Public Key Cryptography System Research Articles

A hardware version of the RSA using the Montgomery's algorithm with systolic arrays

Rivest–Shamir–Adleman (RSA) is one of the most widely preferred algorithms used in public-key cryptography systems. RSA has a very slow ciphering rate if used in software. The use of a specific hardware is the only reasonable solution in applications where performance is the key factor. To speed up the modular multiplication and squaring, bit level systolic arrays are used with the Montgomery's modular multiplication algorithm to constitute the core of modular exponentiation operation. The squaring systolic structure is also performed in parallel with the systolic multiplication in the modular exponentiation. The novel idea in this paper is to use the systolic array cells with increased performance of up to 20% and use them in a single row organization. The final RSA design is configurable and can operate both for encryption and decryption. 1024-bit RSA algorithm is designed for the Xilinx Virtex FPGA and 0.7 μ ASIC.

A hardware version of the RSA using the Montgomery's algorithm with systolic arrays

Rivest–Shamir–Adleman (RSA) is one of the most widely preferred algorithms used in public-key cryptography systems. RSA has a very slow ciphering rate if used in software. The use of a specific hardware is the only reasonable solution in applications where performance is the key factor. To speed up the modular multiplication and squaring, bit level systolic arrays are used with the Montgomery's modular multiplication algorithm to constitute the core of modular exponentiation operation. The squaring systolic structure is also performed in parallel with the systolic multiplication in the modular exponentiation. The novel idea in this paper is to use the systolic array cells with increased performance of up to 20% and use them in a single row organization. The final RSA design is configurable and can operate both for encryption and decryption. 1024-bit RSA algorithm is designed for the Xilinx Virtex FPGA and 0.7 μ ASIC.

Maintaining Legal Requirements of Digital Signature through Public Key Cryptographic System

The signatures in the real world represent and reveal the senders identity. They also bind the signer with the contents of message. Requirement of any signature system is two folded, first it represent a unique mark by creator of the document in a distinguished manner, secondly the recipient as well as third party may verify the ‘genuineness’ of the document. The authentication and verification of signed document in digital medium is far more complex then hand written signatures. Adoption of digital signature system addresses several issues like privacy, confidentiality and integrity of the document apart from authentication and verification of the document. For digital message system, a solution must be found to these problems simultaneously addressing the legal requirement as laid down in IT Act 2000. In this paper, we present the general model of cryptographic system and will show how public key cryptographic system serves the requirement of digital signature in the light of IT Act 2000.

The NHS as a proving ground for cryptosystems

This paper examines the challenges that the National Health Service poses as an environment for public key cryptography systems. The NHS is Europe’s largest single employer, with over 1.2 million staff. It provides lifetime healthcare for most of its population, and has done so for 55 years. In the last decade, it has launched several major programmes to develop NHS-wide information systems. Just the scale of the NHS is daunting. But systems that handle patients’ medical records are subject to a plethora of laws, policies, guidelines and practices for controlling the access, use and storage of the information. Taken together, the rules are complex and sometimes contradictory and, in addition, must be balanced against both patients’ express wishes and their clinical needs. Cryptography is an obvious means to secure and protect confidential information. Recently, identity-based public key cryptography schemes not only seem easier to deploy than previous schemes, but also seem equal to the challenges. In this paper, we give a detailed overview of the features and challenges that the NHS environment presents to uses of cryptography, to qualify our impressions of our cryptosystem and to guide our future efforts to develop it.

Computing Prime Factorization And Discrete Logarithms: From Index Calculus To Xedni Calculus

The integer factorization problem (IFP), the finite field discrete logarithm problem (DLP) and the elliptic curve discrete logarithm problem (ECDLP) are essentially the only three mathematical problems that the practical public-key cryptographic systems are based on. For example, the most famous RSA cryptosystem is based on IFP, the US government's Digital Signature Standard, DSS, is based on DLP, whereas the ECC (Elliptic Curve Cryptography) and Elliptic Curve Digital Signature Algorithm (ECDSA) are based on ECDLP. The security of such cryptographic systems relies on the computational intractability of these three mathematical problems. In this paper, we shall present a survey of various methods for solving the IFP/DLP and particularly the ECDLP problems. More specifically, we shall first discuss how the index calculus as well as quantum algorithms can be used to solve IFP/DLP. Then we shall show why the index calculus cannot be used to solve ECDLP. Finally, we shall introduce a new method, xedni calculus , due to Joseph Silverman, for attack ECDLP; some open problems and new research directions, will also be addressed.

Applying evolutionary algorithm to public key cryptosystems

A best algorithm generated scheme is proposed in the paper by making use of the thought of evolutionary algorithm, which can generate dynamically the best algorithm of generating primes in RSA cryptography under different conditions. Taking into account the factors of time, space and security integrated, this scheme possessed strong practicability. The paper also proposed a model of multi-degree parallel evolutionary algorithm to evaluate synthetically the efficiency and security of the public key cryptography. The model contributes to designing public key cryptography system too.

Speedy public key cryptography system

US company NTRU Cryptosystems Inc. has announced the availability of the Tumbler software toolkit implementing NTRU. NTRU delivers encryption, decryption, authentication and digital signature features at speeds over 100 times faster than alternative systems. Jim Kotanchik, NTRU Vice President of Engineering states: “Prior to NTRU, users had to accept slow operation or make security compromises. NTRU allows the highest security levels at speeds two orders of magnitude faster than competitive systems, eliminating the need to compromise either speed or security.” The product is suitable for applications where high performance, high security and low power consumption are required, such as wireless data communications, Internet music and video distribution, micropayments, E-commerce and embedded devices.

The elliptic curve cryptosystem: A synopsis

There are three types of public key cryptographic systems that are currently considered both secure and efficient. These cryptographic systems, classified according to the mathematical problems upon which they are based, are: the Integer Factorization Systems (of which the RSA algorithm is the most well known example), the Discrete Logarithm Systems (such as the US Government's Digital Signature Algorithm), and the Elliptic Curve Cryptosystem (ECC). 1 1 Certicom White Paper, “ Current Public-Key Cryptographic Systems”, http://www.certicom. ca/ecc/wecc2.htm. Although much has been written about the RSA algorithm and the Digital Signature Algorithm (DSA), little about the ECC appears in the literature written for information systems security practitioners. This is perhaps because the ECC, since its introduction in 1985, has been a subject of interest to more mathematicians than security professionals.

A Survey of Fast Exponentiation Methods

Public-key cryptographic systems often involve raising elements of some group (e.g.,GF(2n),Z/NZ, or elliptic curves) to large powers. An important question is how fast this exponentiation can be done, which often determines whether a given system is practical. The best method for exponentiation depends strongly on the group being used, the hardware the system is implemented on, and whether one element is being raised repeatedly to different powers, different elements are raised to a fixed power, or both powers and group elements vary.This problem has received much attention, but the results are scattered through the literature. In this paper we survey the known methods for fast exponentiation, examining their relative strengths and weaknesses.

Elliptic curve cryptosystem — The answer to strong, fast public-key cryptography for securing constrained environments

This article presents a personal view on the current status of an important new area of cryptography — Elliptic Curves. Only three classes of public-key cryptosystems are today considered both secure and efficient: Integer Factorization Systems, Discrete Logarithm Systems, and the Elliptic Curve Cryptosystem (ECC). While the security of all three is based on the difficulty of an underlying mathematical problem, extensive research has concluded that, for a given key size, ECC is the strongest public-key cryptographic system known today. This article compares the three cryptosystems, and explains the significant strength and efficiency advantages in terms of computational overheads, key sizes and bandwidth. In implementations, these savings mean higher processing speeds, lower power consumption and code size reductions. This article also provides an overview of current ECC standards and applications in which the use of ECC is highly advantageous.

PARALLEL COMPUTATION OF THE MODULAR CASCADE EXPONENTIATION

For modern public key cryptographic systems, the modular cascade exponentiation ((πi=1 pxi ni)modu) is one of the most important arithmetic fundamentals to ensure security. However, the large computing effort needed by this operation also causes the cryptosystems inefficient. The purpose of this paper is to develop some fast methods for computing the modular cascade exponentiation. Two new parallel schemes, called the parallel multi-dimensional binary method and the parallel merging binary method, are proposed. The concept of the shortest parallel vectorial addition chain, which is an optimal approach for parallel computing the modular cascade exponentiation, is also given. The two proposed parallel schemes are faster than the best known serial or parallel modular cascade exponentiation methods. In addition, the computation time of the proposed parallel merging binary method is very close to the lower bound of the shortest parallel vectorial addition chain.

Public-key cryptography and open systems interconnection

The role of public-key cryptography in open systems interconnection (OSI) is discussed. A short tutorial introduction to public-key cryptography is followed by a discussion of how security fits into the OSI architecture, and what standards are being developed in this area. The use being made of public-key cryptography in the network layer and in the message handling system and directory application is also discussed. >

Public key management for network security

A tutorial is given on two public key cryptographic systems that provide an alternative to classical cryptographic key management techniques: the RSA system and the SEEK system. The certification of public numbers is discussed.

On the security of the Merkle- Hellman cryptographic scheme (Corresp.)

A simplified version of the Merkle-Hellman public key cryptographic system is breakable. While their full-fledged system seems to be resistant to the cryptanalytic attack we propose, the result suggests some ways in which the security of their system can be enhanced.

Implementation of Mitre public key cryptographic system

The letter presents an observation of theoretical interest regarding exponentiation in a finite field. The result can be applied towards reducing the time required for the first of two exponentiations specified by the Mitre public key cryptographic system.