An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verifier that the n users did indeed sign the n original messages (i.e., user i signed message M i for i = 1; : : : ; n). In this paper we introduce the concept of an aggregate signature scheme, present security models for such signatures, and give several applications for aggregate signatures. We construct an efficient aggregate signature from a recent short signature scheme based on bilinear maps due to Boneh, Lynn, and Shacham. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols such as SBGP. We also show that aggregate signatures give rise to verifiably encrypted signatures. Such signatures enable the verifier to test that a given ciphertext C is the encryption of a signature on a given message M . Verifiably encrypted signatures are used in contract-signing protocols. Finally, we show that similar ideas can be used to extend the short signature scheme to give simple ring signatures.

We propose a robust proactive threshold signature scheme, a multisignature scheme and a blind signature scheme which work in any Gap Diffie-Hellman (GDH) group (where the Computational Diffie-Hellman problem is hard but the Decisional Diffie-Hellman problem is easy). Our constructions are based on the recently proposed GDH signature scheme of Boneh et al. [8]. Due to the instrumental structure of GDH groups and of the base scheme, it turns out that most of our constructions are simpler, more efficient and have more useful properties than similar existing constructions. We support all the proposed schemes with proofs under the appropriate computational assumptions, using the corresponding notions of security.

An aggregate signature scheme (recently proposed by Boneh, Gentry, Lynn, and Shacham) is a method for combining n signatures from n different signers on n different messages into one signature of unit length. We propose sequential aggregate signatures, inwhichthesetof signers is ordered. The aggregate signature is computed by having each signer, in turn, add his signature to it. We show how to realize this in such a way that the size of the aggregate signature is independent of n. This makes sequential aggregate signatures a natural primitive for certificate chains, whose length can be reduced by aggregating all signatures in a chain. We give a construction in the random oracle model based on families of certified trapdoor permutations, and show how to instantiate our scheme based on RSA. 1

Abstract. We present the first aggregate signature, the first multisignature, and the first verifiably encrypted signature provably secure without random oracles. Our constructions derive from a novel application of a recent signature scheme due to Waters. Signatures in our aggregate signature scheme are sequentially constructed, but knowledge of the order in which messages were signed is not necessary for verification. The aggregate signatures obtained are shorter than Lysyanskaya et al. sequential aggregates and can be verified more efficiently than Boneh et al. aggregates. We also consider applications to secure routing and proxy signatures. 1

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Applications such as e-commerce payment protocols, elec-tronic contract signing, and certified e-mail delivery require that fair exchange be assured. A fair-exchange protocol al-lows two parties to exchange items in a fair way so that either each party gets the other's item, or neither party does. We describe a novel method of constructing very ef-ficient fair-exchange protocols by distributing the computa-tion of RSA signatures. Specifically, we employ multisig-natures based on the RSA-signature scheme. To date, the vast majority of fair-exchange protocols require the use of zero-knowledge proofs, which is the most computationally intensive part of the exchange protocol. Using the intrinsic features of our multisignature model, we construct protocols that require no zero-knowledge proofs in the exchange proto-col. Use of zero-knowledge proofs is needed only in the pro-tocol setup phase--this is a one-time cost. Furthermore, our scheme uses multisignatures that are compatible with the underlying standard (single-signer) signature scheme, which makes it possible to readily integrate the fair-exchange fea-ture with existing e-commerce systems.

Peer-to-Peer (P2P) applications and services are very common in today's computing. The popularity of the P2P paradigm prompts the need for specialized security services which makes P2P security an important and challenging research topic. Most prior work in P2P security focused on authentication, key management and secure communication. However, an important pre-requisite for many P2P security services is secure admission, or how one becomes a peer in a P2P setting. This issue has been heretofore largely untouched.

Security in collaborative peer groups is an active research topic. Most previous work focused on key management without addressing an important pre-requisite: admission control, i.e., how to securely admit a new member. This paper represents an initial attempt to sketch out an admission control framework suitable for di#erent flavors of peer groups and match them with appropriate cryptographic techniques and protocols. Open problems and directions for future work are identified and discussed.

Abstract. An identity (ID)-based signature scheme allows any pair of users to verify each other’s signatures without exchanging public key certificates. With the advent of Bilinear maps, several ID-based signatures based on the discrete logarithm problem have been proposed. While these signatures have an advantage in the fact that the system secret can be shared by several parties using a threshold scheme (thereby overcoming the security problem of RSA-based ID-based signature schemes), they all share the same efficiency disadvantage. To overcome this, some schemes have focused on finding ways to verify multiple signatures at the same time (i.e. the batch verification problem). While they had some success in improving efficiency of verification, each had a slightly diversified definition of batch verification. In this paper, we propose a taxonomy of batch verification against which we analyze security of well-known ID-based signature schemes. We also propose a new ID-based signature scheme that allows for all types of multiple signature batch verification, and prove its security in random oracle model. Key words: ID-based signatures, Batch verifications 1

Peer-to-peer (P2P) and grid systems allow their users to exchange information and share resources, with little centralised or hierarchical control, instead relying on the fairness of the users to make roughly as much resources available as they use. To enforce this balance, some kind of currency or barter (called karma) is needed that must be exchanged for resources thus limiting abuse. We present a completely decentralised, o#-line karma implementation for P2P and grid systems, that detects double-spending and other types of fraud under varying adversarial scenarios. The system is based on tracing the spending pattern of coins, and distributing the normally central role of a bank over a predetermined, but random, selection of nodes. The system is designed to allow nodes to join and leave the system at arbitrary times.