Breaking data barriers with homomorphic encryption: The HEGS platform for secure joint genomic selection in animal breeding

• Encrypted Numerical Fidelity: We encrypt phenotypes and genotypes using orthogonal-matrix transformations, solving mixed-model equations in the encrypted domain with identical results to plaintext analyses (correlation=1.0). • Methodological Generalization: HEGS supports BLUP, GBLUP, and ssGBLUP within a unified framework using secure factorization and recombination of A and H relationship matrices. • Platform and Data Resources: We provide a dual-mode platform (web/local) with encryption scripts and 180 pre-encrypted datasets from five populations across 36 traits. Synthetic population evaluations show significant improvements in small populations. Genomic selection (GS) is one of the most effective approaches for accelerating genetic improvement in animals and plants, but its efficiency largely depends on the size of the training population. However, establishing a large training population is often time-consuming and costly. An alternative strategy is to combine multiple populations distributed across different breeding farms or companies for joint GS, but this is greatly constrained by data-security concerns and the lack of a public platform for secure collaborative analysis. In this study, we developed HEGS (Homomorphic Encryption Genomic Selection), an open-source platform for privacy-preserving joint GS across institutions, which is in principle applicable to diploid species. HEGS uses homomorphic encryption to perform genomic analyses directly on encrypted data without revealing raw information, and extends the encrypted analysis framework from the initial genomic best linear unbiased prediction (GBLUP) model to include both conventional best linear unbiased prediction (BLUP) and single-step GBLUP (ssGBLUP), thereby broadening its applicability in breeding evaluation. To demonstrate the utility of the platform, we constructed a large encrypted pig dataset comprising four breeds (Duroc, Yorkshire, Landrace, and Pietrain), 36 economically important traits, 180 pre-encrypted datasets, and more than 580,000 phenotypic records, enabling immediate joint analyses without exposing raw data. Using both simulated and real datasets, we demonstrated the feasibility and effectiveness of GS under homomorphic encryption. After model fitting, HEGS outputs genomic estimated breeding values (GEBVs) for genotyped candidates without phenotypic records, facilitating selection without additional phenotyping. Overall, HEGS provides a deployable and scalable open-source solution for privacy-preserving cross-institutional collaboration in animal breeding.