An efficient single-photon source based on low-density InGaAs quantum dots in a photonic-crystal nanocavity is demonstrated. The single-photon source features the effects of a photonic band gap, yielding a single-mode spontaneous emission coupling efficiency as high as beta = 92% and a linear polarization degree up to p = 95%. This appealing performance makes it well suited for practical implementation of polarization-encoded schemes in quantum cryptography.