Anna Lysyanskaya

An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation

A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance because it is the best means of providing privacy for users. In this paper we propose a practical anonymous credential system that is based on the strong RSA assumption and the decisional Diffie-Hellman assumption modulo a safe prime product and is considerably superior to existing ones: (1) We give the first practical solution that allows a user to unlinkably demonstrate possession of a credential as many times as necessary without involving the issuing organization. (2) To prevent misuse of anonymity, our scheme is the first to offer optional anonymity revocation for particular transactions. (3) Our scheme offers separability: all organizations can choose their cryptographic keys independently of each other. Moreover, we suggest more effective means of preventing users from sharing their credentials, by introducing all-or-nothing sharing: a user who allows a friend to use one of her credentials once, gives him the ability to use all of her credentials, i.e., taking over her identity. This is implemented by a new primitive, called circular encryption, which is of independent interest, and can be realized from any semantically secure cryptosystem in the random oracle model.

Signature Schemes and Anonymous Credentials from Bilinear Maps

We propose a new and efficient signature scheme that is provably secure in the plain model. The security of our scheme is based on a discrete-logarithm-based assumption put forth by Lysyanskaya, Rivest, Sahai, and Wolf (LRSW) who also showed that it holds for generic groups and is independent of the decisional Diffie-Hellman assumption. We prove security of our scheme under the LRSW assumption for groups with bilinear maps. We then show how our scheme can be used to construct efficient anonymous credential systems as well as group signature and identity escrow schemes. To this end, we provide efficient protocols that allow one to prove in zero-knowledge the knowledge of a signature on a committed (or encrypted) message and to obtain a signature on a committed message.

Dynamic Accumulators and Application to Efficient Revocation of Anonymous Credentials

We introduce the notion of a dynamic accumulator. An accumulator scheme allows one to hash a large set of inputs into one short value, such that there is a short proof that a given input was incorporated into this value. A dynamic accumulator allows one to dynamically add and delete a value, such that the cost of an add or delete is independent of the number of accumulated values. We provide a construction of a dynamic accumulator and an efficient zero-knowledge proof of knowledge of an accumulated value. We prove their security under the strong RSA assumption. We then show that our construction of dynamic accumulators enables efficient revocation of anonymous credentials, and membership revocation for recent group signature and identity escrow schemes.

Compact e-cash

This paper presents efficient off-line anonymous e-cash schemes where a user can withdraw a wallet containing 2 coins each of which she can spend unlinkably. Our first result is a scheme, secure under the strong RSA and the y-DDHI assumptions, where the complexity of the withdrawal and spend operations is O( + k) and the users wallet can be stored using O( + k) bits, where k is a security parameter. The best previously known schemes require at least one of these complexities to be O(2 . k). In fact, compared to previous e-cash schemes, our whole wallet of 2 coins has about the same size as one coin in these schemes. Our scheme also offers exculpability of users, that is, the bank can prove to third parties that a user has double-spent. We then extend our scheme to our second result, the first e-cash scheme that provides traceable coins without a trusted third party. That is, once a user has double spent one of the 2 coins in her wallet, all her spendings of these coins can be traced. However, the price for this is that the complexity of the spending and of the withdrawal protocols becomes O( . k) and O( . k+ k 2 ) bits, respectively, and wallets take O( . k) bits of storage. All our schemes are secure in the random oracle model.

Sequential Aggregate Signatures from Trapdoor Permutations

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, in which the set of 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.

How to securely outsource cryptographic computations

We address the problem of using untrusted (potentially malicious) cryptographic helpers. We provide a formal security definition for securely outsourcing computations from a computationally limited device to an untrusted helper. In our model, the adversarial environment writes the software for the helper, but then does not have direct communication with it once the device starts relying on it. In addition to security, we also provide a framework for quantifying the efficiency and checkability of an outsourcing implementation. We present two practical outsource-secure schemes. Specifically, we show how to securely outsource modular exponentiation, which presents the computational bottleneck in most public-key cryptography on computationally limited devices. Without outsourcing, a device would need O(n) modular multiplications to carry out modular exponentiation for n-bit exponents. The load reduces to O(log2n) for any exponentiation-based scheme where the honest device may use two untrusted exponentiation programs; we highlight the Cramer-Shoup cryptosystem [13] and Schnorr signatures [28] as examples. With a relaxed notion of security, we achieve the same load reduction for a new CCA2-secure encryption scheme using only one untrusted Cramer-Shoup encryption program.

How to win the clonewars: efficient periodic n-times anonymous authentication

We create a credential system that lets a user anonymously authenticate at most

Randomizable Proofs and Delegatable Anonymous Credentials

n

Algorithmic tamper-proof (ATP) security: Theoretical foundations for security against hardware tampering

times in a single time period. A user withdraws a dispenser of n e-tokens. She shows an e-token to a verifier to authenticate herself; each e-token can be used only once, however, the dispenser automatically refreshes every time period. The only prior solution to this problem, due to Damgård et al. [29], uses protocols that are a factor of k slower for the user and verifier, where k is the security parameter. Damgård et al. also only support one authentication per time period, while we support n. Because our construction is based on e-cash, we can use existing techniques to identify a cheating user, trace all of her e-tokens, and revoke her dispensers. We also offer a new anonymity service: glitch protection for basically honest users who (occasionally) reuse e-tokens. The verifier can always recognize a reused e-token; however, we preserve the anonymity of users who do not reuse e-tokens too often.

Group Blind Digital Signatures: A Scalable Solution to Electronic Cash

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 k ?(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).