Security of algebraic curves in cryptography

椭圆曲线密码术(ECC)和超椭圆曲线密码术等推广代表了当今可用于给定安全级别的最有效的可实现公钥密码系统。所有其他公钥密码系统，如RSA(Rivest-Shamir-Adleman)，要么承认次指数时间攻击，要么在足够长的时间内没有受到足够长时间的相同水平的审查，以保证其安全性。因此，ECC在国际标准中被广泛采用，成为安全敏感或资源受限环境下的首选密码体制。ECC的一个值得注意的应用是在移动电话安全领域，计算能力较低通常会阻止使用效率较低的替代方案。

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.