Backtracking Based Integer Factorisation, Primality Testing and Square Root Calculation
نویسنده
چکیده
Breaking a big integer into two factors is a famous problem in the field of Mathematics and Cryptography for years. Many crypto-systems use such a big number as their key or part of a key with the assumption it is too big that the fastest factorisation algorithms running on the fastest computers would take impractically long period of time to factorise. Hence, many efforts have been provided to break those crypto-systems by finding two factors of an integer for decades. In this paper, a new factorisation technique is proposed which is based on the concept of backtracking. Binary bit by bit operations are performed to find two factors of a given integer. This proposed solution can be applied in computing square root, primality test, finding prime factors of integer numbers etc. If the proposed solution is proven to be efficient enough, it may break the security of many crypto-systems. Implementation and performance comparison of the technique is kept for future research.
منابع مشابه
Primality Testing and Integer Factorisation
The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the Rivest-Shamir-Adelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisati...
متن کاملComputer algebra — a beginners course using SAGE Universität Hannover , WS 2012
1 Integer arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Modular arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 The RSA cryptosystem . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Primality testing . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملOn Taking Square Roots and Constructing Quadratic Nonresidues over Finite Fields
We present a novel idea to compute square roots over some families of finite fields. Our algorithms are deterministic polynomial time and can be proved by elementary means (without assuming any unproven hypothesis). In some particular finite fields Fq, there are algorithms for taking square roots with Õ(log q) bit operations. As an application of our square root algorithms, we show a determinis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014