Data authenticated aggregation is always a significant issue for wireless sensor networks (WSNs). The marine sensors are deployed far away from the security monitoring. Secure data aggregation for marine WSNs has emerged and attracted the interest of researchers and engineers. A multi-signature enables the data aggregation through one signature to authenticate various signers on the acknowledgement of a message, which is quite fit for data authenticated aggregation marine WSNs. However, most of the previous multi-signature schemes rely on the technique of bilinear pairing involving heavy computational overhead or the management of certificates, which cannot be afforded by the marine wireless sensors. Combined with the concept of identity-based cryptography, a few pairing-free identity-based multi-signature (IBMS) schemes have been designed on the basis of the integer factorization problem. In this paper, we propose two efficient IBMS schemes that can be used to construct provably secure data authenticated aggregation protocols under the cubic residue assumption, which is equal to integer factorization. We also employ two different methods to calculate a cubic root for the cubic residue number during the signer’s private key extraction. The algorithms are quite efficient compared to the previous work, especially for the algorithms of the multi-signature generation and its verification.
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