Peter Sebastian Nordholt

A New Approach to Practical Active-Secure Two-Party Computation

We propose a new approach to practical two-party computation secure against an active adversary. All prior practical protocols were based on Yaos garbled circuits. We use an OT-based approach and get efficiency via OT extension in the random oracle model. To get a practical protocol we introduce a number of novel techniques for relating the outputs and inputs of OTs in a larger construction. We also report on an implementation of this approach, that shows that our protocol is more efficient than any previous one: For big enough circuits, we can evaluate more than 20000 Boolean gates per second. As an example, evaluating one oblivious AES encryption

Signature schemes secure against hard-to-invert leakage

\sim 34000

Lower and upper bounds for deniable public-key encryption

gates takes 64i¾?seconds, but when repeating the task 27i¾?times it only takes less than 3i¾?seconds per instance.

Signature Schemes Secure Against Hard-to-Invert Leakage

One of the main tools to construct secure two-party computation protocols are Yao garbled circuits. Using the cut-and-choose technique, one can get reasonably efficient Yao-based protocols with security against malicious adversaries. At TCC 2009, Nielsen and Orlandi [28] suggested to apply cut-and-choose at the gate level, while previously cut-and-choose was applied on the circuit as a whole. This idea allows for a speed up with practical significance (in the order of the logarithm of the size of the circuit) and has become known as the “LEGO” construction. Unfortunately the construction in [28] is based on a specific number-theoretic assumption and requires public-key operations per gate of the circuit. The main technical contribution of this work is a new XOR-homomorphic commitment scheme based on oblivious transfer, that we use to cope with the problem of connecting the gates in the LEGO construction. Our new protocol has the following advantages:

Minimising Communication in Honest-Majority MPC by Batchwise Multiplication Verification

In the auxiliary input model an adversary is allowed to see a computationally hard-to-invert function of the secret key. The auxiliary input model weakens the bounded leakage assumption commonly made in leakage resilient cryptography as the hard-to-invert function may information-theoretically reveal the entire secret key. In this work, we propose the first constructions of digital signature schemes that are secure in the auxiliary input model. Our main contribution is a digital signature scheme that is secure against chosen message attacks when given an exponentially hard-to-invert function of the secret key. As a second contribution, we construct a signature scheme that achieves security for random messages assuming that the adversary is given a polynomial-time hard to invert function. Here, polynomial-hardness is required even when given the entire public-key --- so called weak auxiliary input security. We show that such signature schemes readily give us auxiliary input secure identification schemes.

High Performance Multi-Party Computation for Binary Circuits Based on Oblivious Transfer.

We report on the design and implementation of a system that uses multiparty computation to enable banks to benchmark their customers’ confidential performance data against a large representative set of confidential performance data from a consultancy house. The system ensures that both the banks’ and the consultancy house’s data stays confidential, the banks as clients learn nothing but the computed benchmarking score. In the concrete business application, the developed prototype helps Danish banks to find the most efficient customers among a large and challenging group of agricultural customers with too much debt. We propose a model based on linear programming for doing the benchmarking and implement it using the SPDZ protocol by Damgard et al., which we modify using a new idea that allows clients to supply data and get output without having to participate in the preprocessing phase and without keeping state during the computation. We ran the system with two servers doing the secure computation using a database with information on about 2500 users. Answers arrived in about 25 s.

Confidential Benchmarking based on Multiparty Computation.

A deniable cryptosystem allows a sender and a receiver to communicate over an insecure channel in such a way that the communication is still secure even if the adversary can threaten the parties into revealing their internal states after the execution of the protocol. This is done by allowing the parties to change their internal state to make it look like a given ciphertext decrypts to a message different from what it really decrypts to. Deniable encryption was in this way introduced to allow to deny a message exchange and hence combat coercion. Depending on which parties can be coerced, the security level, the flavor and the number of rounds of the cryptosystem, it is possible to define a number of notions of deniable encryption. In this paper we prove that there does not exist any non-interactive receiver-deniable cryptosystem with better than polynomial security. This also shows that it is impossible to construct a non-interactive bi-deniable public-key encryption scheme with better than polynomial security. Specifically, we give an explicit bound relating the security of the scheme to how efficient the scheme is in terms of key size. Our impossibility result establishes a lower bound on the security. As a final contribution we give constructions of deniable public-key encryption schemes which establishes upper bounds on the security in terms of key length. There is a gap between our lower and upper bounds, which leaves the interesting open problem of finding the tight bounds.

Minimising Communication in Honest-Majority MPC by Batchwise Multiplication Verification.

Side-channel attacks allow the adversary to gain partial knowledge of the secret key when cryptographic protocols are implemented in real-world hardware. The goal of leakage resilient cryptography is to design cryptosystems that withstand such attacks. In the auxiliary input model, an adversary is allowed to see a computationally hard-to-invert function of the secret key. The auxiliary input model weakens the bounded leakage assumption commonly made in leakage resilient cryptography as the hard-to-invert function may information-theoretically reveal the entire secret key. In this work, we propose the first constructions of digital signature schemes that are secure in the auxiliary input model. Our main contribution is a digital signature scheme that is secure against chosen message attacks when given any exponentially hard-to-invert function of the secret key. As a second contribution, we construct a signature scheme that achieves security for random messages assuming that the adversary is given a polynomial-time hard-to-invert function (where both the challenge as well as the signatures seen prior to that are computed on random messages). Here, polynomial hardness is required even when given the entire public key. We further show that such signature schemes readily give us auxiliary input secure identification schemes.