Key Stream Generation for Homomorphic Encryption Efficiency
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Solution Overview
Problem
Current homomorphic encryption systems face inefficiencies due to large encrypted data sizes, while symmetric key encryption lacks the ability to analyze data without decryption, and existing modular operation-based methods have high multiplication depth, requiring inefficient rebooting techniques.
Innovation Solution
A method and apparatus for generating a key stream using r round keys as N-dimensional integer vectors based on a prime number, random bit string, and secret key, employing modular addition and linear/nonlinear transformations to create a key stream for modular operation-based symmetric key encryption, avoiding the need for rebooting techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If modular operation-based symmetric key encryption methods are used to obtain integer homomorphic ciphertext, then the ability to analyze encrypted data is improved, but the multiplication depth becomes large requiring inefficient rebooting techniques
Solution Approach 1:
The encryption process is divided into multiple rounds (r≥3), where each round performs a limited number of modular multiplications. This segmentation prevents any single round from creating excessive multiplication depth, thereby avoiding the need for rebooting techniques while maintaining the ability to analyze encrypted data through homomorphic operations.
Solution Approach 2:
The patent employs dynamic key scheduling where round keys are generated through a key stream that combines modular addition and multiplication operations. This dynamic approach allows the system to maintain security while controlling multiplication depth by distributing computational complexity across multiple rounds rather than concentrating it in fewer operations.
2Productivity
If bit operation-based symmetric key encryption (AES) is combined with homomorphic encryption using ciphertext conversion framework, then data transmission and storage efficiency is improved, but the overall efficiency is reduced due to incompatibility
Solution Approach 1:
The patent changes the operational parameters from bit operations (AES) to modular arithmetic operations. By using modular addition and multiplication in the encryption process, the system achieves compatibility with homomorphic encryption schemes that operate on integers, thereby maintaining both transmission efficiency and analytical capability.
Solution Approach 2:
The patent substitutes the mechanical bit operation structure of AES with a mathematical modular arithmetic structure. This substitution replaces the bitwise XOR, substitution, and permutation operations with modular addition and multiplication, enabling the encryption to work within the homomorphic encryption framework while preserving efficiency.
3Adaptability or versatility
If homomorphic encryption is used to enable analysis of encrypted data, then data analysis capability is improved, but the size of encrypted data becomes very large increasing network transmission and server storage costs
Solution Approach 1:
The patent performs preliminary key preparation by generating multiple round keys through a key stream before the actual encryption process. This preliminary action ensures that the encryption can be performed efficiently with pre-computed keys, reducing the computational overhead and data size during the encryption process itself while maintaining homomorphic analysis capability.
Data Source
AI summary
A method for generating a key stream according to an embodiment includes generating r round keys that are each N-dimensional integer vectors including elements of an integer set defined based on a prime number t, based on a random bit string, an encryption counter, and a secret key that is an N-dimensional integer vector consisting of elements of the integer set , generating a first round output vector x1 by performing a modular addition operation on an initial vector and a first round key RK1 of the r round keys with the prime number t as a modulus, and generating a key stream that is an N-dimensional integer vector consisting of elements of the integer set from the first round output vector x1 by using a second to r-th round keys of the r round keys, and one or more first round functions and a second round function.