Re-linearization for Multiparty Homomorphic Encryption

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Solution Overview

Problem

In threshold Fully Homomorphic Encryption (FHE), multiplication of ciphertexts results in non-linear encryption, requiring a non-linear decryption key that exposes the secret key when generated, compromising security.

Innovation Solution

A re-linearization technique that transforms ciphertexts encrypted by higher-order non-linear keys back to linear keys, allowing collaborative decryption without exposing the secret key, using a re-linearization key generated interactively by parties to swap encryption keys from non-linear to linear, preserving the linear additive properties of key shares.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If ciphertexts are multiplied in threshold FHE, then non-linear encryption is achieved, but the secret key must be exposed to generate the non-linear decryption key

Engineering Contradiction:

Improvemultiplication capabilityVSAvoidsecret key security

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent segments the decryption process into multiple independent partial decryptions, where each party contributes a partial decryption using their secret key share. The final plaintext is obtained by combining these partial decryptions additively, eliminating the need to reconstruct the full secret key and thereby maintaining security while enabling multiplication operations.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent introduces an intermediary mechanism where parties exchange encrypted intermediate values rather than secret key shares. Each party encrypts their partial decryption contribution and shares it with others, allowing collaborative decryption of the multiplication result without directly exposing secret key material, thus preserving security while achieving computational versatility.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Ease of operation

If the complete secret key is reconstructed to decrypt non-linear encryption, then decryption is possible, but the linear additive property of key shares is lost

Engineering Contradiction:

Improvedecryption capabilityVSAvoidkey management complexity

Core Design Contradiction:

Ease of operationVSDevice complexity

Solution Approach 1:

The decryption functionality is segmented into independent partial decryptions performed by each party using their secret key share. These partial results are combined through simple addition to produce the final plaintext, maintaining operational simplicity while avoiding the complexity of managing and reconstructing complete secret keys.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Each party performs only a partial decryption action using their secret key share, which is sufficient when combined with other parties' partial decryptions. This partial action approach enables decryption capability without requiring any single party to handle or reconstruct the complete secret key, reducing key management complexity.

Inventive Principle:

Principle #16Partial or excessive action

3Adaptability or versatility

If secret key shares are combined to generate non-linear decryption key, then multiplication is supported, but secret key exposure occurs

Engineering Contradiction:

Improvecomputation supportVSAvoidsecret key exposure

Core Design Contradiction:

Adaptability or versatilityVSObject-affected harmful factors

Solution Approach 1:

The patent uses encrypted intermediate values as mediators between parties during the multiplication process. Instead of directly combining secret key shares, each party encrypts their contribution and shares the encrypted form. This intermediary encryption layer prevents secret key exposure while still enabling the necessary computations for multiplication support.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent replaces the mechanical process of directly combining secret key shares with a cryptographic substitution using homomorphic encryption properties. Computations are performed on encrypted data and keys without direct manipulation of secret key material, eliminating the security vulnerability of key exposure while maintaining computational versatility.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS11962679B2Secure distributed key generation for multiparty homomorphic encryption

Publication Date: 2024.04.16 DUALITY TECHNOLOGIES INC

AI summary

Collaborative multiparty homomorphic encryption comprising receiving a linear common public key collaboratively generated by a plurality of parties as a sum of linear public key shares associated with the respective plurality of parties. Each of two ciphertexts may be encrypted with the linear common public key and the two ciphertexts may be combined by a non-linear computation to generate a result ciphertext encrypted by a non-linear public key. The result ciphertext may be re-encrypted with a re-linearization key to swap encryption keys from the non-linear public key to a linear public key. The re-encrypted result ciphertext may be distributed to the plurality of parties to each partially decrypt the re-encrypted result ciphertext by a linear secret key share associated with the party, which in combination fully decrypts the result by a linear common secret key that is a sum of the secret key shares of the respective plurality of parties.