# homomorphic secret sharing

> secret sharing algorithm in which the secret is encrypted via homomorphic encryption

**Wikidata**: [Q5891458](https://www.wikidata.org/wiki/Q5891458)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Homomorphic_secret_sharing)  
**Source**: https://4ort.xyz/entity/homomorphic-secret-sharing

## Summary
Homomorphic secret sharing is a cryptographic method that combines secret sharing with homomorphic encryption, allowing multiple parties to collaborate on encrypted data without revealing the underlying secret. It is a subclass of secret sharing where the secret is encrypted before distribution. This technique enables secure multi-party computation while maintaining data confidentiality.

## Key Facts
- Uses homomorphic encryption to encrypt the secret before sharing
- Classified as a subclass of secret sharing
- Has a freebase ID of /m/02qxrgn
- Wikipedia title is "Homomorphic secret sharing"
- Available in English on Wikipedia
- Described on Wikidata as "secret sharing algorithm in which the secret is encrypted via homomorphic encryption"
- Has a Microsoft Academic ID of 132161212 (discontinued)

## FAQs
### Q: What is homomorphic secret sharing?
A: Homomorphic secret sharing is a cryptographic technique that combines secret sharing with homomorphic encryption, allowing multiple parties to work with encrypted data without revealing the original secret.

### Q: How does homomorphic secret sharing differ from regular secret sharing?
A: Unlike regular secret sharing, homomorphic secret sharing encrypts the secret using homomorphic encryption before distribution, enabling computations on encrypted data while maintaining confidentiality.

### Q: What is the main advantage of homomorphic secret sharing?
A: The main advantage is that it allows multiple parties to collaborate on encrypted data without needing to decrypt it first, preserving privacy while enabling distributed computation.

## Why It Matters
Homomorphic secret sharing represents a significant advancement in secure multi-party computation and privacy-preserving technologies. By combining the benefits of secret sharing with homomorphic encryption, it enables organizations to collaborate on sensitive data without compromising confidentiality. This is particularly valuable in scenarios where multiple parties need to perform computations on shared data but cannot trust each other with the raw information. The technique has applications in areas such as secure voting systems, private data analysis, and distributed machine learning, where maintaining data privacy is crucial while still allowing for meaningful computation and collaboration.

## Notable For
- Combines two powerful cryptographic techniques: secret sharing and homomorphic encryption
- Enables secure multi-party computation without revealing underlying secrets
- Provides a foundation for privacy-preserving distributed systems
- Represents an evolution in cryptographic protocols for collaborative computing
- Maintains data confidentiality while allowing meaningful computation on encrypted data

## Body
### Technical Foundation
Homomorphic secret sharing builds upon two fundamental cryptographic concepts: secret sharing and homomorphic encryption. Secret sharing, developed by Adi Shamir and George Blakley in 1979, allows a secret to be divided into shares distributed among multiple parties. Homomorphic encryption, first proposed by Ronald Rivest, Leonard Adleman, and Michael Dertouzos in 1978, enables computations on encrypted data without requiring decryption.

### Implementation Details
The process involves encrypting the secret using homomorphic encryption before applying the secret sharing algorithm. This creates shares that are themselves encrypted, allowing parties to perform computations on the shares without accessing the underlying plaintext. The homomorphic properties ensure that operations on the encrypted shares correspond to meaningful operations on the original secret.

### Applications
Homomorphic secret sharing finds applications in various domains requiring secure collaboration. In healthcare, it enables multiple institutions to analyze patient data without sharing sensitive information. Financial institutions use it for joint risk assessment while maintaining client confidentiality. Government agencies employ it for secure information sharing across departments. The technology also supports privacy-preserving machine learning, where multiple parties can train models on combined datasets without exposing individual data points.

### Security Properties
The security of homomorphic secret sharing relies on the strength of both the secret sharing scheme and the homomorphic encryption system used. Common choices include Shamir's secret sharing combined with fully homomorphic encryption schemes. The system provides information-theoretic security for the secret sharing component and computational security for the encryption layer, creating a robust framework for secure distributed computation.

## References

1. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)