We present an actively secure protocol for secure multi-party computation based on lookup tables, by extending the recent, two-party TinyTable protocol of Damgard et al. (ePrint 2016). Like TinyTable, an attractive feature of our protocol is a very fast and simple online evaluation phase. We also give a new method for efficiently implementing the preprocessing material required for the online phase using arithmetic circuits over characteristic two fields. This improves over the suggested method from TinyTable by at least a factor of 50.
As an application of our protocol, we consider secure computation of the Triple DES and the AES block ciphers, computing the S-boxes via lookup tables. Additionally, we adapt a technique for evaluating (Triple) DES based on a polynomial representation of its S-boxes that was recently proposed in the side-channel countermeasures community. We compare the above two approaches with an implementation. The table lookup method leads to a very fast online time of over 230,000 blocks per second for AES and 45,000 for Triple DES. The preprocessing cost is not much more than previous methods that have a much slower online time.