In card-based cryptography for performing secure computation, after each player places an input commitment consisting of two face-down cards, all players cooperate to manipulate a sequence of cards according to a protocol. In the presence of a malicious player who does not follow the protocol, prior work has considered the active card-revealing attack and defined the t-secureness as the ability to prevent information about the input from being leaked even if at most t cards are turned over illegally. In this paper, we first propose an efficient 1-secure AND protocol: our proposed protocol uses only eight cards and one shuffle, whereas the existing protocol requires 16 cards and eight shuffles. Our 1-secure AND protocol is quite simple and easy to implement. We next design a committed-format 1-secure AND protocol by adding four more cards; a committed-format protocol produces its output in the same format as its inputs.