Encryption system, encryption method, and computer readable medium

An encryption method comprising:

• generating a ciphertext by double encrypting a plaintext using a first internal public key and a first external public key;
• generating a randomized internal secret key by randomizing a first internal secret key using a second random number, generating a second encrypted random number by encrypting the second random number using a second internal public key, generating a randomized external secret key by randomizing a first external secret key using a first random number, and generating a first encrypted random number by encrypting the first random number using a second external public key;
• obtaining a randomized decryption text by decrypting the ciphertext using the randomized external secret key and the randomized internal secret key, and generating a re-encrypted text by encrypting the randomized decryption text using the second internal public key and the second external public key;
• and
• decrypting the second random number from the second encrypted random number using the second internal secret key, decrypting the first random number from the first encrypted random number using the second external secret key, decrypting the randomized decryption text from the re-encrypted text using the second external secret key and the second internal secret key, and calculating the plaintext using the randomized decryption text, the second random number, and the first random number.

A non-transitory computer readable medium storing an encryption program comprising:

• an encrypting program for causing a computer to execute an encrypting process to generate a ciphertext by double encrypting a plaintext using a first internal public key and a first external public key;
• a re-encryption key generation program for causing a computer to execute a re-encryption key generation process to generate a randomized internal secret key by randomizing a first internal secret key using a second random number, to generate a second encrypted random number by encrypting the second random number using a second internal public key, to generate a randomized external secret key by randomizing a first external secret key using a first random number, and to generate a first encrypted random number by encrypting the first random number using a second external public key;
• a re-encrypting program for causing a computer to execute a re-encrypting process to obtain a randomized decryption text by decrypting the ciphertext using the randomized external secret key and the randomized internal secret key, and to generate a re-encrypted text by encrypting the randomized decryption text using the second internal public key and the second external public key;
• and
• a decryption program for causing a computer to execute a decryption process to decrypt the second random number from the second encrypted random number using the second internal secret key, to decrypt the first random number from the first encrypted random number using the second external secret key, to decrypt the randomized decryption text from the re-encrypted text using the second external secret key and the second internal secret key, and to calculate the plaintext using the randomized decryption text, the second random number, and the first random number.