In this March, Dr. Kyoohyung Han visited CDSL and held a lecture on homomorphic encryption and bootstrapping. Dr. Han has co-written several papers with CDSL regarding encrypted control systems, and has contributed with his expertise on homomorphic encryption. He received his Ph.D. degree of mathematics in Seoul National University and is currently in Samsung SDS.
In this lecture, Dr. Han introduced various homomorphic encryption schemes and their principles in a general sense, such as BGV and BFV, other than LWE(Learning With Error)-based scheme that has been mainly used in CDSL. He also showed rigorous computation time of homomorphic operation on those schemes and how such operations are realized. Though homomorphic encryption enables operations on encrypted data, bootstrapping is required to operate several times on a ciphertext.
Moreover, Dr. Han explained how bootstrapping techniques can re-encrypt a ciphertext without decrypting it and refresh its error, which enhances security while growing unbearably large through homomorphic operations. We learned that in order to use bootstrapping, one should transform the decryption algorithm into composition of homomorphic operations. Dr. Han showed the idea of approximately realizing modular operation by using only addition and multiplication.
Since bootstrapping techniques are complicated and requires heavy computation cost, research on encrypted controllers has avoided bootstrapping and instead developed other methods to re-encrypt ciphertext signals, such as in this paper from CDSL. However, it is still necessary to understand the principle of bootstrapping and follow state of the art techniques that overcome its shortcomings, for further research on encrypted controllers. Thus, this seminar was very informative for researchers of CDSL who are interested in encrypted control systems.
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