RLWE Ciphertext Compression via Polynomial Expansion

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Solution Overview

Problem

Conventional Private Information Retrieval (PIR) schemes face challenges in efficiently compressing and expanding RLWE ciphertexts, leading to high bandwidth consumption and long download times when retrieving multiple data blocks from cloud storage, while maintaining privacy and obscuring access patterns.

Innovation Solution

A method and system that compress integers into an encrypted polynomial using a secret encryption key, allowing a server to expand the polynomial using a public key without learning the plaintext values, utilizing a fully homomorphic encryption scheme and tree data structures to efficiently retrieve encrypted integers, thereby reducing communication costs and preserving privacy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of information

If conventional PIR schemes are used to retrieve data from cloud storage, then privacy is maintained, but bandwidth consumption increases significantly and download time becomes too long

Engineering Contradiction:
ImproveprivacyVSAvoidbandwidth consumption
Core Design Contradiction:
Loss of informationVSLoss of energy

Solution Approach 1:

The patent segments the retrieval process into two distinct phases: an offline preprocessing phase where the client prepares encrypted query polynomials and stores them locally, and an online retrieval phase where only minimal encrypted data is exchanged. This segmentation allows the computationally intensive operations to be performed offline, reducing online bandwidth consumption while maintaining privacy through encrypted polynomial operations.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary actions by pre-computing and storing encrypted query polynomials locally on the client device before actual data retrieval. This preliminary preparation includes generating the secret key, creating the polynomial structure, and encrypting query parameters, so that during actual retrieval, only small encrypted fragments need to be transmitted, dramatically reducing bandwidth consumption.

Inventive Principle:
Principle #10Preliminary action

2Loss of information

If all content is downloaded from cloud storage to maintain privacy, then access patterns are obscured, but retrieval time becomes excessively long

Engineering Contradiction:
Improveaccess pattern privacyVSAvoidretrieval time
Core Design Contradiction:
Loss of informationVSLoss of time

Solution Approach 1:

The patent extracts only the essential encrypted components needed for private retrieval from the full download approach. Instead of downloading all content, the system extracts and transmits only the minimal encrypted polynomial coefficients and evaluation points required to compute the desired function, achieving both privacy and efficiency.

Inventive Principle:
Principle #2Taking out (Extraction)

Solution Approach 2:

The patent changes the parameters of the retrieval protocol by working in polynomial space rather than direct data space. By transforming the retrieval problem into evaluating encrypted polynomials at specific points, the system achieves privacy without requiring full downloads, as the polynomial evaluation can be performed on compressed encrypted representations.

Inventive Principle:
Principle #35Parameter changes

3Productivity

If multiple data blocks are retrieved using conventional PIR, then comprehensive data access is achieved, but bandwidth consumption increases significantly

Engineering Contradiction:
Improvedata access capabilityVSAvoidbandwidth consumption
Core Design Contradiction:
ProductivityVSLoss of energy

Solution Approach 1:

The patent creates a universal encrypted polynomial structure that can serve multiple retrieval purposes. The same encrypted polynomial and secret key can be used to retrieve different data blocks by evaluating the polynomial at different points, allowing comprehensive data access while maintaining consistent low bandwidth consumption across multiple retrieval operations.

Inventive Principle:
Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent merges multiple retrieval queries into a single encrypted polynomial representation. Instead of transmitting separate encrypted data for each retrieval request, the system combines multiple query intentions into one polynomial structure that can be evaluated at multiple points, achieving multi-block retrieval with the bandwidth cost of a single transmission.

Inventive Principle:
Principle #5Merging (Combining)

Data Source

PatentEP3959841B1Compression and oblivious expansion of RLWE ciphertexts
Publication Date: 2022.06.08 GOOGLE LLC
  • EP3959841B1 patent drawingFigure 1
  • EP3959841B1 patent drawingFigure 2A
  • EP3959841B1 patent drawingFigure 2B

AI summary

A method (600) includes obtaining a plaintext query (134) that includes a sequence of plaintext integers (136) and generating a polynomial (172) having coefficients (173) that include the sequence of plaintext integers of the plaintext query. The method also includes encrypting the polynomial using a secret encryption key (132) and transmitting the encrypted polynomial (182) to a server (111). The secret encryption key is randomly sampled from a ciphertext space and the server is configured to expand the encrypted polynomial using a public encryption key (130) to obtain a sequence of encrypted integers (210) corresponding to the sequence of plaintext integers. The method also includes receiving an encrypted result (192) from the server. The encrypted result is based on the sequence of encrypted integers.