Homomorphic Secret Sharing (survey)

by Yuval Ishai

Oded's comments

This is a highly inspiring survey talk. In the first part, Yuval provided a historical perspective on current research in the foundations of cryptography as oppopse to the research in that area in and arround the 1980s. He then presented Homomorphic Secret Sharing (HSS) as related to the notion of Fully Homomorphic Encryption (FHE), while highlighting the differences and their effect when replacing FHE by HSS in some cetral applications. The second part tried to touch some of the constructions, applications, and open questions, but was cut short by the discrepancy between the vast amount of material and the limited time. Since I am most interested in the complexity theoretic applications, I wish to highlight the connection to random self-reducibility and the construction of locally decdable codes, although Yuval only mentioned them. (I will try to get him to explain them to me some day.)

The original abstract

A homomorphic secret-sharing scheme is a secret-sharing scheme that allows locally mapping shares of a secret to compact shares of a function of the secret. The talk will survey the current state of the art on homomorphic secret sharing, covering efficient constructions, applications in cryptography and complexity theory, and open questions.

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