The recent advances in genome sequencing technologies provide unprecedented opportunities to understand the relationship between human genetic variation and diseases. However, genotyping whole genomes from a large cohort of individuals is still cost prohibitive. Imputation methods to predict genotypes of missing genetic variants are widely used, especially for genome-wide association studies. Accurate genotype imputation requires complex statistical methods. Due to the data and computingintensive nature of the problem, imputation is increasingly outsourced, raising serious privacy concerns. In this work, we investigate solutions for fast, scalable, and accurate privacy-preserving genotype imputation using Machine Learning (ML) and a standardized homomorphic encryption scheme, Paillier cryptosystem. ML-based privacy-preserving inference has been largely optimized for computation-heavy non-linear functions in a single-output multi-class classification setting. However, having a large number of multiclass outputs per genome per individual calls for further optimizations and/or approximations specific to this application. Here we explore the effectiveness of linear models for genotype imputation to convert them to privacy-preserving equivalents using standardized homomorphic encryption schemes. Our results show that performance of our privacy-preserving genotype imputation method is equivalent to the state-of-theart plaintext solutions, achieving up to 99% micro area under curve score, even on real-world large-scale datasets upto 80,000 targets.INDEX TERMS Genotype imputation, machine learning, privacy-preserving computation.

The rapid expansion and increased popularity of cloud computing comes with no shortage of privacy concerns about outsourcing computation to semi-trusted parties. Leveraging the power of encryption, in this paper we introduce Cryptoleq: an abstract machine based on the concept of One Instruction Set Computer, capable of performing general-purpose computation on encrypted programs. The program operands are protected using the Paillier partially homomorphic cryptosystem, which supports addition on the encrypted domain. Full homomorphism over addition and multiplication, which is necessary for enabling general-purpose computation, is achieved by inventing a heuristically obfuscated software re-encryption module written using Cryptoleq instructions and blended into the executing program. Cryptoleq is heterogeneous, allowing mixing encrypted and unencrypted instruction operands in the same program memory space. Programming with Cryptoleq is facilitated using an enhanced assembly language that allows development of any advanced algorithm on encrypted datasets. In our evaluation, we compare Cryptoleq's performance against a popular fully homomorphic encryption library, and demonstrate correctness using a typical Private Information Retrieval problem.

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A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming language. The interesting point is that the computation can be done without logic operations such as AND or OR. The compiler and emulator of this language with sample programs are available on the Internet.

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