Classic secret sharing schemes vs Homomorphic secret sharing schemes

Hunger Learn

4/21/23, 4:48 PM

What is the difference between the classic secret sharing schemes that are used in the protocols of Ben-or and Rabin, Ben-Or, M., Goldwasser, S., Wigderson (that is the Shamir's secret sharing scheme) with the homomorphic secret sharing schemes? Could anybody provide a paradigm? Can we use a homomorphic secret sharing scheme to design a protocol of communication? I would like some reference for the latter.

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protocol-design

reference-request

homomorphic-encryption

secret-sharing

homomorphic-signatures

Daniel

4/21/23, 6:18 PM

In traditional secret-sharing you distribute a secret among several parties, who can reconstruct it later on. In a homomorphic secret-sharing on the other hand, you want to enable the parties to apply certain *local* operation to their shares before reconstructing, so that the reconstructed secret is not the original distributed value but rather a function of it. For instance, in a linear secret-sharing scheme (such as Shamir's), each party can multiply their share by a constant $c$ to reconstruct not the secret, but the secret times $c$. Actual HSS papers consider other functions.

Hunger Learn

4/21/23, 9:10 PM

@Daniel I rephrase my question. Could we use the homomorphic secret sharing scheme to design a secure multiparty protocols of communication like Ben-or and Rabin, or Ben-Or, M., Goldwasser, S., Wigderson protocols?

Daniel

4/21/23, 9:20 PM

Homomorphic secret sharing (HSS) for arbitrary functions trivially gives you secure computation for any function: just secret-share the inputs, each party locally applies the required operation, and then the secret is reconstructed to obtain the result of the computation on the inputs. You don't need to involve BGW or any other protocol once you have HSS for arbitrary functionalities. The challenge, however, lies in designing such HSSs.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Classic secret sharing schemes vs Homomorphic secret sharing schemes

TH: แผนการแบ่งปันความลับแบบคลาสสิก vs แผนการแบ่งปันความลับแบบโฮโมมอร์ฟิก

RO: Scheme clasice de partajare a secretelor vs schemele homomorfe de partajare a secretelor

RU: Классические схемы разделения секретов против гомоморфных схем разделения секретов

VI: Sơ đồ chia sẻ bí mật cổ điển vs Sơ đồ chia sẻ bí mật đồng hình

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