This article was revisited and updated in October 2018. Introduction We strive to use the best state-of-the-art cryptography for our library Themis. So when we wanted to implement an important novel feature Secure Comparator (that includes the so-called "Socialist Millionaire Protocol"), we needed to replace the prime-field modular arithmetic with something stronger. The obvious choice for such replacement was the ed25519 signature system: it provides even more protection from side-channel analy...