We describe an elliptic curve encryption scheme, PSEC (provably secure elliptic curve encryption scheme), which has two versions: PSEC-1 and PSEC-2. PSEC-1 is a public-key encryption system that uses the elliptic curve ElGamal trapdoor function and a random function (hash function). PSEC-2 is a public-key encryption system that uses the elliptic curve ElGamal trapdoor function, two random functions (hash functions) and a symmetrickey encryption (e.g., one-time padding and block-ciphers). PSEC has several outstanding properties as follows: 1. PSEC-1 is semantically secure or non-malleable against chosen ciphertext attacks (INDCCA2 or NM-CCA2) in the random oracle model under the elliptic curve decision Diffie-Hellman (EC-DDH) assumption. 2. PSEC-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 elliptic curve Diffie-Hellman (EC-DH) assumption. 3. PSEC-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 elliptic curve Diffie-Hellman (EC-DH) assumption, if the underlying symmetric encryption is secure against passive attacks. 4. If the underlying random function is replaced by a practical random like function (e.g., SHA and MD5), PSEC is almost as efficient as the elliptic curve ElGamal scheme, and is almost three times as efficient as the elliptic curve Cramer-Shoup scheme. The encryption scheme described in this contribution is obtained by using two results on conversion techniques using random functions [10, 11].
[1]
Cynthia Dwork,et al.
A public-key cryptosystem with worst-case/average-case equivalence
,
1997,
STOC '97.
[2]
Mihir Bellare,et al.
Optimal Asymmetric Encryption
,
1994,
EUROCRYPT.
[3]
Mihir Bellare,et al.
DHAES: An Encryption Scheme Based on the Diffie-Hellman Problem
,
1999,
IACR Cryptol. ePrint Arch..
[4]
Adi Shamir,et al.
A method for obtaining digital signatures and public-key cryptosystems
,
1978,
CACM.
[5]
N. Koblitz.
Elliptic curve cryptosystems
,
1987
.
[6]
Moni Naor,et al.
Non-malleable cryptography
,
1991,
STOC '91.
[7]
Taher El Gamal.
A public key cryptosystem and a signature scheme based on discrete logarithms
,
1984,
IEEE Trans. Inf. Theory.
[8]
Mihir Bellare,et al.
Relations among Notions of Security for Public-Key Encryption Schemes
,
1998,
IACR Cryptol. ePrint Arch..
[9]
Mihir Bellare,et al.
Random oracles are practical: a paradigm for designing efficient protocols
,
1993,
CCS '93.
[10]
Martin E. Hellman,et al.
Hiding information and signatures in trapdoor knapsacks
,
1978,
IEEE Trans. Inf. Theory.
[11]
Whitfield Diffie,et al.
New Directions in Cryptography
,
1976,
IEEE Trans. Inf. Theory.
[12]
Tatsuaki Okamoto,et al.
How to Enhance the Security of Public-Key Encryption at Minimum Cost
,
1999,
Public Key Cryptography.