Showing papers by "Moni Naor published in 2000"

Nonmalleable Cryptography

Abstract: The notion of nonmalleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. The same concept makes sense in the contexts of string commitment and zero-knowledge proofs of possession of knowledge. Nonmalleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other system users. Our cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.

Certificate revocation and certificate update

Abstract: We present a solution for the problem of certificate revocation. This solution represents certificate revocation lists by authenticated dictionaries that support: (1) efficient verification whether a certificate is in the list or not and (2) efficient updates (adding/removing certificates from the list). The suggested solution gains in scalability, communication costs, robustness to parameter changes, and update rate. Comparisons to the following solutions (and variants) are included: "traditional" certificate revocation lists (CRLs), Micali's (see Tech. Memo MIT/LCS/TM-542b, 1996) certificate revocation system (CRS), and Kocher's (see Financial Cryptography-FC'98 Lecture Notes in Computer Science. Berlin: Springer-Verlag, 1998, vol.1465, p.172-7) certificate revocation trees (CRT). We also consider a scenario in which certificates are not revoked, but frequently issued for short-term periods. Based on the authenticated dictionary scheme, a certificate update scheme is presented in which all certificates are updated by a common message. The suggested solutions for certificate revocation and certificate update problems are better than current solutions with respect to communication costs, update rate, and robustness to changes in parameters, and are compatible, e.g., with X.500 certificates.

Efficient Trace and Revoke Schemes

Abstract: Our goal is to design encryption schemes for mass distribution of data in which it is possible to (1) deter users from leaking their personal keys, (2) trace which users leaked keys to construct an illegal decryption device, and (3) revoke these keys as to render the device dysfuctional.We start by designing an efficient revocation scheme, based on secret sharning. It remove up to t parties and is secure against coalitions of size t. The performance of this scheme is more efficient than that of previous schemes with the same properties. We then show how to combine the revocation scheme with traitor tracing and self enforcement schemes. More precisely, how to construct schemes such that (1) Each user's personal key contains some sensitive information of that user (e.g., the user's credit card number), and therefore users would be reluctant to disclose their keys. (2) An illegal decryption device discloses the identity of users that contributed keys to construct the device. And, (3) it is possible to revoke the keys of corrupt, users. For the last point it is important to be able to do so without publicly disclosing the sensitive information.

Tracing traitors

Abstract: We give cryptographic schemes that help trace the source of leaks when sensitive or proprietary data is made available to a large set of parties. A very relevant application is in the context of pay television, where only paying customers should be able to view certain programs. In this application, the programs are normally encrypted, and then the sensitive data is the decryption keys that are given to paying customers. If a pirate decoder is found, it is desirable to reveal the source of its decryption keys. We describe fully resilient schemes which can be used against any decoder which decrypts with nonnegligible probability. Since there is typically little demand for decoders which decrypt only a small fraction of the transmissions (even if it is nonnegligible), we further introduce threshold tracing schemes which can only be used against decoders which succeed in decryption with probability greater than some threshold. Threshold schemes are considerably more efficient than fully resilient schemes.

Timed Commitments

Abstract: We introduce and construct timed commitment schemes, an extension to the standard notion of commitments in which a potential forced opening phase permits the receiver to recover (with effort) the committed value without the help of the committer. An important application of our timed-commitment scheme is contract signing: two mutually suspicious parties wish to exchange signatures on a contract. We show a two-party protocol that allows them to exchange RSA or Rabin signatures. The protocol is strongly fair: if one party quits the protocol early, then the two parties must invest comparable amounts of time to retrieve the signatures. This statement holds even if one party has many more machines than the other. Other applications, including honesty preserving auctions and collective coin-flipping, are discussed.

Zaps and their applications

Abstract: A zap is a two-round, witness-indistinguishable protocol in which the first round, consisting of a message from the verifier to the prover, can be fixed "once-and-for-all" and applied to any instance, and where the verifier does not use any private coins. We present a zap for every language in NP, based on the existence of non-interactive zero-knowledge proofs in the shared random string model. The zap is in the standard model, and hence requires no common guaranteed random string. We introduce and construct verifiable pseudo-random bit generators (VPRGs), and give a complete existential characterization of both noninteractive zero-knowledge proofs and zaps in terms of approximate VPRGs. We present several applications for zaps; In the timing model of C. Dwork et al. (1998) and using moderately hard functions, we obtain 3-round concurrent zero knowledge and 2-round concurrent deniable authentication (the latter protocol also operates in the resettable model of R. Canetti et al. (2000)). In the standard model we obtain 2-round oblivious transfer using public keys (3-round otherwise). We note that any zap yields resettable 2-round witness-indistinguishability and obtain a 3-round timing-based resettable zero-knowledge argument system for any language in NP.

Distributed Oblivious Transfer

Abstract: This work describes distributed protocols for oblivious transfer, in which the role of the sender is divided between several servers, and a chooser (receiver) must contact a threshold of these servers in order to run the oblivious transfer protocol. These distributed oblivious transfer protocols provide information theoretic security, and do not require the parties to compute exponentiations or any other kind of public key operations. Consequently, the protocols are very efficient computationally.

Pseudo-random functions and factoring (extended abstract)

Abstract: Factoring integers is the most established problem on which cryptographic primitives are based. This work presents an efficient construction of pseudorandom functions whose security is based on the intractability of factoring. In particular, we are able to construct efficient length-preserving pseudorandom functions where each evaluation requires only a constant number of modular multiplications per output bit. This is substantially more efficient than any previous construction of pseudorandom functions based on factoring, and matches (up to a constant factor) the efficiency of the best known factoring-based pseudorandom bit generators.