Machine learning and statistical techniques are powerful tools for analyzing large amounts of medical and genomic data. On the other hand, ethical concerns and privacy regulations prevent free sharing of this data. Encryption techniques such as fully homomorphic encryption (FHE) enable evaluation over encrypted data. Using FHE, machine learning models such as deep learning, decision trees, and naive Bayes have been implemented for privacy-preserving applications using medical data. These applications include classifying encrypted data and training models on encrypted data. FHE has also been shown to enable secure genomic algorithms, such as paternity and ancestry testing and privacy-preserving applications of genome-wide association studies. This survey provides an overview of fully homomorphic encryption and its applications in medicine and bioinformatics. The high-level concepts behind FHE and its history are introduced and details on current open-source implementations are provided. The state of fully homomorphic encryption for privacy-preserving techniques in machine learning and bioinformatics is reviewed, along with descriptions of how these methods can be implemented in the encrypted domain. CCS Concepts: • Security and privacy → Cryptography; Usability in security and privacy; • Social and professional topics → Medical information policy.

Objective Given the long natural history of prostate cancer we assessed differing graphical formats for imparting knowledge about the longitudinal risks of prostate cancer recurrence with or without therapy. Methods Male volunteers without a history of prostate cancer were randomized to one of eight risk communication instruments that depicted the likelihood of prostate cancer returning or spreading over 1, 2, and 3 years. The tools differed in format (line, pie, bar, or pictograph) and whether the graph also included no numbers, 1 number (indicating the number of affected individuals) or 2 numbers (indicting both the number affected and the number unaffected). The main outcome variables evaluated were graphical preference and knowledge. Results A total of 420 men were recruited with respondents being least familiar and experienced with pictographs (p<0.0001) and only 10% preferred this particular format. Overall accuracy ranged from 79-92%, and when assessed across all graphical sub-types the addition of numerical information did not improve verbatim knowledge (p=0.1). Self-reported numeracy was a strong predictor of accuracy of responses ((OR=2.6, p=0.008), and the impact of high numeracy varied across graphical type having a greater impact upon line (OR= 5.1 95%CI [1.6,16],p=0.04) and pie charts (OR=7.1 95%CI [2.6,19],p=0.01) without an impact on pictographs (OR=0.4 95%CI [0.1,1.7], p=0.17) or bar charts (OR=0.5 95%CI [0.1,1.8], p=0.24). Conclusion For longitudinal presentation of risk, baseline numeracy was strongly prognostic for outcome. However, The addition of numbers to risk graphs only improved the delivery of verbatim knowledge for subjects with lower numeracy. Although subjects reported the least familiarity with pictographs they were one of the most effective means of transferring information regardless of numeracy.

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