We propose the first practical attribute-based signature (ABS) scheme with attribute privacy without pairings in the random oracle model. Our strategy is in the Fiat-Shamir paradigm; we first provide a generic construction of a boolean proof system of Σ-protocol type. Our boolean proof system is a generalization of the well-known OR-proof system; that is, it can treat any boolean formula instead of a single OR-gate. Then, by combining our boolean proof system with a credential bundle scheme of the Fiat-Shamir signature, we obtain a generic attribute-based identification (ABID) scheme of proof of knowledge. Finally, we apply the Fiat-Shamir transform to our ABID scheme to obtain a generic ABS scheme which possesses attribute privacy and can be proved to be secure in the random oracle model. Our ABS scheme can be constructed without pairings.