Design of Rabin-like cryptosystem without decryption failure

In this work, we design a new, efficient and practical Rabin-like cryptosystem without using the Jacobi symbol, redundancy in the message and avoiding the demands of extra information for finding the correct plaintext. Decryption outputs a unique plaintext without any decryption failure. In addition, decryption only requires a single prime. Furthermore, the decryption procedure only computes a single modular exponentiation instead of two modular exponentiation executed by other Rabin variants. As a result, this reduces the computational effort during the decryption process. Moreover the Novak’s side channel attack is impractical over the proposed Rabin-like cryptosystem. In parallel, we prove that the Rabin-p cryptosystem is indeed as intractable as the integer factorization problem

Efficient methods to overcome Rabin cryptosystem decryption failure

Rabin cryptosystem is an efficient factoring-based scheme, however, its decryption produces 4-to-1 output, which leads to decryption failure. In this work, in order to overcome the 4-to-1 decryption problem for the Rabin cryptosystem, we propose two distinct methods using the modulus of the type N=p2q coupled with the restriction on the plaintext space M. In the first method, the plaintext space is limited to M ∈ Zpq. For the second method, we restrict the plaintext in the range of M ∈ (0,22n−2). Importantly, we prove that the decryption output of the proposed methods is unique and without decryption failure. The results in this work indicate that the decryption problem of Rabin cryptosystem is overcome

Analytical Study of Modified RSA Algorithms for Digital Signature

Digital signature has been providing security services to secure electronic transaction. Rivest Shamir Adleman (RSA) algorithm was most widely used to provide security technique for many applications, such as e-mails, electronic funds transfer, electronic data interchange, software distribution, data storage, electronic commerce and secure internet access. In order to include RSA cryptosystem proficiently in many protocols, it is desired to formulate faster encryption and decryption operations. This paper describes a systematic analysis of RSA and its variation schemes for Digital Signature. DOI: 10.17762/ijritcc2321-8169.15031

A usability study of elliptic curves

In the recent years, the need of information security has rapidly increased due to an enormous growth of data transmission. In this thesis, we study the uses of elliptic curves in the cryptography. We discuss the elliptic curves over finite fields, attempts to attack; discrete logarithm, Pollard’s rho algorithm, baby-step giant-step algorithm, Pohlig-Hellman algorithm, function field sieve, and number field sieve. The main cryptographic reason to use elliptic curves over finite fields is to provide arbitrarily large finite cyclic groups having a computationally difficult discrete logarithm problem

EXPLORING CONFIDENTIALITY AND PRIVACY OF IMAGE IN CLOUD COMPUTING

With the increasing popularity of cloud computing, clients are storing their data in cloud servers and are using “software as a service” for computing services. However, clients’ data may be sensitive, critical, and private, and processing such data with cloud servers may result in losing data privacy or compromising data confidentiality. Some cloud servers may be dishonest, while malicious entities may compromise others. In order to protect data privacy and confidentiality, clients need to be able to hide their actual data values and send the obfuscated values to cloud servers. This thesis deals with the outsourcing of computing to cloud servers, in which clients’ images can be computed and stored. This thesis proposes a technique that obfuscates images before sending them to servers, so these servers can perform computations on images without knowing the actual images. The proposed technique is expected to ensure data privacy and confidentiality. Servers will not be able to identify an individual whose images are stored and manipulated by the server. In addition, our approach employs an obfuscating technique to maintain the confidentiality of images, allowing cloud servers to compute obfuscated data accurately without knowing the actual data value, thus supporting privacy and confidentiality. The proposed approach is based on the Rabin block cipher technique, which has some weaknesses, however. The main drawback is its decryption technique, which results in four values, and only one of these values represents the actual value of plain data. Another issue is that the blocking technique requires a private key for each block that requires a high-computing effort; requiring one private key for each block of data demands that a great number of keys be stored by the client. As a result, it decreases the robustness of the Rabin block cipher. This thesis proposes additional techniques to overcome some of the weaknesses of the Rabin block cipher by introducing some new features, such as tokenization, a digit counter, and a set of blocks. The new technique increases the privacy of data and decreases the computational complexity by requiring fewer private keys. The new features have been implemented in image processing in order to demonstrate their applicability. However, in order to apply our approach to images, we must first apply some preprocessing techniques on images to make them applicable to being obfuscated by our proposed obfuscating system

Investigation of the efficiency of the Elliptic Curve Cryptosystem for multi-application smart card

Thesis (M.E.Sc.) -- University of Adelaide, Dept. of Engineering, 199

Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

On the hardness of the shortest vector problem

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 77-84).An n-dimensional lattice is the set of all integral linear combinations of n linearly independent vectors in Rm. One of the most studied algorithmic problems on lattices is the shortest vector problem (SVP): given a lattice, find the shortest non-zero vector in it. We prove that the shortest vector problem is NP-hard (for randomized reductions) to approximate within some constant factor greater than 1 in any 1, norm (p >\=1). In particular, we prove the NP-hardness of approximating SVP in the Euclidean norm 12 within any factor less than [square root of]2. The same NP-hardness results hold for deterministic non-uniform reductions. A deterministic uniform reduction is also given under a reasonable number theoretic conjecture concerning the distribution of smooth numbers. In proving the NP-hardness of SVP we develop a number of technical tools that might be of independent interest. In particular, a lattice packing is constructed with the property that the number of unit spheres contained in an n-dimensional ball of radius greater than 1 + [square root of] 2 grows exponentially in n, and a new constructive version of Sauer's lemma (a combinatorial result somehow related to the notion of VC-dimension) is presented, considerably simplifying all previously known constructions.by Daniele Micciancio.Ph.D