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Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance. In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from either the subgroup decision assumption in composite-order groups or from the $k$-Lin assumption in prime-order groups for any $k \ge 1$). Previously, batch arguments for NP were only known from LWE, or a combination of multiple assumptions, or from non-standard/non-falsifiable assumptions. Moreover, our work introduces a new direct approach for batch verification and avoids heavy tools like correlation-intractable hash functions or probabilistically-checkable proofs common to previous approaches. As corollaries to our main construction, we obtain the first publicly-verifiable non-interactive delegation scheme for RAM programs (i.e., a succinct non-interactive argument (SNARG) for P) with a CRS of sublinear size (in the running time of the RAM program), as well as the first aggregate signature scheme (supporting bounded aggregation) from standard assumptions on bilinear maps.

We introduce the Spiral family of single-server private information retrieval (PIR) protocols. Spiral relies on a composition of two lattice-based homomorphic encryption schemes: the Regev encryption scheme and the Gentry-Sahai-Waters encryption scheme. We introduce new ciphertext translation techniques to convert between these two schemes and in doing so, enable new trade-offs in communication and computation. Across a broad range of database configurations, the basic version of Spiral simultaneously achieves at least a 4.5x reduction in query size, 1.5x reduction in response size, and 2x increase in server throughput compared to previous systems. A variant of our scheme, SpiralStreamPack, is optimized for the streaming setting and achieves a server throughput of 1.9 GB/s for databases with over a million records (compared to 200 MB/s for previous protocols) and a rate of 0.81 (compared to 0.24 for previous protocols). For streaming large records (e.g., a private video stream), we estimate the monetary cost of SpiralStreamPack to be only 1.9x greater than that of the no-privacy baseline where the client directly downloads the desired record.

The main goal of traceable cryptography is to protect against unauthorized redistribution of cryptographic functionalities. Such schemes provide a way to embed identities (i.e., a “mark”) within cryptographic objects (e.g., decryption keys in an encryption scheme, signing keys in a signature scheme). In turn, the tracing guarantee ensures that any “pirate device” that successfully replicates the underlying functionality can be successfully traced to the set of identities used to build the device. In this work, we study traceable pseudorandom functions (PRFs). As PRFs are the workhorses of symmetric cryptography, traceable PRFs are useful for augmenting symmetric cryptographic primitives with strong traceable security guarantees. However, existing constructions of traceable PRFs either rely on strong notions like indistinguishability obfuscation or satisfy weak security guarantees like single-key security (i.e., tracing only works against adversaries that possess a single marked key). In this work, we show how to use fingerprinting codes to upgrade a single-key traceable PRF into a fully collusion resistant traceable PRF, where security holds regardless of how many keys the adversary possesses. We additionally introduce a stronger notion of security where tracing security holds even against active adversaries that have oracle access to the tracing algorithm. In conjunction with known constructionsmore »of single-key traceable PRFs, we obtain the first fully collusion resistant traceable PRF from standard lattice assumptions. Our traceable PRFs directly imply new lattice-based secret-key traitor tracing schemes that are CCA-secure and where tracing security holds against active adversaries that have access to the tracing oracle.« less

Software watermarking schemes allow a user to embed an identifier into a piece of code such that the resulting program is nearly functionally-equivalent to the original program, and yet, it is difficult to remove the identifier without destroying the functionality of the program. Such schemes are often considered for proving software ownership or for digital rights management. Existing constructions of watermarking have focused primarily on watermarking pseudorandom functions (PRFs). In this work, we revisit the definitional foundations of watermarking, and begin by highlighting a major flaw in existing security notions. Existing security notions for watermarking only require that the identifier be successfully extracted from programs that preserve the exact input/output behavior of the original program. In the context of PRFs, this means that an adversary that constructs a program which computes a quarter of the output bits of the PRF or that is able to distinguish the outputs of the PRF from random are considered to be outside the threat model. However, in any application (e.g., watermarking a decryption device or an authentication token) that relies on PRF security, an adversary that manages to predict a quarter of the bits or distinguishes the PRF outputs from random would be consideredmore »to have defeated the scheme. Thus, existing watermarking schemes provide very little security guarantee against realistic adversaries. None of the existing constructions of watermarkable PRFs would be able to extract the identifier from a program that only outputs a quarter of the bits of the PRF or one that perfectly distinguishes. To address the shortcomings in existing watermarkable PRF definitions, we introduce a new primitive called a traceable PRF. Our definitions are inspired by similar definitions from public-key traitor tracing, and aim to capture a very robust set of adversaries: namely, any adversary that produces a useful distinguisher (i.e., a program that can break PRF security), can be traced to a specific identifier. We provide a general framework for constructing traceable PRFs via an intermediate primitive called private linear constrained PRFs. Finally, we show how to construct traceable PRFs from a similar set of assumptions previously used to realize software watermarking. Namely, we obtain a single-key traceable PRF from standard lattice assumptions and a fully collusion-resistant traceable PRF from indistinguishability obfuscation (together with injective one-way functions).« less

Zero-knowledge succinct arguments of knowledge (zkSNARKs) enable efficient privacy-preserving proofs of membership for general NP languages. Our focus in this work is on post-quantum zkSNARKs, with a focus on minimizing proof size. Currently, there is a 1000x gap in the proof size between the best pre-quantum constructions and the best post-quantum ones. Here, we develop and implement new lattice-based zkSNARKs in the designated-verifier preprocessing model. With our construction, after an initial preprocessing step, a proof for an NP relation of size 2^20 is just over 16 KB. Our proofs are 10.3x shorter than previous post-quantum zkSNARKs for general NP languages. Compared to previous lattice-based zkSNARKs (also in the designated-verifier preprocessing model), we obtain a 42x reduction in proof size and a 60x reduction in the prover's running time, all while achieving a much higher level of soundness. Compared to the shortest pre-quantum zkSNARKs by Groth (Eurocrypt 2016), the proof size in our lattice-based construction is 131x longer, but both the prover and the verifier are faster (by 1.2x and 2.8x, respectively). Our construction follows the general blueprint of Bitansky et al. (TCC 2013) and Boneh et al. (Eurocrypt 2017) of combining a linear probabilistically checkable proof (linear PCP) together withmore »a linear-only vector encryption scheme. We develop a concretely-efficient lattice-based instantiation of this compiler by considering quadratic extension fields of moderate characteristic and using linear-only vector encryption over rank-2 module lattices.« less

We introduce CryptGPU, a system for privacy-preserving machine learning that implements all operations on the GPU (graphics processing unit). Just as GPUs played a pivotal role in the success of modern deep learning, they are also essential for realizing scalable privacy-preserving deep learning. In this work, we start by introducing a new interface to losslessly embed cryptographic operations over secret-shared values (in a discrete domain) into floating-point operations that can be processed by highly-optimized CUDA kernels for linear algebra. We then identify a sequence of “GPU-friendly” cryptographic protocols to enable privacy-preserving evaluation of both linear and non-linear operations on the GPU. Our microbenchmarks indicate that our private GPU-based convolution protocol is over 150x faster than the analogous CPU-based protocol; for non-linear operations like the ReLU activation function, our GPU-based protocol is around 10x faster than its CPU analog. With CryptGPU, we support private inference and private training on convolutional neural networks with over 60 million parameters as well as handle large datasets like ImageNet. Compared to the previous state-of-the-art, when considering large models and datasets, our protocols achieve a 2x to 8x improvement in private inference and a 6x to 36x improvement for private training. Our work not only showcasesmore »the viability of performing secure multiparty computation (MPC) entirely on the GPU to enable fast privacy-preserving machine learning, but also highlights the importance of designing new MPC primitives that can take full advantage of the GPU's computing capabilities.« less