The frequency hopping sequence plays a crucial role in determining the system's anti-jamming performance, in frequency hopping communication systems. If the adjacent frequency points of FHS can ensure wide-gap, it will better improve the anti-interference capability of the FH communication system. Moreover, if the period of the sequence is expanded, and each frequency point does not repeat in the same sequence, the system's ability to resist electromagnetic interference will be enhanced. And a one-coincidence frequency-hopping sequence set consists of FHSs with maximum Hamming autocorrelation 0 and cross-correlation 1. In this paper, we present two constructions of wide-gap frequency-hopping sequence sets. One construction is a new class of wide-gap one-coincidence FHS set, and the other is a WGFHS set with long period. These two WGFHS sets are optimal with respect to WG-Peng-Fan bound. And each sequence of these WGFHS sets is optimal with respect to WG-Lempel-Greenberger bound.

In this paper, we propose an on-line e-coin system with four parties: Consumer, Merchant, Bank and Issuer. The proposed system not only circulates anonymous e-coins but also protects the profits of the Merchant and the Consumer during a transaction. An e-coin, consisting of a secret value c and a public value c'=h(c) where h() is a secure one-way hash function with collision resistant property, is generated by its owner. The public value of a legal e-coin is published on the bulletin board of Issuer. Only the owner who releases the secret values of the published e-coins can spend money. Instead of Bank, Issuer has to be on-line to verify and replace the public values of the Consumer's e-coins with the Merchant's while the Consumer pays money to the Merchant in a transaction. Such a replacement represents that the coins are passed from one person to another.