A Novel Proxy Signcryption Scheme and its Elliptic Curve Variant

Abstract

Proxy signcryption scheme allows an original signer to delegate his signing power to a proxy such that the latter can signcrypt a message on behalf of the former. In this paper, a new proxy signcryption scheme is proposed based on Discrete Logarithm Problem (DLP) and Diffie-Hellman Problem (DHP) with a reduced computational cost compared to other schemes in literature. The proposed scheme achieves public ciphertext authentication as the signcrypted message before being accepted, the receiver first verifies the signature. This property is very useful as the receiver can filter some incorrect ciphertext before decrypting it which achieves more efficient unsigncryption. Also, a variant of the main scheme that works over elliptic curves will be considered, since it has proven to provide better security with shorter keys and hence less storage requirements which makes it more suitable for resource constrained devices such as pagers and mobile phones. Numerical examples have been given with Mathematica to emphasize the ease of its practical use.

A Hyperelliptic Curve Cryptosystem Based Proxy Promised Signcryption Scheme

“…Typically, these operations include hyperelliptic curve divisor multiplications (HECdM). In Table 2, we illustrate the computational cost comparison of the proposed scheme with all the three schemes [31,41] and [29] in terms of operations. We inspected, in the proposed scheme and the schemes [31,41] and [29], that the costliest operations (major operations) are the hyperelliptic curve divisor multiplication (HECdM) and elliptic curve point's scalar multiplications (ECPM).…”

“…Table 3 demonstrates the comparison of the proposed with the other three schemes [31,41] and [33] with respect to milliseconds. It is observed that the single scalar [42][43][44].…”

“…In Table 4, we show communication cost comparisons of the proposed scheme with existing schemes [31,41] and [29] with respect to different ciphertext sizes, for example, 128, 256, 512, and 1,024 bits. In the proposed scheme, wireless communication is involved, and there the factor of importance is communication overhead.…”

“…Hence, the selection of parameters will mark most of the communication cost for the proposed system and the amount of information that are to be transmitted. For simplification, we assume that: For the sake to compare communication cost of proposed scheme |C| + |n|+|H (value)| with scheme [31] and scheme [29,41], we know that the communication cost of scheme [31] is |C| + |mw|+3|q|+| (value)| and schemes [29,41]are |C|+|q|+|H (value)|.…”

“…Communication overhead reduction of the proposed scheme as compared with the scheme [31] Communication overhead reduction of the proposed scheme as compared with the scheme [29,41]…”