Zero-Knowledge Proofs

This paper describes a login system utilizing Two Factor Authentication and Zero Knowledge Proof using Schnorr NIZK. The proposed system is designed to prevent password leak when being sent over insecure network or when used in an untrusted devices. Zero Knowledge Proof is used for maintaining the confidentiality of the password and Two Factor Authentication is used to secure login process on untrusted devices. The proposed system has been tested and initial results indicates that such system is able to secure the login process without leaking the user's password.

The notion of Zero Knowledge Proofs (of knowledge) [ZKP] is central to cryptography; it provides a set of security properties that proved indispensable in concrete protocol design. These properties are defined for any given input and also for any auxiliary verifier private state, as they are aimed at any use of the protocol as a subroutine in a bigger application. Many times, however, moving the theoretical notion to practical designs has been quite problematic. This is due to the fact that the most efficient protocols fail to provide the above ZKP properties for all possible inputs and verifier states. This situation has created various problems to protocol designers who have often either introduced imperfect protocols with mistakes or with lack of security arguments, or they have been forced to use much less efficient protocols in order to achieve the required properties. In this work we address this issue by introducing the notion of "protocol portability," a property that identifies input and verifier state distributions under which a protocol becomes a ZKP when called as a subroutine in a sequential execution of a larger application. We then concentrate on the very efficient and heavily employed "Generalized Schnorr Proofs" (GSP) and identify the portability of such protocols. We also point to previous protocol weaknesses and errors that have been made in numerous applications throughout the years, due to employment of GSP instances while lacking the notion of portability (primarily in the case of unknown order groups). This demonstrates that cryptographic application designers who care about efficiency need to consider our notion carefully. We provide a compact specification language for GSP protocols that protocol designers can employ. Our specification language is consistent with the ad-hoc notation that is currently widely used and it offers automatic derivation of the proof protocol while dictating its portability (i.e., the proper initial state and inputs) and its security guarantees. Finally, as a second alternative to designers wishing to use GSPs, we present a modification of GSP protocols that is unconditionally portable (i.e., ZKP) and is still quite efficient. Our constructions are the first such protocols proven secure in the standard model (while the previously known efficient constructions relied on the Random Oracle model).