A cryptographic accumulator is a compressed data structure with associated algorithms used for secure membership testing. In the growing space of digital credentials, accumulators are used to manage sets of valid credentials, giving efficient and anonymous methods for credential holders to prove their validity. Unlike traditional credentials like digital signatures, one can easily revoke credentials with an accumulator; however, each revocation forces existing credential holders to engage in an expensive update process. Previous works make this faster and easier by sacrificing anonymity. To improve performance without compromising privacy, we present ALLOSAUR, a multi-party accumulator based on pairings. In ALLOSAUR, we eliminate the cost of accumulating new credentials, let "credential managers" manage the accumulator values with secure multiparty computation, and allow anonymous credential updates with a square-root reduction in communication costs as compared to existing work.

We construct an algebraic pseudorandom function (PRF) that is more efficient than the classic Naor-Reingold algebraic PRF. Our PRF is the result of adapting the cascade construction, which is the basis of HMAC, to the algebraic settings. To do so we define an augmented cascade and prove it secure when the underlying PRF satisfies a property called parallel security. We then use the augmented cascade to build new algebraic PRFs. The algebraic structure of our PRF leads to an efficient large-domain Verifiable Random Function (VRF) and a large-domain simulatable VRF.

Fingerprinting codes, originally designed for embedding traceable fingerprints in digital content, have many applications in cryptography; most notably, they are used to construct traitor tracing systems. Recently there has been some interest in constructing robust fingerprinting codes: codes capable of tracing words even when the pirate adversarially destroys a δ fraction of the marks in the fingerprint. An early construction due to Boneh and Naor produces codewords whose length is proportional to c4/(1-δ)2 where c is the number of words at the adversary's disposal. Recently Nuida developed a scheme with codewords of length proportional to (c log c)2/(1-δ) 2. In this paper we introduce a new technique for constructing codes whose length is proportional to (c log c)2/(1-δ), which is asymptotically optimal up to logarithmic factors. These new codes lead to traitor tracing systems with constant size ciphertext and asymptotically shorter secret keys than previously possible.