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Number-Theoretic Reference Problems
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
3.3 Definition The integer factorization problem (FACTORING) is the following: given a positive integer n, find its prime factorization; that is, write n=p1e1p2e2⋯pkek where the pi are pairwise distinct primes and each ei ≥ 1.
Key Generation
Published in Vinay Rishiwal, Sudeep Tanwar, Rashmi Chaudhry, Blockchain for 6G-Enabled Network-Based Applications, 2023
Surendra Kumar, Narander Kumar
ECC needs fewer significant keys than non-ECC cryptography to afford the same security. Elliptic curves are appropriate for encoding, digital marks, and other tasks. They are also used in some integer factorization techniques that have relevance in cryptography. Public key cryptography is based on tortuous mathematics. Early public key systems are protected, assuming that it is hard to factor a big integer composed of two or more huge prime factors.
Number Theory
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
The problem of efficient integer factorization is not only a fundamental problem in computational number theory, but one that has large practical ramifications for cryptography and cyber security. As large-scale computing has become common, the factorization of large integers has even become somewhat of a benchmark for computing itself.
A Framework for Filtering Step of Number Field Sieve and Function Field Sieve
Published in IETE Journal of Research, 2023
Rahul Janga, R. Padmavathy, S. K. Pal, S. Ravichandra
Integer Factorization Problem To factor a large number into its prime divisors efficiently has been a challenging problem for a long time. Mathematicians use this problem as a one-way function which is easy to compute and hard to invert. RSA is based on the integer factorization problem. It uses two large prime. Computation of the product of these two primes is easy but the factorization of the product is hard. The RSA 768 [16] has been broken using the most efficient known integer factorization algorithm, i.e. NFS. More recently December 2019 RSA 795 has been broken using open-source CADO-NFS [28].