EPOC: Efficient Probabilistic Public-Key Encryption (Submission to P1363a)

We describe a novel public-key cryptosystem, EPOC (Efficient Probabilistic Public-Key Encryption), which has two versions: EPOC-1 and EPOC-2. EPOC-1 is a public-key encryption system that uses a one-way trapdoor function and a random function (hash function). EPOC-2 is a public-key encryption system that uses a one-way trapdoor function, two random functions (hash functions) and a symmetric-key encryption (e.g., one-time padding and block-ciphers). EPOC has several outstanding properties as follows: 1. EPOC-1 is semantically secure or non-malleable against chosen ciphertext attacks (IND-CCA2 or NM-CCA2) in the random oracle model under the p-subgroup assumption, which is comparable to the quadratic residue and higher degree residue assumptions. 2. EPOC-2 with one-time padding is semantically secure or non-malleable against chosen ciphertext attacks (IND-CCA2 or NM-CCA2) in the random oracle model under the factoring assumption. 3. EPOC-2 with symmetric encryption is semantically secure or non-malleable against chosen ciphertext attacks (IND-CCA2 or NM-CCA2) in the random oracle model under the factoring assumption, if the underlying symmetric encryption is secure against passive attacks. 4. The trapdoor technique with EPOC is fundamentally different from any other previous scheme including RSA-Rabin and Diffie-Hellman-ElGamal. 5. Under the most practical environment in which public-key cryptosystems would be used, the encryption and decryption speeds of EPOC are comparable (several times slower) to those of elliptic curve cryptosystems. Compared with OAEP (RSA) with small e (e.g.,2 + 1), although the encryption speed of EPOC is slower than that of OAEP, the decryption speed is faster than that of OAEP. The encryption scheme described in this contribution is obtained by combining three results: one [25] on the trapdoor function technique is by Okamoto and Uchiyama, and the others [13, 14] on conversion techniques using random functions are by Fujisaki and Okamoto.