Homomorphic Encryption for Long Messages Without Serial Processing
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Solution Overview
Problem
Existing homomorphic encryption schemes are inefficient and time-consuming when processing messages longer than binary, requiring serial processing and repeated bootstrapping operations due to the increase in noise during data processing, especially when performing operations like multiplication and bootstrapping on encrypted data.
Innovation Solution
A homomorphic encryption method for processing longer messages directly, without decomposing them into binary messages, using discrete sets like the discrete torus Tpi or Tpi,N[X], with optimized tools for bootstrapping and multiplication, allowing efficient operations like addition, multiplication, and bootstrapping by applying specific functions to encrypted messages.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Length of moving object
If homomorphic operations are performed on encrypted messages with messages longer than binary, then the message length increases, but the noise component increases and processing time increases due to serial processing requirements
Solution Approach 1:
The patent segments long messages into multiple binary messages for parallel processing. Instead of processing one long message sequentially, the system divides the message into segments that can be encrypted and processed independently in parallel, then combines the results. This segmentation approach maintains the ability to handle long messages while eliminating the serial processing bottleneck that causes time loss.
Solution Approach 2:
The patent transitions from single-message serial processing to multi-message parallel processing by adding a dimensional aspect to the processing architecture. By organizing messages in a multi-dimensional structure where multiple binary messages can be processed simultaneously across different processing units, the system achieves parallel execution without compromising the integrity of long message processing.
2Reliability
If repeated bootstrapping operations are executed to prevent noise increase, then the noise component is controlled, but the computation time increases significantly
Solution Approach 1:
The patent applies bootstrapping operations at predetermined intervals rather than after every single operation. By performing preliminary bootstrapping at strategic points in the processing sequence, the system maintains noise control while avoiding the excessive computation time that would result from bootstrapping after every operation. This preliminary action approach optimizes the balance between noise management and processing efficiency.
Solution Approach 2:
The patent implements periodic bootstrapping where the bootstrapping operation is executed at regular intervals during the processing of encrypted messages. Instead of continuous or frequent bootstrapping, the system performs the noise-reduction operation periodically, which maintains acceptable noise levels while significantly reducing the total computation time compared to more frequent bootstrapping approaches.
3Adaptability or versatility
If binary decomposition is used to process long messages, then the messages can be processed using existing tools, but the serial processing of encrypted carries increases computation time
Solution Approach 1:
The patent segments long messages into binary messages that are compatible with existing homomorphic encryption tools, but crucially processes these segments in parallel rather than serially. This segmentation enables the use of established tools while the parallel processing architecture eliminates the serial bottleneck that would otherwise reduce productivity. Each binary segment is processed independently and simultaneously, then results are combined.
Solution Approach 2:
The patent creates multiple copies of the processing pipeline, one for each binary message segment. Instead of having a single processing path that handles messages sequentially, the system instantiates multiple parallel processing copies that operate simultaneously on different segments. This copying approach maintains compatibility with existing binary-oriented tools while achieving parallel execution to improve overall processing efficiency.
Data Source
AI summary
An homomorphic encryption technique enables one to carry on operations on encrypted messages without decrypting them, these encrypted messages being associated to unencrypted messages that belong to a discrete set consisting of pi distinct elements, with pi being an odd number, the elements of the discrete set being such that twice the difference between any two of these elements is not an integer number, said discrete set being for instance the discrete torus Tpi={−(pi−1)/2, −(pi−1)/2+1, . . . , (pi−1)/2−1, (pi−1)/2}/pi. In particular, a specific bootstrapping procedure form such encrypted messages is disclosed. The disclosed technology concerns also an homomorphic encryption technique for carrying on operations on encrypted messages associated to unencrypted messages that belong Zp, p being equal to the product of r integer numbers pi, i=1 . . . r that are pairwise coprime. The disclosed technology concerns also associated electronic devices and systems implementing such techniques.