Abstract Private set intersection (PSI) allows two mutually distrusting parties each with a set as input, to learn the intersection of both their sets without revealing anything more about their respective input sets. Traditionally, PSI studies the static setting where the computation is performed only once on both parties’ input sets. We initiate the study of updatable private set intersection (UPSI), which allows parties to compute the intersection of their private sets on a regular basis with sets that also constantly get updated. We consider two specific settings. In the first setting called UPSI with addition, parties can add new elements to their old sets. We construct two protocols in this setting, one allowing both parties to learn the output and the other only allowing one party to learn the output. In the second setting called UPSI with weak deletion, parties can additionally delete their old elements every t days. We present a protocol for this setting allowing both parties to learn the output. All our protocols are secure against semi-honest adversaries and have the guarantee that both the computational and communication complexity only grow with the set updates instead of the entire sets. Finally, we implement our UPSI with addition protocols and compare with the state-of-the-art PSI protocols. Our protocols compare favorably when the total set size is sufficiently large, the new updates are sufficiently small, or in networks with low bandwidth.

Token-based authentication is commonly used to enable a single-sign-on experience on the web, in mobile applications and on enterprise networks using a wide range of open standards and network authentication protocols: clients sign on to an identity provider using their username/password to obtain a cryptographic token generated with a master secret key, and store the token for future accesses to various services and applications. The authentication server(s) are single point of failures that if breached, enable attackers to forge arbitrary tokens or mount offline dictionary attacks to recover client credentials. Our work is the first to introduce and formalize the notion of password-based threshold token-based authentication which distributes the role of an identity provider among n servers. Any t servers can collectively verify passwords and generate tokens, while no t-1 servers can forge a valid token or mount offline dictionary attacks. We then introduce PASTA, a general framework that can be instantiated using any threshold token generation scheme, wherein clients can "sign-on" using a two-round (optimal) protocol that meets our strong notions of unforgeability and password-safety. We instantiate and implement our framework in C++ using two threshold message authentication codes (MAC) and two threshold digital signatures with different trade-offs. Our experiments show that the overhead of protecting secrets and credentials against breaches in PASTA, i.e. compared to a naive single server solution, is extremely low (1-5%) in the most likely setting where client and servers communicate over the internet. The overhead is higher in case of MAC-based tokens over a LAN (though still only a few milliseconds) due to public-key operations in PASTA. We show, however, that this cost is inherent by proving a symmetric-key only solution impossible.