The human genome can identify an individual and determine the individual’s biological characteristics, and hence has to be securely protected in order to prevent privacy issues. In this paper we point out, however, that current standard privacy-preserving cryptographic protocols may be insufficient to protect genome privacy. This is mainly due to typical characteristics of genome information; it is immutable, and an individual’s genome has correlations to those of the individual’s progeny. Then, as an alternative, we propose to protect genome privacy by cryptographic protocols with everlasting security, which provides an appropriate mixture of computational and information-theoretic security. We construct a concrete example of a protocol with everlasting security, and discuss its practical efficiency.