Achintya Manohar Desai received his MS in Computer Science and Engineering (CSE). His research work was supervised by Dr. Srinathan Kannan. Here’s a summary of his research work on Channel asynchrony and communication complexity in multi-party computation:
Ever since secure multi-party computation was successfully showed, it has remained an interesting research field in the cryptography community. Multi-party computation is one of the most important primitives in modern cryptography, in which mutually distrusting parties want to compute a functionality over their private data without revealing any additional information about their data. It is well established that the information theoretic multi-party computation among, n, number of parties is possible if the number of corrupted nodes is less than n/2 for semi-honest adversary and the number of corrupted nodes is less than n/3 for malicious adversary.
Despite the progress over past 3 decades, multi-party computation has many improvements to go through before it becomes viable for practical scenarios. Also, there happens to exist many areas which are little explored. In this dissertation we explore one such path where we rely on physical cryptographic assumption rather than the traditional assumptions. The traditional assumptions such as discrete log problem, RSA, etc. are always subject to non-existence of poly time algorithm for computational problems of certain nature.
Also, these assumptions do not cover computationally unbounded adversary. The motivation to study such assumption is that the physical cryptographic assumptions can be characterized in a way that they are realistic as well as provide required security guarantees. In this thesis, we discover that channel asynchrony is one such assumption where the channel may not deliver the messages in the same order as they were sent. Usually, we use solutions such as sequence number to order the messages in such case but for security such asynchrony happens to be a boon. It is also more efficient practically compared to the protocols in the information theoretic setting.
This thesis also solves a minor open problem in the multi-party computation literature. “Is it possible to remove the dependency on the multiplicative depth of the circuit in the overall communication complexity of a secure MPC protocol while maintaining its efficiency and the restrictions on the number of corruptions such that 3ta + 2tp + tf < n ?”. This work is based on the works of Goyal et al. and Hirt et al. Goyal et. al. solves a similar question for active adversarial setting instead of mixed adversary. Hirt et al. have also given the multiplicative depth dependent protocol for mixed adversarial setting. We combine these two works to answer the question stated above in affirmative.