Securing E-passports with Elliptic Curves

In this paper, security of ID documents (such as passports) is discussed. A class of cryptographic protocols called Password-Authenticated Key Exchange (PAKE) provides a more robust solution to this problem. PAKE protocols ensure that an eavesdropper can't learn any information on the low-entropy secret. They're also required to be as secure as possible against all passive and active attacks. Basically, all an adversary can do to learn the password is an online dictionary attack (guess the password and try to execute the protocol with one of the parties). We can prevent this through latency, smart card blocking, and so on. For implementing PAKE protocols, especially in constrained environments such as e-passports, elliptic-curve cryptography is fast and requires little memory. However, it involves representing numeric values (in this case, passwords) as points on an elliptic curve, and how to do this efficiently and se curely isn't obvious.