Affiliation: Orange Labs
Divisible E-Cash from Constrained Pseudo-Random Functions
Electronic cash (e-cash) is the digital analogue of regular cash which aims at preserving users’ privacy. Following Chaum’s seminal work, several new features were proposed for e-cash to address the practical issues of the original primitive. Among them, divisibility has proved very useful to enable efficient storage and spendings. Unfortunately, it is also very difficult to achieve and, to date, quite a few constructions exist, all of them relying on complex mechanisms that can only be instantiated in one specific setting. In addition security models are incomplete and proofs sometimes hand-wavy.In this work, we first provide a complete security model for divisible e-cash, and we study the links with constrained pseudo-random functions (PRFs), a primitive recently formalized by Boneh and Waters. We exhibit two frameworks of divisible e-cash systems from constrained PRFs achieving some specific properties: either key homomorphism or delegability. We then formally prove these frameworks, and address two main issues in previous constructions: two essential security notions were either not considered at all or not fully proven. Indeed, we introduce the notion of clearing, which should guarantee that only the recipient of a transaction should be able to do the deposit, and we show the exculpability, that should prevent an honest user to be falsely accused, was wrong in most proofs of the previous constructions. Some can easily be repaired, but this is not the case for most complex settings such as constructions in the standard model. Consequently, we provide the first construction secure in the standard model, as a direct instantiation of our framework.
Pattern Matching on Encrypted Streams
Pattern matching is essential in applications such as deep-packet inspection (DPI), searching on genomic data, or analyzing medical data. A simple task to do on plaintext data, pattern matching is much harder to do when the privacy of the data must be preserved. Existent solutions involve searchable encryption mechanisms with at least one of these three drawbacks: requiring an exhaustive (and static) list of keywords to be prepared before the data is encrypted (like in symmetric searchable encryption); requiring tokenization, i.e., breaking up the data to search into substrings and encrypting them separately (e.g., like BlindBox); relying on symmetric-key cryptography, thus implying a token-regeneration step for each encrypted-data source (e.g., user). Such approaches are ill-suited for pattern-matching with evolving patterns (e.g., updating virus signatures), variable searchword lengths, or when a single entity must filter ciphertexts from multiple parties.In this work, we introduce Searchable Encryption with Shiftable Trapdoors (SEST): a new primitive that allows for pattern matching with universal tokens (usable by all entities), in which keywords of arbitrary lengths can be matched to arbitrary ciphertexts. Our solution uses public-key encryption and bilinear pairings.In addition, very minor modifications to our solution enable it to take into account regular expressions, such as fully- or partly-unknown characters in a keyword (wildcards and interval/subset searches). Our trapdoor size is at most linear in the keyword length (and independent of the plaintext size), and we prove that the leakage to the searcher is only the trivial one: since the searcher learns whether the pattern occurs and where, it can distinguish based on different search results of a single trapdoor on two different plaintexts.To better show the usability of our scheme, we implemented it to run DPI on all the SNORT rules. We show that even for very large plaintexts, our encryption algorithm scales well. The pattern-matching algorithm is slower, but extremely parallelizable, and it can thus be run even on very large data. Although our proofs use a (marginally) interactive assumption, we argue that this is a relatively small price to pay for the flexibility and privacy that we are able to attain.