Sparse Matrix Basis Transformation for Inner-Product Encryption
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Solution Overview
Problem
In inner-product encryption, the sizes of public parameters and master secret keys are proportional to N^2, and the generation process of secret keys and encryption take time proportional to N^2, which is inefficient.
Innovation Solution
A cryptographic processing system uses a sparse matrix to transform a basis A into bases B and B*, reducing the sizes of public parameters and master secret keys, and shortening the time for key generation and encryption processes by employing these transformed bases for cryptographic operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a basis A is used for inner-product encryption, then the cryptographic system achieves functional correctness, but the sizes of public parameters and master secret key become proportional to N^2 and the generation process takes time proportional to N^2
Solution Approach 1:
The patent segments the basis transformation by introducing a sparse matrix S that transforms the initial basis A into a new basis B. This segmentation allows the cryptographic system to maintain functionality while reducing the representation size from O(N^2) to O(N) by exploiting the sparsity pattern where most elements are zero.
Solution Approach 2:
The patent changes the parameter representation by using a sparse matrix S with specific structural properties (most elements are zero) to transform the basis. This parameter change reduces the storage and computation requirements from proportional to N^2 to proportional to N, while maintaining the cryptographic functionality through the relationship B = S·A.
2Reliability
If a basis A is used for inner-product encryption, then the cryptographic system achieves functional correctness, but the generation process of secret key and encryption process take time proportional to N^2
Solution Approach 1:
The patent segments the computational workload by introducing the sparse matrix S, which divides the basis transformation into manageable components. This segmentation reduces the computational complexity from O(N^2) to O(N) for key generation and encryption operations by exploiting the sparsity structure.
Solution Approach 2:
The patent changes the computational parameters by using a sparse matrix representation that reduces the number of operations required. The sparse structure allows key generation and encryption to be performed in time proportional to N rather than N^2, significantly improving efficiency while maintaining cryptographic correctness.
Data Source
AI summary
The object is to decrease the sizes of public parameters and a master secret key, and to shorten the time taken for the generation process of the secret key to be supplied to the user and the encryption process. A generation device 100 generates a basis B and a basis B* that form public parameters and a master secret key using a sparse matrix in which each row and each column have at least one value other than 0. An encryption device 200 generates a vector in the basis B, the vector being embedded with predetermined information, as a cipher vector. A decryption device 300, by treating a predetermined vector in the basis B* as a key vector, conducts a pairing operation for the cipher vector and the key vector, to decrypt the cipher vector.