Functional encryption is an extension of the ordinary public key encryption where decryption results vary depending on the functions (or key attributes) associated to secret keys. In this paper, we show an embedding lemma for functional encryption, which provides a sufficient criterion for implication from one FE to FE with another function class. The lemma is an extension of the embedding lemma for attribute-based encryption that was introduced in the previous work by Boneh and Hamburg (Asiacrypt 2008). As an application of our lemma, we show that FE for cubic forms can be constructed from FE for inner product or FE for quadratic forms.

A secure integer comparison protocol is one of the most fundamental building blocks to construct protocols of rich functionality in multi-party computation. It allows parties to compute the less-than functionality on shared values in privacy preserving manner. In this paper, we present a tree-based secure two-party comparison protocol in the client-aided client-server model, which outperforms existing approaches in terms of round complexity when it is used for 64-bit data. Our proposed protocol requires only 9 communication rounds to compare 64-bit data, which is at least 3 times fewer rounds than existing protocols. This suggests that our protocol is adequate to be used in low-latency networks such as WAN.

We present a new secure integer division protocol with private divisor. Our protocol is based loosely on the Bogdanov et al. (Int. J. Inf. Secur.'12) protocol, which securely computes the classical Goldschmidt's division algorithm. While the Bogdanov et al. scheme was designed specifically to work only on a 3-out-of-3 secret sharing scheme, our scheme works on a 2-out-of-2 secret sharing scheme. This has an advantage since the latter setting is more widely used in the literature of secure computation, and our protocol can thus be used as an efficient building block in this setting. We implement our protocol in Python and provide its benchmark. As a main application of our division protocol, we implement a secure protocol for privacy-preserving chi-squared tests on genomic data. This demonstrates that the proposed protocol is suitable for the statistical analysis on sensitive data.

We provide efficient constructions for trace-and-revoke systems with public traceability in the black-box confirmation model. Our constructions achieve adaptive security, are based on standard assumptions and achieve significant efficiency gains compared to previous constructions.