Prime Factoring and The Complexity Of
نویسنده
چکیده
Prime factoring is important for multiple reasons. One is its central role in several cryptographic schemes. The central element of factoring is to find two prime numbers p, q where n = p ∗ q, given the value of n. A mathematical expression is developed that is amenable to iterative resolution of prime factors for a composite. The expression is then shown to admit a factoring process of P-complexity. The method may be used to determine if an integer is a prime.
منابع مشابه
Factoring RSA Moduli with Weak Prime Factors
In this paper, we study the problem of factoring an RSA modulus N = pq in polynomial time, when p is a weak prime, that is, p can be expressed as ap = u0 + M1u1 + . . . + Mkuk for some k integers M1, . . . ,Mk and k+2 suitably small parameters a, u0, . . . uk. We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval [2, 2] and...
متن کامل1 Ju n 20 04 A precise estimation of the computational complexity in Shor ’ s factoring algorithm
Abstract. A precise estimation of the computational complexity in Shor’s factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number theory. Compared with Shor’s original estimation, our estimation shows that one can obtain the solution under such a condition, by less computation...
متن کاملConstruction of the Tsujii-Shamir-Kasahara (TSK) Type Multivariate Public Key Cryptosystem, which relies on the Difficulty of Prime Factorization
A new multivariate public-key cryptosystem (MPKC) with the security based on the difficulty of the prime factoring is proposed. Unlike conventional cryptosystems such as RSA, most MPKCs are expected secure against quantum computers, and their operation of encryption and decryption is expected quick, because they do not need exponential operation. However, their security against quantum computer...
متن کاملAn improvement on the complexity of factoring read-once Boolean functions
Read-once functions have gained recent, renewed interest in thefields of theory and algorithmsofBoolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A.Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. M...
متن کاملAutomorphisms of Rings and Applications to Complexity
Rings are fundamental mathematical objects with two operations, addition and multiplication, suitably defined. A known way of studying the structure of rings is to consider automorphisms of rings. In my PhD thesis I consider finite dimensional rings represented in terms of their additive basis and study the computational complexity of various automorphism problems of rings in this representatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1602.06910 شماره
صفحات -
تاریخ انتشار 2016