Abstract
The existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC), which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC) based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.
Highlights
Signcryption is a cryptographic primitive that provides both signature and encryption simultaneously to sensitive information at a lower computation and communication overhead than the traditional signature--encryption approach [1]
Multivariate public key cryptography (MPKC) schemes were proposed, and they are mainly based on four basic MPKC schemes including the Matsumoto Imai (MI) cryptosystem, the Hidden Field Equation (HFE) cryptosystem, the Oil Vinegar (OV) cryptosystem and the Stepwise Triangular System [20]
With the knowledge of the most efficient attacks on the Isomorphism of Polynomials (IP) problem, in order to strengthen the security of our scheme, we suggest that the parameters of our scheme should satisfy the following conditions: the transformations T and V should be affine; the polynomials in P and Q should be homogeneous
Summary
Signcryption is a cryptographic primitive that provides both signature and encryption simultaneously to sensitive information at a lower computation and communication overhead than the traditional signature--encryption approach [1]. The new scheme has the advantage of the certificateless cryptosystem, which avoids the problem of key management, and resists quantum attack only with light-weight computation like the multivariate quadratic polynomial operations. A certificateless multi-receiver signcryption scheme is Type-2-CCA2 secure if no probabilistic polynomial-time attacker A has a nonnegligible advantage in winning the IND-CLMSC-CCA2-2 game [11]. A certificateless multi-receiver signcryption scheme is Type-2-sEUFCMA-2 secure if no probabilistic polynomial-time attacker A has a non-negligible advantage in winning the EUF-CLMSC-CMA-2 game [11]. No Replace Public Key query is allowed on any of the challenge identities
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