Lossy encryption was originally studied as a means of achieving efficient and composable oblivious transfer. Bellare, Hofheinz and Yilek showed that lossy encryption is also selective opening secure. We present new and general constructions of lossy encryption schemes and of cryptosystems secure against selective opening adversaries.We show that every re-randomizable encryption scheme gives rise to efficient encryptions secure against a selective opening adversary. We show that statistically-hiding 2-round Oblivious Transfer implies Lossy Encryption and so do smooth hash proof systems. This shows that private information retrieval and homomorphic encryption both imply Lossy Encryption, and thus Selective Opening Secure Public Key Encryption.Applying our constructions to well-known cryptosystems, we obtain selective opening secure commitments and encryptions from the Decisional Diffie-Hellman, Decisional Composite Residuosity and Quadratic Residuosity assumptions.In an indistinguishability-based model of chosen-ciphertext selective opening security, we obtain secure schemes featuring short ciphertexts under standard number theoretic assumptions. In a simulation-based definition of chosen-ciphertext selective opening security, we also handle non-adaptive adversaries by adapting the Naor-Yung paradigm and using the perfect zeroknowledge proofs of Groth, Ostrovsky and Sahai.

Secure multi-party computation (MPC) allows a group of mutually distrustful parties to compute a joint function on their inputs without revealing any information beyond the result of the computation. This type of computation is extremely powerful and has wide-ranging applications in academia, industry, and government. Protocols for secure computation have existed for decades, but only recently have general-purpose compilers for executing MPC on arbitrary functions been developed. These projects rapidly improved the state of the art, and began to make MPC accessible to non-expert users. However, the field is changing so rapidly that it is difficult even for experts to keep track of the varied capabilities of modern frameworks.In this work, we survey general-purpose compilers for secure multi-party computation. These tools provide high-level abstractions to describe arbitrary functions and execute secure computation protocols. We consider eleven systems: EMP-toolkit, Obliv-C, ObliVM, TinyGarble, SCALE-MAMBA (formerly SPDZ), Wysteria, Sharemind, PICCO, ABY, Frigate and CBMC-GC. We evaluate these systems on a range of criteria, including language expressibility, capabilities of the cryptographic back-end, and accessibility to developers. We advocate for improved documentation of MPC frameworks, standardization within the community, and make recommendations for future directions in compiler development. Installing and running these systems can be challenging, and for each system, we also provide a complete virtual environment (Docker container) with all the necessary dependencies to run the compiler and our example programs.

Abstract. The primary goal of compressed sensing and (non-adaptive) combinatorial group testing is to recover a sparse vector x from an underdetermined set of linear equations Φx = y. Both problems entail solving Φx = y given Φ and y but they use different models of arithmetic, different models of randomness models for Φ, and different guarantees upon the solution x and the class of signals from which it is drawn. In [32], Lipton introduced a model for error correction where the channel is computationally bounded, subject to standard cryptographic assumptions, and produces the error vector x that must be found and then corrected. This has been extended in [24, 34] to create more efficient schemes against polynomial and logspace bounded channels. Inspired by these results in error correction, we view compressed sensing and combinatorial group testing as an adversarial process, where Mallory the adversary produces the vector x to be measured, with limited information about the matrix Φ. We define a number of computationally bounded models for Mallory and show that there are significant gains (in the minimum number of measurements) to be had by relaxing the model from adversarial to computationally or information-theoretically bounded, and not too much (in some cases, nothing at all) is lost by assuming these models over oblivious or statistical models. We also show that differences in adversarial power give rise to different lower bounds for the number of measurements required to defeat such an adversary. By contrast we show that randomized one pass log space streaming Mallory is almost as powerful as a fully adversarial one for group testing while for compressed sensing such an adversary as weak as an oblivious one.

In this work, we give the first construction of high-rate locally list-recoverable codes. Listrecovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving globally list-decodable codes with nearly linear time list decoding algorithm (once more, over constant-sized alphabet); and a randomized construction of binary codes on the Gilbert-Varshamov bound that can be uniquely decoded in near-linear-time, with higher rate than was previously known.Our techniques are actually quite simple, and are inspired by an approach of Gopalan, Guruswami, and Raghavendra (Siam Journal on Computing, 2011) for list-decoding tensor codes. We show that tensor powers of (globally) list-recoverable codes are 'approximately' locally list-recoverable, and that the 'approximately' modifier may be removed by pre-encoding the message with a suitable locally decodable code. Instantiating this with known constructions of high-rate globally list-recoverable codes and high-rate locally decodable codes finishes the construction.

Abstract. Determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse.In the American Economic Review, Elliott, Golub and Jackson proposed a simple model for capturing the dynamics of complex financial networks. In Elliott, Golub and Jackson's model, the institutions in the network are connected by linear dependencies (cross-holdings) and if any institution's value drops below a critical threshold, its value suffers an additional failure cost. This work shows that even in this simple model there are fundamental barriers to understanding the risks that are inherent in a network.First, if institutions are not required to maintain a minimum amount of self-holdings, any change in investments by a single institution can have an arbitrarily magnified influence on the net worth of the institutions in the system. This implies that if institutions have small self-holdings, then estimating the market value of an institution requires almost perfect information about every cross-holding in the system. Second, even if a regulator has complete information about all cross-holdings in the system, it may be computationally intractable to estimate the number of failures that could be caused by a small shock to the system.