An IND-CPA cryptosystem from Demytko's primitive

A new encryption algorithm over elliptic curve

“…Theorem 1 The two non-identity based receiptor-oriented encryption schemes in section 4 both have the soundness. In other words, if {ff, f4} is a legal ciphertext returned by the encryptioner on plaintext m C {0, 1}n, then the decryptioner will surely recover the plaintext m E {0, 1}n such that Dup,u,sp,vp,p(Eup,sp,s,sp,p(m, r)) = m (2) where E and D are the encryption and the decryption algorithms respectively; r is a random element chosen by the encryptioner; and other data are the same to what in the two non-identity based ROE schemes in section 4.…”

“…Recall what is the expansion factor of encryption schemes, it is the ratio between the lengths of the cipher text and the plaintext. The expansion factor of the proposed new schemes is the same as that of [2]. By this definition, we can use some compression technique applying to the cipher text {f,, f4} (of message m) to get its length equal to f4 [81.…”

“…Generally speaking, semantic security means that: the view of the ciphertext gives no additional information about the plaintext. Galindo et al proposed these two schemes [1], [2] in 2003, which are based on elliptic curves. Both of them present semantic security.…”

“…However, prior to [2], [4], [9], the supersingular curves were undesirable in cryptographic settings since Weil pairing can reduce the discrete logarithm problems in supersingular curves to that in an extension of the underlying finite field. Thanks to Joux [4] and Boneh et al [2], the pairings have become desirable and applied to various cryptographic primitives: public key encryption [2], digital signature [5], key agreement [4]; and signcryptions [6]. In our paper, we propose several new public key encryption schemes V. Potdar School of Information Systems Curtin University of Technology different from [2].…”

“…Thanks to Joux [4] and Boneh et al [2], the pairings have become desirable and applied to various cryptographic primitives: public key encryption [2], digital signature [5], key agreement [4]; and signcryptions [6]. In our paper, we propose several new public key encryption schemes V. Potdar School of Information Systems Curtin University of Technology different from [2]. And the new constructions are motivated by some techniques from [7], [1], [9].…”