The integer factorization problem (IFP), the finite field discrete logarithm problem (DLP) and the elliptic curve discrete logarithm problem (ECDLP) are essentially the only three mathematical problems that the practical public-key cryptographic systems are based on. For example, the most famous RSA cryptosystem is based on IFP, the US government's Digital Signature Standard, DSS, is based on DLP, whereas the ECC (Elliptic Curve Cryptography) and Elliptic Curve Digital Signature Algorithm (ECDSA) are based on ECDLP. The security of such cryptographic systems relies on the computational intractability of these three mathematical problems. In this paper, we shall present a survey of various methods for solving the IFP/DLP and particularly the ECDLP problems. More specifically, we shall first discuss how the index calculus as well as quantum algorithms can be used to solve IFP/DLP. Then we shall show why the index calculus cannot be used to solve ECDLP. Finally, we shall introduce a new method, xedni calculus , due to Joseph Silverman, for attack ECDLP; some open problems and new research directions, will also be addressed.
Computing Prime Factorization And Discrete Logarithms: From Index Calculus To Xedni Calculus
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.