Genomics has profoundly influenced the field of medicine, with advancements in DNA sequencing contributing to personalized medicine and a more comprehensive understanding of various diseases' genomic underpinnings. Sharing genomic data is vital for progressing the field and devising novel approaches to decipher the genome. Nevertheless, the sensitive nature of this information necessitates robust security measures for protection during storage and transfer. In this paper, we introduce SecureFASTA, a novel tool for securely encrypting and decrypting FASTA files without requiring a shared secret while minimizing the number of keys exchanged between pairs. Our approach combines symmetric and asymmetric encryption techniques, utilizing the Advanced Encryption Standard (AES) cypher and Rivest-Shamir-Adleman (RSA) encryption. Additionally, we implement a checksum function using the Secure Hash Algorithm (SHA-256) to verify the integrity of transferred FASTA files. Our evaluation demonstrates that SecureFASTA is fast, reliable, and secure, surpassing existing tools in terms of security and user-friendliness. Consequently, it offers a valuable solution for securely sharing and leveraging sensitive genomic data, marking a significant breakthrough in genomics. The tool's source code is available at https://github.com/bioinformatics-ua/SecureFASTA.