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Elliptic curves in cryptography: past, present and future. (Chinese. English summary) Zbl 1290.14018

Summary: From the beginning of the nineteenth century, mathematicians have put elliptic curves as a research objective of algebra, geometry and number theory to study in-depth. So far, the theory of elliptic curves has been applied not only in the field of mathematics, and also widely in computing science, information security, physics and other fields. In this paper, we review the application of elliptic curves in cryptography, from the primality testing, integer factorization to elliptic curve cryptosystem, bilinear pairing based cryptosystem and the quantum-resistant cryptosystems from elliptic curve isogenies. We introduce the basic principles and the status of these applications. Finally, we briefly discuss some open questions and possible future progress in this area.

MSC:

14G50 Applications to coding theory and cryptography of arithmetic geometry
14H52 Elliptic curves
94A60 Cryptography
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