Today, genome sequencing is more accessible and affordable than ever. It is also possible for individuals to share their genomic data with service providers or on public websites. Although genomic data has significant impact and widespread usage on medical research, it puts individuals' privacy in danger, even if they anonymously or partially share their genomic data. In this work, first, we improve the existing work on inference attack on genomic privacy using observable Markov model, recombination model between the haplotypes, kinship relations, and phenotypic traits. Then to address this privacy concern, we present a differential privacy-based framework for sharing individuals' genomic data while preserving their privacy. Different from existing differential privacy-based solutions for genomic data (which consider privacy-preserving release of summary statistics), we focus on privacy-preserving sharing of actual genomic data. We assume an individual with some sensitive portion on his genome (e.g., mutations or single nucleotide polymorphisms - SNPs that reveal sensitive information about the individual). The goals of the individual are to (i) preserve the privacy of his sensitive data, (ii) preserve the privacy of interdependent data (data that belongs to other individuals that is correlated with his data), and (iii) share as much data as possible to maximize utility of data sharing. As opposed to traditional differential privacy-based data sharing schemes, the proposed scheme does not intentionally add noise to data; it is based on selective sharing of data points. Previous studies show that hiding the sensitive SNPs while sharing the others does not preserve individual's (or other interdependent peoples') privacy. By exploiting auxiliary information, an attacker can run e cient inference attacks and infer the sensitive SNPs of individuals. In this work, we also utilize such inference attacks, which we discuss in details first, in our differential privacy-based data sharing framework and propose a SNP sharing platform for individuals that provides differential privacy guarantees. We show that the proposed framework

does not provide sensitive information to the attacker while it provides a high data sharing utility. Through experiments on real data, we extensively study the relationship between utility and several parameters that effect privacy. We also compare the proposed technique with the previous ones and show our advantage both in terms of privacy and data sharing utility.