields (The ElGamal scheme). The proposed works in this thesis is divided into seven chapters

Elgamal digital signature scheme with integrated CFEA-technique

One of the four security goals is authentication. Authentication is a mechanism to ensure that we are communicating with the intended party. If Alice and Bob want to communicate securely, then the authentication mechanism will be able to ensure that Alice is truly communicating with Bob, and Bob is truly communicating with Alice. This mechanism can be provided by the cryptography. One of the most established cryptography schemes is ElGamal cryptosystem. The original version of this cryptosystem is to provide confidentiality through encryption and decryption procedures. By manipulating these procedures, the authentication mechanism can be carried out. Thus, ElGamal Digital Signature Scheme emerges as one of the most popular authentication mechanisms. In order to provide good level of security, proper parameters must be used in this scheme. This includes the size of the parameters. Larger parameters will provide a better level of security. As a consequence, the performance of the scheme becomes an issue in real life application. In this paper, we proposed the enhancement of the ElGamal Digital Signature Scheme by integrating the Continued-Fraction-Euclidean-Algorithm (CFEA) technique. This technique is able to reduce the number of data to be processed in the signing and verification procedures. By integrating the CFEA-technique into the ElGamal Digital Signature Scheme, any number of documents can be compressed becomes a pair of documents. Therefore, the signing and verification procedures can be done in smaller number of steps

NEW HIDING TECHNIQUE IN DIGITAL SIGNATURE BASED ON ZIGZAG TRANSFORM AND CHAOTIC MAPS

Abstract This paper presents a novel approach to digital signature by integrating the ElGamal or Schnorr digital signature algorithms, chaotic systems, and scanning techniques. Briefly, ZZBCRP is a zigzag transformation that is used firstly to construct a permuted transaction, which technique starts from any random position and intersects in both directions, which is more complex than zigzag transform techniques. Then using ElGamal or Schnorr signature schemes based on chaotic maps. This modification aims to make private key and random number dependent on discrete chaotic maps. Even if the private key chosen is small, it is easy by using the huge amount of points in chaotic maps 2-D or 3-D to extract strong and unique key. This change complicates the relationship between the private key, public key and the transaction signature. A two-dimensional trigonometric discrete chaotic map is used that integrated Logistic-sine-cosine maps, and a three-dimensional hyperchaotic map (3-D SCC) which are based on a sine map. Our performance analysis shows that compared to schemes; this scheme not only improves the level of efficiency but also assures safety. The performance analysis shows that our scheme is not only more efficient compared to other related systems, but also safer

Structure and Randomness of the Discrete Lambert Map

We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM). The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS