International Association
for Cryptologic Research

We present a new template for building oblivious transfer from quantum information that we call the "fixed basis'' framework. Our framework departs from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the *correct* choice of measurement basis used by each player, except for some hidden *trap* qubits that are intentionally measured in a conjugate basis. We instantiate this template in the quantum random oracle model (QROM) to obtain simple protocols that implement, with security against malicious adversaries: 1. *Non-interactive* random-input bit OT in a model where parties share EPR pairs a priori. 2. Two-round random-input bit OT without setup, obtained by showing that the protocol above remains secure even if the (potentially malicious) OT receiver sets up the EPR pairs. 3. Three-round chosen-input string OT from BB84 states without entanglement or setup. This improves upon natural variations of the CK88 template that require at least five rounds. Along the way, we develop technical tools that may be of independent interest. We prove that natural functions like XOR enable *seedless* randomness extraction from certain quantum sources of entropy. We also use idealized (i.e. extractable and equivocal) bit commitments, which we obtain by proving security of simple and efficient constructions in the QROM.

We put forth a new paradigm for program obfuscation, where obfuscated programs are endowed with proofs of ``well formedness.'' In addition to asserting existence of an underlying plaintext program with an attested structure, these proofs also prevent mauling attacks, whereby an adversary surreptitiously creates an obfuscated program based on secrets which are embedded in other obfuscated programs. We call this new guarantee Chosen Obfuscation Attacks (COA) security. We show how to enhance a large class of obfuscation mechanisms to be COA-secure, assuming subexponentially secure IO for circuits and subexponentially secure one-way functions.To demonstrate the power of the new notion, we also use it to realize: - A new form of software watermarking, which provides significantly broader protection than current schemes against counterfeits that pass a keyless, public verification process. - Completely CCA encryption, which is a strengthening of completely non-malleable encryption.

Recently Boyle et al. (TCC 2019) proposed a new approach for secure computation in the {\em preprocessing model} building on {\em function secret sharing} (FSS). This approach can be used to realize any circuit containing gates that admit efficient FSS schemes. In this work, we make the following three technical contributions: {\bf Improved Key Size.} The complexity of the preprocessing phase directly depends on the FSS key size. We improve the size of FSS keys for several existing FSS constructions through two important steps. First, we present a roughly $4\times$ reduction in FSS key size for the Distributed Comparison Function (DCF), i.e. ($f_\alpha(x) = \beta$ for all $x < \alpha$ and $0$, otherwise). Second, prior FSS schemes for many important function classes are obtained via reductions to multiple instances of DCF; for example, 2 instances for interval containment and $2m$ for splines with $m$ pieces. We significantly improve these reductions for public intervals and obtain {\em optimal} FSS schemes, i.e., through a {\em single instance of DCF}, thereby reducing the key sizes by up to $6-22\times$ for commonly used functions in mixed-mode secure computation such as ReLU and sigmoid. {\bf FSS for New Function Families.} We present the first constructions of FSS schemes for arithmetic and logical right shift, as well as for bit-decomposition, where the output bits must be secret shared in a larger ring. These functions are crucial for many applications such as fixed-point arithmetic and machine learning. {\bf FSS for Fixed-Point Arithmetic and Barrier.} One of the important functions in the realization of secure fixed-point arithmetic is that of multiply-then-truncate. While our work shows how to obtain a construction for this function in 2 rounds using sequential calls to FSS schemes for multiply and shift, we demonstrate a barrier towards improving this via FSS beyond what we achieve. Specifically, we show that a 1-round solution would require settling a major open problem in the area of FSS: namely, building an FSS for the class of bit-conjunction functions based on only symmetric-key cryptographic assumptions.