This paper presents an efficient secure auction protocol for M+1st price auction. In our proposed protocol, a bidding price of a player is represented as a binary expression, while in the previous protocol it is represented as an integer. Thus, when the number of players is m and the bidding price is an integer up to p, compared to the complexity of the previous protocol which is a polynomial of m and p, the complexity of our protocol is a polynomial of m and log p. We apply the Boneh-Goh-Nissim encryption to the mix-and-match protocol to reduce the computation costs.