Security of algebraic curves in cryptography

点击翻译按钮获取中文摘要

Elliptic curve cryptography (ECC) and generalizations such as hyperelliptic curve cryptography represent the most efficiently implementable public key cryptosystems available today for a given level of security. All other public key cryptosystems, such as RSA (Rivest-Shamir-Adleman) either admit subexponential time attacks or have not been subjected to the same level of scrutiny for a sufficiently long period of time to warrant confidence in their security. For this reason, ECC has been widely adopted in international standards as the preferred cryptosystem for security sensitive or resource constrained environments. A notable application of ECC is in the area of security for mobile phones, where lower computational power often precludes the use of less efficient alternatives.