In this paper, we introduce P-signatures. A P-signature scheme consists of a signature scheme, a commitment scheme, and (1) an interactive protocol for obtaining a signature on a committed value; (2) a non-interactive proof system for proving that the contents of a commitment has been signed; (3) a noninteractive proof system for proving that a pair of commitments are commitments to the same value. We give a definition of security for P-signatures and show how they can be realized under appropriate assumptions about groups with a bilinear map. We make extensive use of the powerful suite of non-interactive proof techniques due to Groth and Sahai. Our P-signatures enable, for the first time, the design of a practical non-interactive anonymous credential system whose security does not rely on the random oracle model. In addition, they may serve as a useful building block for other privacy-preserving authentication mechanisms.
We construct an efficient delegatable anonymous credentials system. Users can anonymously and unlinkably obtain credentials from any authority, delegate their credentials to other users, and prove possession of a credential L levels away from a given authority. The size of the proof (and time to compute it) is O(Lk), where k is the security parameter. The only other construction of delegatable anonymous credentials (Chase and Lysyanskaya, Crypto 2006) relies on general non-interactive proofs for NP-complete languages of size kΩ(2 L ). We revise the entire approach to constructing anonymous credentials and identify randomizable zero-knowledge proof of knowledge systems as the key building block. We formally define the notion of randomizable non-interactive zero-knowledge proofs, and give the first instance of controlled rerandomization of non-interactive zero-knowledge proofs by a third-party. Our construction uses Groth-Sahai proofs (Eurocrypt 2008).
Efficient non-interactive zero-knowledge proofs are a powerful tool for solving many cryptographic problems. We apply the recent Groth-Sahai (GS) proof system for pairing product equations (Eurocrypt 2008) to two related cryptographic problems: compact e-cash (Eurocrypt 2005) and simulatable verifiable random functions (CRYPTO 2007). We present the first efficient compact e-cash scheme that does not rely on a random oracle. To this end we construct efficient GS proofs for signature possession, pseudo randomness and set membership. The GS proofs for pseudorandom functions give rise to a much cleaner and substantially faster construction of simulatable verifiable random functions (sVRF) under a weaker number theoretic assumption. We obtain the first efficient fully simulatable sVRF with a polynomial sized output domain (in the security parameter). IntroductionSince their invention [BFM88] non-interactive zero-knowledge proofs played an important role in obtaining feasibility results for many interesting cryptographic primitives [BG90,GO92,Sah99], such as the first chosen ciphertext secure public key encryption scheme [BFM88,RS92,DDN91]. The inefficiency of these constructions often motivated independent practical instantiations that were arguably conceptually less elegant, but much more efficient ([CS98] for chosen ciphertext security).We revisit two important cryptographic results of pairing-based cryptography, compact e-cash [CHL05] and simulatable verifiable random functions [CL07], that have very elegant constructions based on non-interactive zero-knowledge proof systems, but less elegant practical instantiations. Our results combine the best of both worlds, a clean design and an efficient implementation.Compact e-cash. Electronic cash (e-cash) was introduced by David Chaum [Cha83] as an electronic analogue of physical money and has been a subject of ongoing cryptographic research since then [CFN90,FY92,CP93,Bra93a,CPS94,Bra93b,SPC95,FTY96,Tsi97]. The participants in an e-cash system are users who withdraw and spend e-cash; a bank that creates e-cash and accepts it for deposit, and merchants who offer goods and services in exchange for e-cash, and then deposit the e-cash to the bank. The main security requirements are (1) anonymity: even if the bank and the merchant and all the remaining users collude with each other, they still cannot distinguish Alice's purchases from Bob's; (2) unforgeability: even if all the users and all the merchants collude against the bank, they still cannot deposit more money than they withdrew.Unfortunately, it is easy to see that, as described above, e-cash is useless. The problem is that here money is represented by data, and it is possible to copy data. Unforgeability will guarantee that the bank will only honor at most one of copy of a given coin for deposit and will reject the others. Anonymity will guarantee that there is no recourse against such a cheating Alice. So one of the merchants will be cheated. There are two known remedies against this double-spending behavior. The ...
Peer-to-peer systems have been proposed for a wide variety of applications, including file-sharing, web caching, distributed computation, cooperative backup, and onion routing. An important motivation for such systems is self-scaling. That is, increased participation increases the capacity of the system. Unfortunately, this property is at risk from selfish participants. The decentralized nature of peer-to-peer systems makes accounting difficult. We show that e-cash can be a practical solution to the desire for accountability in peerto-peer systems while maintaining their ability to self-scale. No less important, e-cash is a natural fit for peer-to-peer systems that attempt to provide (or preserve) privacy for their participants. We show that e-cash can be used to provide accountability without compromising the existing privacy goals of a peer-to-peer system.We show how e-cash can be practically applied to a file sharing application. Our approach includes a set of novel cryptographic protocols that mitigate the computational and communication costs of anonymous e-cash transactions, and system design choices that further reduce overhead and distribute load. We conclude that provably secure, anonymous, and scalable peer-to-peer systems are within reach.
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