Idempotent Factorizations of Square-Free Integers
Department of Computer Science, US Air Force Academy, Colorado Springs, CO 80840, USA
Received: 20 June 2019 / Accepted: 3 July 2019 / Published: 6 July 2019
PDF [311 KB, uploaded 6 July 2019]
We explore the class of positive integers n
that admit idempotent factorizations
is the Carmichael lambda function. Idempotent factorizations with
prime have received the most attention due to their cryptographic advantages, but there are an infinite number of n
with idempotent factorizations containing composite
. Idempotent factorizations are exactly those
that generate correctly functioning keys in the Rivest–Shamir–Adleman (RSA) 2-prime protocol with n
as the modulus. While the resulting
have no cryptographic utility and therefore should never be employed in that capacity, idempotent factorizations warrant study in their own right as they live at the intersection of multiple hard problems in computer science and number theory. We present some analytical results here. We also demonstrate the existence of maximally idempotent
integers, those n
for which all bipartite factorizations are idempotent. We show how to construct them, and present preliminary results on their distribution.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Fagin, B. Idempotent Factorizations of Square-Free Integers. Information 2019, 10, 232.
Fagin B. Idempotent Factorizations of Square-Free Integers. Information. 2019; 10(7):232.
Fagin, Barry. 2019. "Idempotent Factorizations of Square-Free Integers." Information 10, no. 7: 232.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.