Research on the privacy of human genomic data has significantly increased these last years to find out effective solutions to protect the most critical information resulting from an alignment operation such as the genomic position, cigar and Read content. In this paper, the authors propose an encoding technique based on homomorphic encryption to protect genomic positions of DNA sequences for a secure storage of BAM file. This technique uses two Discrete Gaussian Sampling algorithms for comparison purposes which is Gauss and Knuth-Yao algorithm. The framework was implemented on Java from scratch using container data structure with standard java HashMap for the representation of duplicates positions elements exiting in BAM file. The proposed method was assessed on the NA12878 dataset with initially 2 million positions to encrypt. Obtained results show that the FV-Knuth-Yao technique with HashMap architecture storing 165667 positions and a polynomial degree equal to 64 ensures a fast encryption time estimated to 6,5 minutes. The decryption operation needs 1 hour with zero loss of information. The acceptable security level reached 2 64 operations to break the cryptosystem. To demonstrate the efficiency, security and reliability of our approach, the FV-Knuth-Yao was compared with the OPE Method as implemented in SECRAM tool which is based on a deterministic encryption scheme. Our work mainly focuses on the security of genomic data without compression of BAM file.