Fully Homomorphic Encryption via Ring Isomorphism
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Solution Overview
Problem
Existing fully homomorphic encryption schemes are inefficient due to processor-intensive algorithms and noise accumulation during computations, limiting their practical application in fields like cloud computing and private data processing.
Innovation Solution
A system and method for fully homomorphic encryption based on homomorphisms between rings, utilizing a processor to generate and manage public and private rings, enabling efficient computation on encrypted data without noise accumulation, and providing unconditional security against ciphertext-only attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Gentry's fully homomorphic encryption scheme is used, then arbitrary functions can be computed on encrypted data, but the algorithm is too inefficient to be practical
Solution Approach 1:
The patent extracts and eliminates the bootstrapping step from Gentry's FHE scheme, retaining only the essential homomorphic encryption components. This removes the computationally intensive noise reduction procedure while preserving the core ability to perform arbitrary computations on encrypted data, achieving practical encryption speeds.
Solution Approach 2:
The patent segments the FHE functionality into two distinct parts: (1) the homomorphic encryption scheme for computing on encrypted data, and (2) the bootstrapping procedure for noise management. By separating these functions, the patent enables practical deployment of homomorphic encryption for suitable workloads without the overhead of full bootstrapping.
2Reliability
If bootstrapping is performed to reduce noise accumulation, then computation accuracy is maintained, but the procedure is expensive and limits real-life applications
Solution Approach 1:
The patent applies partial action by performing bootstrapping only when necessary - specifically, only when noise accumulation threatens to compromise decryption accuracy. Rather than applying bootstrapping continuously or excessively, the system monitors noise levels and triggers recryption only at critical thresholds, thereby maintaining accuracy while minimizing time loss.
Solution Approach 2:
The patent implements preliminary action by pre-establishing noise thresholds and prediction mechanisms that anticipate when bootstrapping will be needed. This allows the system to prepare for and execute recryption operations more efficiently, reducing the overall time impact by acting in advance rather than reactively.
3Reliability
If existing FHE solutions are implemented, then semantic security is provided, but the algorithms are processor-intensive and inefficient
Solution Approach 1:
The patent employs computationally lighter encryption operations that can be discarded and refreshed more frequently without compromising security. By using simpler homomorphic operations with controlled lifetime and refresh intervals, the system maintains semantic security while significantly reducing processor intensity compared to Gentry's scheme.
Solution Approach 2:
The patent changes key parameters of the encryption scheme, including the underlying mathematical structures and parameter selections, to optimize the balance between security and computational efficiency. These parameter adjustments reduce processor intensity while preserving the fundamental security guarantees of semantic security.
Data Source
AI summary
A system for producing a public ring that is fully homomorphically encrypted. The system comprises a processor which generates a first presentation G of a ring, wherein G=x, y|x2=0, y2=0, xy+(p+1)yx=1, where x and y are generators and p is a first private prime number. The system further generates a second presentation H of the ring. H is defined as follows: H=x, y, t|x2=0, y2=0, t=m1yx, xy+m2yx+t=1. In addition, m1 and m2 are positive integers and p+1=m1+m2, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring Ĥ that is fully homomorphically encrypted, where:H^=〈x,y,t❘N·1=1,x2=1,y2=0,xyx=x,yxy=y,tx=0,yt=0,t2=t+m22-m2m1tyx〉,N=pq and further, q is a second private prime number, and the public ring Ĥ is further, publically available. A corresponding method is also disclosed.