R. Padmavathy

An Improved Fast and Secure Hash Algorithm

Abstract —Recently, a fast and secure hash function SFHA – 256 has been proposed and claimed as more secure and as having a better performance than the SHA – 256. In this paper an improved version of SFHA – 256 is proposed and analyzed using two parameters, namely the avalanche effect and uniform deviation. The experimental results and further analysis ensures the performance of the newly proposed and improved SFHA-256. From the analysis it can be concluded that the newly proposed algorithm is more secure, efficient, and practical. Keywords —SHA-256, SFHA-256, Improved SFHA-256 1. I NTRODUCTION The hash function H accepts the variable-sized message M as input and outputs a fixed-size representation H(M) of M, which is sometimes called a message digest [1]. I.B. Damgard et.el., discussed the construction of hash functions and presented an efficient and much more secure scheme with the combination of RSA system with the collision free hash function based on fac-toring [2]. Hash functions for message authentications are proposed in [3]. A universal one-way hash function family is discussed in [4]. SHA-1 is a cryptographic hash function published by the National Institute of Standards and Technology (NIST). The three SHA algorithms are SHA-0, SHA-1, and SHA-2. The SHA-0 algorithm was not used in many applications. On the other hand, SHA-2 differs from the SHA-1 hash function. SHA-1 is the most widely used hash function. Several widely-used security ap-plications and protocols are based on SHA-1. In 2005, security flaws were identified in SHA-1 [5]. A prime motivation for the publication of the Secure Hash Algorithm was the Digital Signa-ture Standard. The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Standard (DSS). The ElGamal signature scheme is a digital signature scheme that is based on the difficulty of com-puting discrete logarithms. It was described by Taher ElGamal in 1984 [6]. The Elliptic Curve Digital Signature Algorithm (ECDSA) is a variant of the Digital Signature Algorithm (DSA) that uses Elliptic curve cryptography [7, 8]. Recently, Hassan. M. Elkamchouchi et el., proposed a fast and secure hash function (SFHA -

Methods to Solve Discrete Logarithm Problem for Ephemeral Keys

The present study investigates the difficulty of solving the mathematical problem, namely DLP (Discrete Logarithm Problem) for ephemeral keys. DLP is the basis for many public key cryptosystems. The ephemeral keys are used in such systems to ensure the security. The DLP defined on a prime field

A Small Subgroup Attack for Recovering Ephemeral Keys in Chang and Chang Password Key Exchange Protocol

\mathbb Z_p^{*}

Block Lanczos to Solve Integer Factorization Problem Using GPU’s

of random prime is considered in the present study. The most effective method to solve the DLP is the Index Calculus Method. In the present study, an efficient way of computing the DLP for ephemeral key by using a new variant of ICM when the factors of

Ephemeral key recovery using index calculus method

p-1

Improved Analysis on Chang and Chang Password Key Exchange Protocol

are known and small is proposed. The ICM has two steps, such as a pre-computation and an individual logarithm computation. The pre-computation step is to compute the logarithms of a subset of a group and the individual logarithm step is to find the DLP using the pre-computed logarithms. Since the ephemeral keys are dynamic and changes for every session, once the logarithms of a subset of a group is known, the DLP for the ephemeral key can be obtained using the individual logarithm step. Therefore, an efficient way of solving the individual logarithm step based on the newly proposed pre-computation method is presented and the performance is analyzed on a comprehensive set of experiments. The ephemeral keys are also solved by using other methods, which are efficient on random primes, such as Pohlig-Hellman, Var-Oorschot method and traditional individual logarithm step. The results are compared with the newly proposed individual logarithm step of ICM. Also, the DLP of ephemeral keys used in a popular password key exchange protocol known as Chang and Chang are computed and reported.

Cryptanalysis on a Three Party Key Exchange Protocol-STPKE'

Three-party authenticated key exchange protocol is an important cryptographic technique in the secure communication areas. Recently Chang and Chang proposed a novel three party simple key exchange protocol and claimed the protocol is secure, efficient and practical. Unless their claim, a key recovery attack is proposed on the above protocol by recovering the ephemeral keys. One way of recovering the ephemeral key is to solve the mathematical hard Discrete Logarithm Problem (DLP). The DLP is solved by using a popular Pohlig-Hellman method in the above key recovery attack. In the present study, a new method based on the small subgroup attack to solve the DLP is discussed to recover the ephemeral keys. Computation of DLP is carried out by two stages, such as the prior-computation and DLP computation. The prior-computation is performed on off-line and the DLP computation is performed on on-line. The method is analyzed on a comprehensive set of experiments and the ephemeral keys are recovered in reduced time. Also, the key recovery attack on Chang and Chang password key exchange protocol is implemented by using the new method to recover the ephemeral key.

Performance analysis of index calculus method

Public key cryptography is based on some mathematically hard problems, such as Integer Factorization and Discrete Logarithm problems. The RSA is based on Integer factorization problem. Number Field Sieve is one of the popular algorithms to solve these two problems. Block Lanczos algorithm is used in the linear algebra stage of Number Filed Sieve method for Integer Factorization. The algorithm solves the system of equations Bx=0 for finding null spaces in the matrix B. The major problems encountered in implementing Block Lanczos are storing the entire sieve matrix and solving the matrix efficiently in reduced time. Implementations of Block Lanczos algorithm have already been carried out using distributed systems. In the current study, the implementation of Block Lanczos Algorithm has been carried out on GPUs using CUDA C as programming language. The focus of the present work has been to design a model to make use of the high computing power of the GPUs. The input matrices are very large and highly sparse and so stored using coordinate format. The GPU on-chip memories have been used to reduce the computation time. The experimental results were obtained for the following problems; RSA100, RSA110, RSA120. From the results it can be concluded that a distributed model over GPUs can be used to reduce the iteration times for Block Lanczos.

Special-q Techniques for Number Field Sieve to Solve Integer Factorization

Abstract The present study investigates the problem of retrieving the ephemeral keys, which are used in the Discrete Logarithm Problem (DLP) based public key cryptosystems. The ephemeral key can be retrieved by solving the mathematical hard problem, namely DLP. The DLP defined over a prime field is considered in the present study. An efficient way of computing the DLP for retrieving the ephemeral key by using a new variant of Index Calculus Method (ICM) when the factors of p − 1 are known and small is proposed. The Pohlig-Hellman is the best known method to solve the DLP on the prime field with factors of p − 1 are small, while the ICM is an efficient method for a general DLP. The ICM has two steps, such as a pre-computation and an individual logarithm computation. In the pre-computation step, the logarithms of elements of a subset of a group, which is known as a factor base is computed and in the individual logarithm step the DLP is computed with the help of pre-computed logarithms of factor base. Since the ephemeral keys are dynamic and changes for every session, once the logarithms of a subset of a group is known, the DLP for the ephemeral key can be obtained by using the individual logarithm step. Therefore, an efficient way of solving the individual logarithm step is presented based on the newly proposed pre-computation method and the performance is analyzed on a comprehensive set of experiments. From the experimental results, it is observed that the individual logarithm (computation) step outperforms the Pohlig-Hellman method on some special cases. The property of generators of prime field is the main motivation for the current study.

BrowserGuard2: A Solution for Drive-by-Download Attacks

The key exchange protocol using passwords achieved great attention due to its simplicity and efficiency. On the other hand, the protocol should resist all types of password guessing attacks, since the password is of low entropy. Recently Chang and Chang proposed a novel three party simple key exchange protocol. They claimed the protocol was secure, efficient and practical. Overriding their claims Yoon and Yoo presented an undetectable online password guessing attack on the above protocol. In the present paper an enhanced protocol has been proposed to eliminate undetectable online password guessing attack proposed by Yoon and Yoo. Moreover, the proposed enhanced protocol could achieve better performance efficiency by requiring only four message transmission rounds and the performance is analyzed on a comprehensive set of experiments.