Certificateless public key cryptography (CL-PKC) promises a practical resolution in establishing practical schemes, since it addresses two fundamental issues, namely the necessity of requiring certificate managements in traditional public key infrastructure (PKI) and the key escrow problem in identity-based (ID-based) setting concurrently. Signcryption is an important primitive that provides the goals of both encryption and signature schemes as it is more efficient than encrypting and signing messages consecutively. Since the concept of certificateless signcryption (CL-SC) scheme was put forth by Barbosa and Farshim in 2008, many schemes have been proposed where most of them are provable in the random oracle model (ROM) and only a few number of them are provable in the standard model. Very recently, Luo and Wan (Wireless Personal Communication, 2018) proposed a very efficient CL-SC scheme in the standard model. Furthermore, they claimed that their scheme is not only more efficient than the previously proposed schemes in the standard model, but also it is the only scheme which benefits from known session-specific temporary information security (KSSTIS). Therefore, this scheme would indeed be very practical. The contributions of this paper are 2-fold. First, in contrast to the claim made by Luo and Wan, we show that unfortunately Luo and Wan made a significant error in the construction of their proposed scheme. While their main intention is indeed interesting and useful, the failure of their construction has indeed left a gap in the research literature. Hence, the second contribution of this paper is to fill this gap by proposing a CL-SC scheme with KSSTIS, which is provably secure in the standard model.
The source coding problem is considered where the only information known about the source is the number of symbols n and the order of the symbol probabilities. In this case, the code which achieves the minimum average redundancy is known as the M code. It is the Huffman code for the average distribution of monotone sources, and thus is a fixed code which does not depend on the symbol probabilities. The M code is a near-optimal code not only in the sense of average redundancy, but also in terms of the redundancy for almost all monotone sources. No simple expression is known for the codeword lengths of the M code for a given alphabet size. In this letter, the structure of this code is investigated, and an estimate is given for the number of codewords of a given length. In particular, the number of codewords of length j + 1 for encoding 2n symbols is shown to be almost twice the number of codewords of length j for encoding n symbols.
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