Fig. 1

The traditional and homomorphic SNP detection scheme. In this figure, \(\mathcal {E}(\cdot)\) and \(\mathcal {D}(\cdot)\) denote encryption and decryption respectively. Encryption needs public key while decryption needs private key. The subscript refers to the owner of the private key. For example, \(\mathcal {E}_{hos} (\cdot)\) means the data is encrypted with hospital’s public key thus only the hospital can decrypt it. a demonstrates traditional way of detecting SNP. ① The patient gives the hospital the raw sequence. In order to protect data from being stolen in the middle, the sequence is encrypted using the hospital’s public key. ② The hospital decrypts patient sequence and performs computation to detect SNP. ③ The hospital returns the SNP existence information encrypted with the patient’s public key to the patient. ④ The patient can decrypt and get the SNP information. b on the other hand, demonstrates the same SNP detection scheme in homomorphic way. ① The patient sends one’s encrypted raw sequence but this time with the public key. ② Due to its homomorphic property, the hospital can perform computations on the sequence only with the public key, without decrypting the sequence. ③ The result is acquired in encrypted form, and the hospital returns the result to patient not knowing its content. ④ The patient can decrypt the result in secure environment