Machine learning applications gain more and more access to highly sensitive information while simultaneously requiring more and more computation resources. Hence, the need for outsourcing these computational expensive tasks while still ensuring security and confidentiality of the data is imminent. In their seminal work, Tramer and Boneh presented the Slalom protocol for privacy-preserving inference by splitting the computation into a data-independent preprocessing phase and a very efficient online phase. In this work, we present a new method to significantly speed up the preprocessing phase by introducing the Carnival protocol. Carnival leverages the pseudo-randomness of the Subset sum problem to also enable efficient outsourcing during the preprocessing phase. In addition to a security proof we also include an empirical study analyzing the landscape of the uniformity of the output of the Subset sum function for smaller parameters. Our findings show that Carnival is a great candidate for real-world implementations.

Masking is a prominent strategy to protect cryptographic implementations against side-channel analysis. Its popularity arises from the exponential security gains that can be achieved for (approximately) quadratic resource utilization. Many variants of the countermeasure tailored for different optimization goals have been proposed. The common denominator among all of them is the implicit demand for robust and high entropy randomness. Simply assuming that uniformly distributed random bits are available, without taking the cost of their generation into account, leads to a poor understanding of the efficiency vs. security tradeoff of masked implementations. This is especially relevant in case of hardware masking schemes which are known to consume large amounts of random bits per cycle due to parallelism. Currently, there seems to be no consensus on how to most efficiently derive many pseudo-random bits per clock cycle from an initial seed and with properties suitable for masked hardware implementations. In this work, we evaluate a number of building blocks for this purpose and find that hardware-oriented stream ciphers like Trivium and its reduced-security variant Bivium B outperform most competitors when implemented in an unrolled fashion. Unrolled implementations of these primitives enable the flexible generation of many bits per cycle, which is crucial for satisfying the large randomness demands of state-of-the-art masking schemes. According to our analysis, only Linear Feedback Shift Registers (LFSRs), when also unrolled, are capable of producing long non-repetitive sequences of random-looking bits at a higher rate per cycle for the same or lower cost as Trivium and Bivium B. Yet, these instances do not provide black-box security as they generate only linear outputs. We experimentally demonstrate that using multiple output bits from an LFSR in the same masked implementation can violate probing security and even lead to harmful randomness cancellations. Circumventing these problems, and enabling an independent analysis of randomness generation and masking, requires the use of cryptographically stronger primitives like stream ciphers. As a result of our studies, we provide an evidence-based estimate for the cost of securely generating $n$ fresh random bits per cycle. Depending on the desired level of black-box security and operating frequency, this cost can be as low as $20n$ to $30n$ ASIC gate equivalents (GE) or $3n$ to $4n$ FPGA look-up tables (LUTs), where $n$ is the number of random bits required. Our results demonstrate that the cost per bit is (sometimes significantly) lower than estimated in previous works, incentivizing parallelism whenever exploitable. This provides further motivation to potentially move low randomness usage from a primary to a secondary design goal in hardware masking research.

A fundamental result dating to Ligero (Des. Codes Cryptogr. '23) establishes that each fixed linear block code exhibits proximity gaps with respect to the collection of affine subspaces, in the sense that each given subspace either resides entirely close to the code, or else contains only a small portion which resides close to the code. In particular, any given subspace's failure to reside entirely close to the code is necessarily witnessed, with high probability, by a uniformly randomly sampled element of that subspace. We investigate a variant of this phenomenon in which the witness is not sampled uniformly from the subspace, but rather from a much smaller subset of it. We show that a logarithmic number of random field elements (in the dimension of the subspace) suffice to effect an analogous proximity test, with moreover only a logarithmic (multiplicative) loss in the possible prevalence of false witnesses. We discuss applications to recent noninteractive proofs based on linear codes, including Brakedown (CRYPTO '23).