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Paper 2008/433
On differences of quadratic residues
Guillermo Morales-Luna
Abstract
Factoring an integer is equivalent to express the integer as the difference of two squares. We test that for any odd modulus, in the corresponding ring of remainders, any element can be realized as the difference of two quadratic residues, and also that, for a fixed remainder value, the map assigning to each modulus the number of ways to express the remainder as difference of quadratic residues is non-decreasing with respect to the divisibility ordering in the odd numbers. The reduction to remainders rings of the problem to express a remainder as the difference of two quadratic residues does not diminish the complexity of the factorization problem.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Contact author(s)
- gmorales @ cs cinvestav mx
- History
- 2008-10-08: received
- Short URL
- https://ia.cr/2008/433
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/433,
author = {Guillermo Morales-Luna},
title = {On differences of quadratic residues},
howpublished = {Cryptology ePrint Archive, Paper 2008/433},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/433}},
url = {https://eprint.iacr.org/2008/433}
}
