Book Chapter10.1007/978-3-642-28926-2_61
Prime Factorization without Using Any Approximations
Pagavathigounder Balasubramaniam,P. Muthukumar,Wan Ainun Mior Othman +2 more
- 16 Mar 2012
- pp 537-541
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TL;DR: This paper proposes a factorization algorithm based on number theory that gets the exact prime factorization without any approximations and the time complexity of the proposed method is less because there is no recursive steps in this proposed algorithm.
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Abstract: Factoring number is a non-trivial operation, and that fact is the source of a lot of cryptographic algorithms. Many cryptosystems are based on the factorization of large integers. In this paper, factorization algorithm based on number theory is proposed and get the exact prime factorization without any approximations. The major advantages of the proposed method are listed and the disadvantages of the existing factorization algorithm based on square root approximation are highlighted. The time complexity of the proposed method is less because there is no recursive steps in this proposed algorithm.
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Citations
Cryptographic Signature Scheme for Mobile Edge Computing Using DLFP Over Semiring
Manimaran A
TL;DR: The Discrete Logarithm Problem with Factor Problem (DLFP) is introduced and its security and complexity is analyzed, and an undeniable signature scheme based on DLFP over semiring is proposed.
References
Speeding the Pollard and elliptic curve methods of factorization
TL;DR: In this paper, a parametrization of elliptic curves is proposed to speed up the p 1 and Monte Carlo methods. But the parametrized elliptic curve method requires n/2 + o(n) multiplications.
Factoring integers with elliptic curves
TL;DR: This paper is devoted to the description and analysis of a new algorithm to factor positive integers that depends on the use of elliptic curves and it is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K( p)(log n)2.
Theorems on factorization and primality testing
J. M. Pollard
- 01 Nov 1974
TL;DR: This paper is concerned with the problem of obtaining theoretical estimates for the number of arithmetical operations required to factorize a large integer n or test it for primality, and uses a multi-tape Turing machine for this purpose.
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Prime factorization using square root approximation
TL;DR: A new factorization method based on the square root approximation is proposed, which allows in reducing the search for candidate prime factors of a given integer by approximating each prime factor before considering it as a candidate.
7
A monte carlo method for factorization
TL;DR: A novel factorization method involving probabilistic ideas is described briefly, and it is suggested that this method should be considered as a viable alternative to traditional factorization methods.