It is well known that the algebraic expression of AES S-box is very simple and only 9 terms are involved. Hence, AES security is suspected although there is no vulnerability on it so far. To eliminate the weakness of extremely small terms in the algebraic expression of AES S-box, one improved AES S-box is proposed, which preserves the algebraic degree invariable but significantly increases the number of its algebraic expression terms from 9 to 255. At the same times Boolean function has good characters in balance and strict avalanche criterion （SAC）, etc. Finally, it is proved that the improved AES S-box scheme is secure against the powerful known differential and linear cryptanalysis.
Ju et al. proposed a certificateless signature scheme with instantaneous revocation by introducing security mediator （SEM） mechanism. This article presents a detailed cryptoanalysis of this scheme and shows that, in their proposed scheme, once a valid signature has been produced, the signer can recover his private key information and the instantaneous revocation property will be damaged. Furthermore, an improved mediated signature scheme, which can eliminate these disadvantages, is proposed, and security proof of the improved scheme under elliptic curve factorization problem （ECFP） assumption and bilinear computational diffie-hellman problem （BCDH） assumption is also proposed.
This paper presents a simple partially blind signature scheme with low computation. By converse using the partially blind signature scheme, we build a simple fair e-payment protocol. In the protocol, two participants achieve the goals of exchanging their digital signatures from each other in a simple way. An ado vantage of this scheme is that this approach does not require the intervention of the third party in any case. The low-computation property makes our scheme very attractive for mobile client and smart-card implementation in many e-commerce applications.
