Elliptic curve cryptography - implementation and security issues

隐私和安全是现代生活的两个显而易见的必需品。然而，当谈到保护数字数据时，这些新概念仍然没有得到很好的理解。1978年公钥密码术的发明使这种努力成为现实，因此现在我们有了一种实用的方法来安全地执行许多电子任务，其中身份证明是必不可少的。签名、认证、密钥协议是当今我们日常电子生活的一部分，无论是在网上交易中，还是在从自动取款机取款时。仍然存在许多问题，也是因为黑客的攻击越来越复杂。在这种思路下，我们要求执行这些任务的公钥基元达到标准的安全级别，并以尽可能快的速度实现。我的研究涉及通过使用椭圆曲线来加速这些计算实现，现在椭圆曲线可能比RSA更快。在另一个方向，我还将研究椭圆曲线的安全性，并确保没有人能产生容易被破解的“伪曲线”。

Privacy and security are two obvious necessities of modern life. Yet, when it comes to protecting digital data, these are new concepts that are still not well understood. The invention of public-key cryptography in 1978 made such endeavours become a reality, so that now we have a practical way of performing securely many electronic tasks where a proof of identity is essential. Signatures, authentications, key agreements are nowadays part of our daily electronic life, be it in an online transaction or when withdrawing money from an ATM.Still many problems remain, also because hackers have increasingly more sophisticated attacks.In this line of thought, we require from the public-key primitives that perform these tasks that they achieve a standard level of security, with the fastest possible implementation.My research involves speeding up these computational implementations through the use of elliptic curves, which  are now faster than RSA.In another direction I will also investigate the security of elliptic curves and make sure that nobody can produce "phony curves" which are easily crackable.