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Lecture notes in computer science

Two-Message, Oblivious Evaluation of Cryptographic Functionalities

Nico Döttling, Nils Fleischhacker, Johannes Krupp, Dominique Schröder

Published Jan 1, 2016• 8 citations
Publisher
DOI
10.1007/978-3-662-53015-3_22

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We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors x λ- y, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of x. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host of cryptographic primitives, all with security reducible to LWE, such as: (a) Adaptively secure laconic function evaluation for depth-D functions f:{0, 1}m→{0, 1}λ.," with communication m+λ.,"+D· poly(λ); (b) A trapdoor hash function for all functions; (c) An (optimally) succinct homomorphic secret sharing for all functions; (d) A rate-1/2 laconic oblivious transfer for batch messages, which is best possible. In particular, we obtain the first laconic function evaluation scheme that is adaptively secure from the standard LWE assumption, improving upon Quach, Wee, and Wichs (FOCS 2018). As a key technical ingredient, we introduce a new notion of adaptive lattice encodings, which may be of independent interest.
Oblivious transfer is a powerful cryptographic primitive that is complete for secure multi-party computation. In oblivious transfer protocols a user sends one or more messages to a receiver, while the sender remains oblivious as to which messages have been received. Protocols for oblivious transfer cannot exist in a classical or fully-quantum world, but can be implemented by restricting the users' power. The isolated qubits model is a cryptographic model in which users are restricted to single-qubit operations and are not allowed to use entangling operations. Furthermore, all parties are allowed to store qubits for a long time before measuring them. In this model, a secure single-bit one-out-of-two randomised oblivious transfer protocol was recently presented by Liu. Motivated by this result, we construct a protocol for secure string one-out-of-two randomised oblivious transfer by simplifying and generalising the existing proof. We then study for the first time interactive protocols for more complex two-party functionalities in this model based on the security of our construction. In order to guarantee the composability of our construction, users are restricted to measurement at the end of each sub-protocol. It is then possible to construct secure one-out-of-two and one-out-of-k oblivious transfer protocols in the isolated qubits model. Moreover, we study secure password-based identification, where a user identifies himself to another user by evaluating the equality function on their inputs, or passwords. We use the oblivious transfer constructions mentioned above as sub-protocols to construct a secure identification protocol. Finally, we prove that constructing a secure identification protocol non-interactively is impossible, even using oblivious transfer.
Oblivious transfer protocol is an important primitive in modern cryptography. Since its introduction, the subject has attracted a lot of attentions and has become the basis for realizing a broad class of cryptographic protocols, such as secret key exchange, contract signing, secure function evaluation, oblivious keyword search, etc. This work describes protocols for proxy oblivious transfer, in which the role of the sender is divided between two proxies, and a receiver (chooser) must contact one proxy in order to run the oblivious transfer protocol and another for some extra information. This proxy oblivious transfer protocol provides a method for the sender to delegate a proxy to transfer one of his messages to a receiver on behalf of him. The proxy oblivious transfer protocol has the same security properties as the oblivious transfer protocol using in our protocol.