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 Mi for i = 1, . . . , n). In this paper we introduce the concept of an aggregate signature, 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.

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Aggregate and verifiably encrypted signatures from bilinear maps

We introduce the spi calculus, an extension of the pi calculus designed for describing and analyzing cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarse-grained notions of protocol equivalence. ] 1999 Academic Press

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A calculus for cryptographic protocols: the spi calculus

We introduce the spi calculus, an extension of the pi calculus designed for describing and analyzing cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarse-grained notions of protocol equivalence.

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A calculus for cryptographic protocols

This paper addresses the problem of designing practical protocols for proving properties about encrypted data. To this end, it presents a variant of the new public key encryption of Cramer and Shoup based on Paillier’s decision composite residuosity assumption, along with efficient protocols for verifiable encryption and decryption of discrete logarithms (and more generally, of representations with respect to multiple bases). This is the first verifiable encryption system that provides chosen ciphertext security and avoids inefficient cut-and-choose proofs. The presented protocols have numerous applications, including key escrow, optimistic fair exchange, publicly verifiable secret and signature sharing, universally composable commitments, group signatures, and confirmer signatures.

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Practical Verifiable Encryption and Decryption of Discrete Logarithms

We present a new protocol that allows two players to exchange digital signatures over the Internet in a fair way, so that either each player gets the other's signature, or neither player does. The obvious application is where the signatures represent items of value, for example, an electronic check or airline ticket. The protocol can also be adapted to exchange encrypted data. It relies on a trusted third party, but is "optimistic," in that the third party is only needed in cases where one player crashes or attempts to cheat. A key feature of our protocol is that a player can always force a timely and fair termination, without the cooperation of the other player, even in a completely asynchronous network. A specialization of our protocol can be used for contract signing; this specialization is not only more efficient, but also has the important property that the third party can be held accountable for its actions: if it ever cheats, this can be detected and proven.

Optimistic fair Exchange of Digital Signatures.

We present protocols for fair exchange of electronic data (digital signatures, payment and confidential data) between two parties A and B. Novel properties of the proposed protocols include: 1) offline trusted third party (TTP), i.e., TTP does not take part in the exchange unless one of the parties behaves improperly; 2) only three message exchanges are required in the normal situation; 3) true fair exchange, i.e., either A and B obtain each other's data or no party receives anything useful; no loss can be incurred to a party no matter how maliciously the other party behaves during the exchange. This last property is in contrast to previously proposed protocols with offline TTP ([1] and [21]), where a misbehaving party may get another party's data while refusing to send his document to the other party, and the TTP can provide affidavits attesting to what happened during the exchange. To our knowledge, the protocols presented here are the first exchange protocols which use offline TTP and at the same time guarantee true fair exchange of digital messages. We introduce a novel cryptographic primitive, called the Certificate of Encrypted Message Being a Signature (CEMBS), as the basic building block of the fair exchange protocols. It is used to prove that an encrypted message is a certain party's signature on a public file, without revealing the signature. We also give two examples to show in detail how the certificate can be constructed.

Efficient and practical fair exchange protocols with off-line TTP

Recently, two major bankcard payment instrument operators VISA and MasterCard published specifications for securing bankcard payment transactions on open networks for open scrutiny. (VISA: Secure Transaction Technology, STT; MasterCard: Secure Electronic Payment Protocol, SEPP.) Based on their success in operating the existing on-line payment systems, both proposals use advanced cryptographic technologies to supply some security services that are well-understood to be inadequate in open networks, and otherwise specify systems similar to today's private-network versions. In this paper we reason that when an open network is used for underlying electronic commerce some subtle vulnerabilities will emerge and the two specifications are seen not in anticipation of them. A number of weaknesses are found as a result of missing and misuse of security services. Missing and misused services include: authentication, nonrepudiation, integrity, and timeliness, We identify problems and devise solutions while trying to keep, the current successful working style of financial institutions being respected.

On two proposals for on-line bankcard payments using open networks: problems and solutions

Argues the necessity of universally verifiable secret sharing for secrets as individual users' cryptographic keys, and proposes protocols to realize such secret sharing for two most common public-key cryptosystems: discrete logarithm-based and integer factorization-based. The universal verifiability achieves the sharing of secrets with multiple third parties as shareholders using two-party protocols in which a single verifier, who can be anybody, can verify the correctness of the secret sharing for the (off-line) multiple shareholders. Several advantages result: (i) dropping of the honesty requirement on the verifier and the shareholders, (ii) dropping of the online availability requirement on the multiple shareholders, and (iii) the simplicity of two-party protocols which provide users with the freedom and flexibility to choose multiple shareholders they trust in real time of share distribution. The two-party protocols proposed offer a practical solution for secure data backup and key recovery services.

Wenbo Mao

Papers

Efficient and practical fair exchange protocols with off-line TTP

On two proposals for on-line bankcard payments using open networks: problems and solutions

Necessity and realization of universally verifiable secret sharing