Homomorphic Encryption Ciphertext Segmentation for Rotation Efficiency
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Solution Overview
Problem
Fully homomorphic encryption (FHE) schemes face limitations in handling large inputs due to slot constraints and efficiency costs, making it difficult to perform operations on ciphertexts beyond a certain size, especially with operations like convolution and matrix-multiplication, which assume inputs fit within a single ciphertext.
Innovation Solution
The system packs received tensors into smaller ciphertexts using designated packing techniques, allowing for efficient simulation of rotation operations by computing rotations on these smaller ciphertexts and storing them in a rotation cache for reuse, thereby removing size constraints and improving processing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If the number of slots in a ciphertext is increased to handle larger inputs, then the capacity to process larger inputs is improved, but the computational efficiency deteriorates
Solution Approach 1:
The patent divides a large ciphertext into multiple smaller ciphertexts, each containing a subset of the original data. This segmentation allows the system to process large inputs by operating on multiple smaller units simultaneously, avoiding the efficiency penalties associated with manipulating single large ciphertexts while maintaining the capacity to handle large datasets.
2Productivity
If FHE algorithms assume a minimum number of slots in a ciphertext, then the operations can be performed efficiently, but the ability to process inputs larger than the slot limit is lost
Solution Approach 1:
The system segments large inputs into multiple smaller ciphertexts that each fit within the standard slot limitations. This allows FHE algorithms to operate efficiently on each small ciphertext using standard optimizations while collectively handling inputs larger than what would fit in a single ciphertext.
Solution Approach 2:
The patent introduces a new dimension to the problem by transitioning from a single large ciphertext to a collection of smaller ciphertexts. This dimensional shift from one-dimensional (single ciphertext) to multi-dimensional (multiple ciphertexts) allows the system to maintain efficient operations while expanding input capacity.
3Quantity of substance
If the ciphertext size is increased to accommodate larger tensors, then the capacity to process larger data is improved, but the processing time increases according to O(n log n)
Solution Approach 1:
By segmenting large ciphertexts into smaller ones, the system reduces the n value in the O(n log n) time complexity formula for each individual operation. While more ciphertexts are processed, each operation on smaller ciphertexts completes faster, and the overall time complexity is managed through parallel processing of multiple smaller units.
Solution Approach 2:
The system employs periodic rotation operations on smaller ciphertexts to achieve the desired data transformation. These periodic operations can be optimized and reused, reducing the total processing time compared to performing equivalent operations on a single large ciphertext.
4Ease of operation
If rotation operations are performed on large ciphertexts, then the complete transformation is achieved, but the computational cost increases
Solution Approach 1:
The patent segments rotation operations into smaller units by applying rotations to individual smaller ciphertexts rather than one large ciphertext. This segmentation reduces the computational cost of each rotation operation while maintaining the completeness of the overall transformation through systematic application across all segments.
Solution Approach 2:
The system performs preliminary packing of the input tensor into smaller ciphertexts before applying rotation operations. This preliminary action optimizes the subsequent rotation operations by working with smaller, more manageable units that require less computational resources.
Data Source
AI summary
An example system includes a processor to pack a received tensor using a designated packing to generate a number of smaller ciphertexts. The processor can compute a rotation using the number of smaller ciphertexts to simulate a rotation operation on the tensor.