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In this paper we propose a secure and efficient off-line electronic transaction protocol based on an IDbased public key encryption system and group signature schemes, which is constructed from bilinear pairings. The anonymity of the customer is revocable by a trustee in case of dispute. Because the amount of communication in the payment protocol is about 1280 bits, our off-line electronic transaction protocol can be used in the wireless networks with the limited bandwidth or the limited-storage environment such as smart card.doi:10.24846/v19i1y201003 fatcat:53dlthfzonhxbfdiennfth4xym