Approximate Homomorphic Encryption for Efficient Encrypted Computation
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Solution Overview
Problem
Current homomorphic encryption schemes are impractical and inefficient, particularly for algebraic or arithmetic operations, which introduce noise and are expensive, making them unsuitable for practical applications that require secure and efficient data processing.
Innovation Solution
The implementation of an approximate fully homomorphic encryption (FHE) scheme that allows for approximate arithmetic operations over encrypted data, using techniques such as the CKKS scheme, which supports operations like square root functions, ReLU, and multiplicative inverses, enabling efficient and accurate computations on encrypted numbers without decrypting them.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exact algebraic operations are performed on encrypted data using current homomorphic encryption schemes, then data confidentiality is preserved, but computational efficiency deteriorates and noise increases
Solution Approach 1:
The patent changes the fundamental parameter of computational precision from exact to approximate. By accepting bounded error in exchange for efficiency, the system performs approximate algebraic operations on encrypted data using optimized algorithms that avoid the noise accumulation and computational overhead of exact operations, while maintaining sufficient accuracy for practical applications
Solution Approach 2:
The patent employs cheaper, simplified cryptographic operations that can be performed efficiently on encrypted data. Instead of using expensive exact algebraic operations that require complex homomorphic encryption schemes, the system uses approximate operations with bounded error that are computationally feasible and do not require decryption
2Reliability
If algebraic operations are performed on ciphertext, then data remains encrypted, but noise is introduced and operations become expensive
Solution Approach 1:
The patent converts the harmful effect of noise accumulation into a beneficial approximation mechanism. By deliberately introducing controlled bounded error through approximate operations, the system avoids the unbounded noise accumulation of exact operations. The error remains within acceptable bounds and does not require expensive noise reduction techniques like bootstrapping
Solution Approach 2:
The patent changes the precision parameter from exact to approximate with bounded error. This parameter change allows algebraic operations to be performed on ciphertext without the noise accumulation problems of exact operations, as the approximate nature of the operations inherently limits error growth
3Reliability
If current homomorphic encryption schemes are used for practical applications, then data security is maintained, but implementation efficiency deteriorates
Solution Approach 1:
The patent changes the operational parameter from exact algebraic operations to approximate operations with bounded error. This enables practical implementation of homomorphic encryption by reducing computational complexity and resource requirements while maintaining data security through the cryptographic properties of the encryption scheme
Solution Approach 2:
The patent performs partial algebraic operations with acceptable approximation rather than exact operations. By accepting bounded error in exchange for efficiency, the system makes homomorphic encryption practically implementable for real-world applications where perfect precision is not always necessary
Data Source
AI summary
Disclosed herein are system, method, and computer program product embodiments for performing a set of operations on one or more encrypted numbers to be an approximation of performing an algebraic operation on the one or more encrypted number. A server can receive from a client, a public key of a fully homomorphic encryption scheme and one or more encrypted numbers, and perform a set of operations comprising a square root function, a rectified linear activation function (ReLU), or a multiplicative inverse function on the one or more encrypted numbers to generate an encrypted operational result. The encrypted operational result generated by the set of operations can be an approximation of performing an algebraic operation on the one or more encrypted number. The server can further transmit to the client the encrypted operational result.