Topic
Strong prime
About: Strong prime is a research topic. Over the lifetime, 128 publications have been published within this topic receiving 1327 citations.
Papers published on a yearly basis
Papers
1 Feb 2015
TL;DR: A modified and an enhanced scheme based on RSA public-key cryptosystem is developed which makes use of four large prime numbers which increases the complexity of the system as compared to traditional RSA algorithm which is based on only two largePrime numbers.
Abstract: Public-key cryptography can be claimed as the greatest and an excellent revolution in the field of cryptography. A public-key cryptosystem is used for both confidentiality and authentication. One such public-key cryptosystem is the RSA cryptosystem. In this paper, a modified and an enhanced scheme based on RSA public-key cryptosystem is developed. The proposed algorithm makes use of four large prime numbers which increases the complexity of the system as compared to traditional RSA algorithm which is based on only two large prime numbers. In the proposed Enhanced and Secured RSA Key Generation Scheme (ESRKGS), the public component n is the product of two large prime numbers but the values of Encryption (E) and Decryption (D) keys are based on the product of four large prime numbers (N) making the system highly secured. With the existing factorization techniques, it is possible only to find the primes p and q. The knowledge of n alone is not sufficient to find E and D as they are based on N. The time required for cryptanalysis of ESRKGS is higher than traditional RSA cryptosystem. Thus the system is highly secure and not easily breakable. A comparison is done between the traditional RSA scheme, a recent RSA modified scheme and our scheme to show that the proposed technique is efficient.
95 citations
1 Dec 1985
TL;DR: It is shown that the problem of finding strong, random,Large primes is only 19% harder than finding random, large primes.
Abstract: A simple method is given for finding strong, random, large primes of a given number of bits, for use in conjunction with the RSA Public Key Cryptosystem. A strong prime p is a prime satisfying: * p = 1 mod r * p = s-1 mod s * r = 1 mod t, where r,s and t are all large, random primes of a given number of bits. It is shown that the problem of finding strong, random, large primes is only 19% harder than finding random, large primes.
80 citations
17 Aug 2000
TL;DR: In this article, a simple way to substantially reduce the value of hidden constants is proposed to provide much more efficient prime number generation algorithms, which are applied to various contexts (DSA, safe primes, ANSI X9.31 compliant primes and strong primes).
Abstract: The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of cryptographic usages, prime number generation algorithms remain scarcely investigated and most real-life implementations are of rather poor performance. Common generators typically output a n-bit prime in heuristic average complexity O(n4) or O(n4/ log n) and these figures, according to experience, seem impossible to improve significantly: this paper rather shows a simple way to substantially reduce the value of hidden constants to provide much more efficient prime generation algorithms. We apply our techniques to various contexts (DSA primes, safe primes, ANSI X9.31-compliant primes, strong primes, etc.) and show how to build fast implementations on appropriately equipped smart-cards, thus allowing on-board key generation.
79 citations
[...]
TL;DR: It is shown that the problem of finding strong, random,Large primes is only 19% harder than finding random, large primes.
Abstract: A simple method is given for finding strong primes for use in conjunction with the RSA Public Key Cryptosystem. A strong prime p is a large prime satisfying the following: (a) p = 1 mod r; (b) p = s?1 mod s; (c) r = 1 mod t; where r, s and t are all large, random primes. It is shown that the problem of finding strong, random, large primes is only 19% harder than finding random, large primes.
77 citations
TL;DR: All methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, they try the patience of even the practiced calculator.
Abstract: Is there an algorithm that can decide whethern is prime or composite and that runs in polynomial time? The Adleman-Rumely algorithm and the Lenstra variations come so close, that it would seem that almost any improvement would give the final breakthrough. Is factoring inherently more difficult than distinguishing between primes and composites? Most people feel that this is so, but perhaps this problem too will soon yield. In his “Disquisitiones Arithmeticae” Gauss [9], p. 396, wrote “The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. Nevertheless we must confess that all methods that have been proposed thus far are either restricted to very special cases or are so laborious and prolix that even for numbers that do not exceed the limits of tables constructed by estimable men, i.e., for numbers that do not yield to artificial methods, they try the patience of even the practiced calculator. And these methods do not apply at all to larger numbers.” The struggle continues!
68 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 1 |
| 2018 | 2 |
| 2017 | 10 |
| 2016 | 7 |
| 2015 | 4 |