In this article, with the help of the concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard's inequality for convex functions is generalized to cases with bounded derivatives of nth order, including the so-called n-convex functions, from which Hermite-Hadamard's inequality is extended and refined.
In a recent paper, Yang et al. (Quant. Inf. Process. 13(9), [2007][2008][2009][2010][2011][2012][2013][2014][2015][2016] 2014) analyzed the security of one-time proxy signature scheme Wang and Wei (Quant. Inf. Process. 11(2), [455][456][457][458][459][460][461][462][463] 2012) and pointed out that it cannot satisfy the security requirements of unforgeability and undeniability because an eavesdropper Eve can forge a valid proxy signature on a message chosen by herself. However, we find that the so-called proxy message-signature pair forged by Eve is issued by the proxy signer in fact, and anybody can obtain it as a requester, which means that the forgery attack is not considered as a successful attack. Therefore, the conclusion that this scheme cannot satisfy the security requirements of proxy signature against forging and denying is not appropriate in this sense. Finally, we study the reason for the misunderstanding and clarify the security requirements for proxy signatures.Keywords Proxy signature · Unforgeability · Undeniability · Quantum cryptography In 1996, Mambo et al. firstly proposed the concept of proxy signature scheme [1], which allows an original signer (say Alice) authorize another person (say Bob), called proxy signer, to issue signatures on behalf of her. Owning to the speciality, proxy signature can be used in grid computing, mobile agent, and e-commerce etc [2][3][4][5]. Since it was firstly
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