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A commitment scheme is a fundamental protocol and an essential component of basic cryptographic tasks, such as zero-knowledge identification. In recent years, lattice-based cryptography has been intensively studied owing to its potential to be promising post-quantum cryptography. Therefore, the commitment schemes based on lattice assumption have been studied for practical applications. Typically, many applications require to commit arbitrary vectors rather than only short ones. In order to send such large messages, one of a crucial challenges of commitment schemes is to increase the size of a message string. Various existing studies have been done to enlarge the size of a message string so far. Baum et al. constructed the commitment scheme, which can allow sending large message size in 2018. However, the domain available for message string is still being used for non-message purposes.In this paper, by improving Baum et al.'s commitment scheme, we propose a commitment scheme that can send a larger message size than Baum et al.'s message string size. Furthermore, we prove that the hiding property of our commitment scheme is based on the hardness of the decisional knapsack problem, and the binding property is based on the hardness of the module small-integer solution problem. We also show how to achieve a statistically hiding commitment scheme by setting appropriate parameters.

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