Isogeny-based cryptography: from theory to practice

当今使用的许多密码协议的安全性依赖于诸如整数因子分解之类的数学问题的计算难度。这些问题可以使用量子计算机来解决，因此，一旦量子计算机建成，我们的大多数安全基础设施将变得完全不安全。后量子密码学的目标是开发安全协议，即使在量子计算机建成后也能保持安全。包括GCHQ和NSA在内的世界上最大的安全机构已经建议向后量子协议迈进，新一代的加密标准将针对后量子安全。该项目将考虑基于isqueries问题的加密，这是一个被认为是后量子安全的特殊协议族。基于同源性的协议特别有吸引力，原因有三：1）与其他后量子密码学候选者相比，它们需要非常小的密钥，节省带宽和存储2）存在广泛使用的Diffie-Hellman协议的基于同源性的版本，其可以用作当前实例的直接替代3）它们的数学基础与当前使用的椭圆曲线协议有很多共同之处，基于等基因的密码协议只是最近才发明的，并且像当前为后量子安全研究的许多其他协议一样，它们还必须经受住“时间的考验”。由于它们没有像目前部署的解决方案那样得到彻底的调查，它们可能更容易出现意想不到的弱点。此外，协议仍处于理论论文阶段，仍有待于根据实际应用的具体限制进行评估。这个项目将推进基于同源性的密码学领域，从它的数学基础一直到协议在真实的世界中的应用。我们将开发新的协议，新的分析技术，并确定基于同源性的加密技术对选定应用程序的适用性。

The security of many cryptographic protocols in use today relies on the computational hardness of mathematical problems such as integer factorization. These problems can be solved using quantum computers, and therefore most of our security infrastructures will become completely insecure once quantum computers are built. Post-quantum cryptography aims at developing security protocols that will remain secure even after quantum computers are built. The biggest security agencies in the world including GCHQ and the NSA have recommended a move towards post-quantum protocols, and the new generation of cryptographic standards will aim at post-quantum security.This project will consider cryptography based on isogeny problems, a particular family of protocols that are considered for post-quantum security. Isogeny-based protocols are particularly appealing for three reasons 1) they require very small keys compared to other post-quantum cryptography candidates, saving on bandwidth and storage 2) there exists an isogeny-based version of the widely used Diffie-Hellman protocol, which can be used as a direct replacement of current instantiations 3) their mathematical grounding has a lot in common with currently used elliptic curve protocols, which will accelerate implementations in a wide range of devices.Isogeny-based cryptography protocols have only been invented recently, and like many other protocols currently investigated for post-quantum security they yet have to survive the "test of time". As they have not been investigated as thoroughly as currently deployed solutions, they may be more vulnerable to unanticipated weaknesses. Moreover, the protocols are still at the stage of theoretical papers and remain to be evaluated against the specific constraints of real-life applications. This project will advance the field of isogeny-based cryptography, from its mathematical grounding right up to the application of protocols in the real world. We will develop new protocols, new analysis techniques, and determine the suitability of isogeny-based cryptography for selected applications.