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Analysis of institutional authors

Urroz JAuthor

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February 13, 2023
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Factorization and malleability of rsa moduli, and counting points on elliptic curves modulo n

Publicated to:Mathematics. 8 (12): 1-10 - 2020-01-01 8(12), DOI: 10.3390/math8122126

Authors: Dieulefait LV; Urroz J

Affiliations

Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, Barcelona, 08007, Spain - Author
Departamento de Matemáticas, Universitat Politécnica Catalunya, Edificio C3—Campus Nord UPC, Carrer de Jordi Girona 1-3, Barcelona, 08034, Spain - Author
Universitat de Barcelona - Author
Universitat Politècnica de Catalunya - Author

Abstract

In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to counting points on a pair of twisted Elliptic curves modulo N. The second problem is related with malleability. This notion was introduced in 2006 by Pailler and Villar, and deals with the question of whether or not the factorization of a given number N becomes substantially easier when knowing the factorization of another one N′ relatively prime to N. Despite the efforts done up to now, a complete answer to this question was unknown. Here we settle the problem affirmatively. To construct a particular N′ that helps the factorization of N, we use the number of points of a single elliptic curve modulo N. Coppersmith’s algorithm allows us to go from the factors of N′ to the factors of N in polynomial time. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Coppersmith algorithmElliptic curvesFactorizationMalleability

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2020, it was in position 24/330, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 3.77, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-07:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 5 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (JIMENEZ URROZ, JORGE).