Efficient Multiparty Computations with Dishonest Minority

We consider verifiable secret sharing (VSS) and multiparty computation (MPC) in the secure channels model, where a broadcast channel is given and a non-zero error probability is allowed. In this model Rabin and Ben-Or proposed VSS and MPC protocols, secure against an adversary that can corrupt any minority of the players. In this paper, we rst observe that a subprotocol of theirs, known as weak secret sharing (WSS), is not secure against an adaptive adversary, contrary to what was believed earlier. We then propose new and adaptively secure protocols for WSS, VSS and MPC that are substantially more efficient than the original ones. Our protocols generalize easily to provide security against general Q2 adversaries

Information-Theoretically Secure Protocols and Security Under Composition

We investigate the question of whether security of protocols in the information-theoretic setting (where the adversary is computationally unbounded) implies the security of these protocols under concurrent composition. This question is motivated by the folklore that all known protocols that are secure in the information-theoretic setting are indeed secure under concurrent composition. We provide answers to this question for a number of different settings (i.e., considering perfect versus statistical security, and concurrent composition with adaptive versus fixed inputs). Our results enhance the understanding of what is necessary for obtaining security under composition, as well as providing tools (i.e., composition theorems) that can be used for proving the security of protocols under composition while considering only the standard stand-alone definitions of security

Secure Hashed Diffie-Hellman over Non-DDH Groups

We show that in applications that use the Diffie-Hellman (DH) transform but take care of hashing the DH output (as required, for example, for secure DH-based encryption and key exchange) the usual requirement to work over a DDH group (i.e., a group in which the Decisional Diffie-Hellman assumption holds) can be relaxed to only requiring that the DH group contains a large enough DDH subgroup. In particular, this implies the security of (hashed) Diffie-Hellman over non-prime order groups such as $Z_p^*$. Moreover, our results show that one can work directly over $Z_p^*$ without requiring any knowledge of the prime factorization of $p-1$ and without even having to find a generator of $Z_p^*$. These results are obtained via a general characterization of DDH groups in terms of their DDH subgroups, and a relaxation (called $t$-DDH) of the DDH assumption via computational entropy. We also show that, under the short-exponent discrete-log assumption, the security of the hashed Diffie-Hellman transform is preserved when replacing full exponents with short exponents

Okamoto-Tanaka Revisited: Fully Authenticated Diffie-Hellman with Minimal Overhead

Okamoto-Tanaka Revisited: Fully Authenticated Diffie-Hellman with Minimal Overhead The Diffie-Hellman protocol (DHP) is one of the most studied protocols in cryptography. Much work has been dedicated to armor the original protocol against active attacks while incurring a minimal performance overhead relative to the basic (unauthenticated) DHP. This line of work has resulted in some remarkable protocols, e.g., MQV, where the protocol\u27s communication cost is identical to that of the basic DHP and the computation overhead is small. Unfortunately, MQV and similar 2-message ``implicitly authenticated protocols do not achieve full security against active attacks since they cannot provide forward secrecy (PFS), a major security goal of DHP, against active attackers. In this paper we investigate the question of whether one can push the limits of authenticated DHPs even further, namely, to achieve communication complexity as in the original DHP (two messages with a single group element per message), maintain low computational overhead, and yet achieve full PFS against active attackers in a provable way. We answer this question in the affirmative by resorting to an old and elegant key agreement protocol: the Okamoto-Tanaka protocol \cite{okta}. We present a variant of the protocol (denoted mOT) which achieves the above minimal communication, incurs a computational overhead relative to the basic DHP that is practically negligible, and yet achieves full provable key agreement security, including PFS, against active attackers. Moreover, due to the identity-based properties of mOT, even the sending of certificates (typical for authenticated DHPs) can be avoided in the protocol. As additional contributions, we apply our analysis to prove the security of a recent multi-domain extension of the Okamoto-Tanaka protocol by Schridde et al. and show how to adapt mOT to the (non id-based) certificate-based setting

Proactive Secret Sharing with Constant Communication

This paper presents the first protocols for Proactive Secret Sharing (PSS) that only require constant (in the number of parties, $n$) communication per party per epoch. By harnessing the power of expander graphs, we are able to obtain strong guarantees about the security of the system. We present the following PSS protocols: – A PSS protocol that provides privacy (but no robustness) against an adversary controlling $O(n)$ parties per epoch. – A PSS protocol that provides robustness (but no privacy) against an adversary controlling $O(n)$ parties per epoch. – A PSS protocol that provides privacy against an adversary controlling $O(n^{a})$ parties per epoch and provides robustness against an adversary controlling $O(n^{1−a})$ parties per epoch, for any constant $0 \leq a \leq 1$. Instantiating this with $a = \frac{1}{2}$ gives a PSS protocol that is proactively secure (private and robust) against an adversary controlling $O(\sqrt{n})$ parties per epoch. Additionally, we discuss how secure channels, whose existence is usually assumed by PSS protocols, are challenging to create in the mobile adversary setting, and we present a method to instantiate them from a weaker assumption

Additive Randomized Encodings and Their Applications

Addition of $n$ inputs is often the easiest nontrivial function to compute securely. Motivated by several open questions, we ask what can be computed securely given only an oracle that computes the sum. Namely, what functions can be computed in a model where parties can only encode their input locally, then sum up the encodings over some Abelian group \G, and decode the result to get the function output. An *additive randomized encoding* (ARE) of a function $f(x_1,\ldots,x_n)$ maps every input $x_i$ independently into a randomized encoding $\hat x_i$, such that $\sum_{i=1}^n$ $\hat x_i$ reveals $f(x_1,\ldots,x_n)$ and nothing else about the inputs. In a *robust* ARE, the sum of any subset of the $\hat x_i$ only reveals the residual function obtained by restricting the corresponding inputs. We obtain positive and negative results on ARE. In particular: * Information-theoretic ARE. We fully characterize the 2-party functions $f:X_1\times X_2\to\{0,1\}$ admitting a perfectly secure ARE. For $n\ge 3$ parties, we show a useful ``capped sum\u27\u27 function that separates statistical security from perfect security. * Computational ARE. We present a general feasibility result, showing that *all functions* can be computed in this model, under a standard hardness assumption in bilinear groups. We also describe a heuristic lattice-based construction. * Robust ARE. We present a similar feasibility result for {\em robust} computational ARE based on ideal obfuscation along with standard cryptographic assumptions. We then describe several applications of ARE and the above results. * Under a standard cryptographic assumption, our computational ARE schemes imply the feasibility of general non-interactive secure computation in the shuffle model, where messages from different parties are shuffled. This implies a general utility-preserving compiler from differential privacy in the central model to computational differential privacy in the (non-robust) shuffle model. * The existence of information-theoretic {\em robust} ARE implies best-possible information-theoretic MPC protocols (Halevi et al., TCC 2018) and degree-2 multiparty randomized encodings (Applebaum et al., TCC 2018). This yields new positive results for specific functions in the former model, as well as a simple unifying barrier for obtaining negative results in both models

Incremental Offline/Online PIR (extended version)

Recent private information retrieval (PIR) schemes preprocess the database with a query-independent offline phase in order to achieve sublinear computation during a query-specific online phase. These offline/online protocols expand the set of applications that can profitably use PIR, but they make a critical assumption: that the database is immutable. In the presence of changes such as additions, deletions, or updates, existing schemes must preprocess the database from scratch, wasting prior effort. To address this, we introduce incremental preprocessing for offline/online PIR schemes, allowing the original preprocessing to continue to be used after database changes, while incurring an update cost proportional to the number of changes rather than the size of the database. We adapt two offline/online PIR schemes to use incremental preprocessing and show how it significantly improves the throughput and reduces the latency of applications where the database changes over time