Keyed Hash Construction Using FHE for Correlation Intractability
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Solution Overview
Problem
Current cryptographic hash functions struggle to achieve somewhere statistical correlation intractability for efficiently enumerable relations, limiting the development of advanced cryptographic protocols that require strong security guarantees, particularly in applications involving program obfuscation and secure computation.
Innovation Solution
A method for generating a keyed hash function using secret-key fully homomorphic encryption (FHE) that incorporates indistinguishability obfuscation, enabling computations on encrypted data while ensuring enhanced security properties such as somewhere statistical correlation intractability, by constructing a hash function that resists attacks on efficiently enumerable relations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional hash functions are used, then the implementation is simple and widely supported, but they cannot achieve somewhere statistical correlation intractability for efficiently enumerable relations
Solution Approach 1:
The patent combines multiple cryptographic primitives including fully homomorphic encryption schemes, indistinguishability obfuscation, and correlation-intractable hash functions into a unified construction. This merging of cryptographic components enables the system to achieve somewhere statistical correlation intractability for efficiently enumerable relations while maintaining the necessary security properties through the synergistic interaction of these primitives.
Solution Approach 2:
The patent introduces an intermediary mechanism using fully homomorphic encryption to enable computations on encrypted data without decryption. This intermediary layer allows the hash function to operate on encrypted inputs while maintaining security, bridging the gap between computational functionality and cryptographic security in the context of correlation intractability.
2Reliability
If advanced cryptographic protocols requiring strong security guarantees are implemented, then security against sophisticated attacks is improved, but the complexity of the system increases
Solution Approach 1:
The patent segments the cryptographic construction into distinct modular components: the fully homomorphic encryption scheme, the indistinguishability obfuscation mechanism, and the correlation-intractable hash function. This segmentation allows each component to be analyzed and implemented independently, reducing overall system complexity while maintaining strong security guarantees through the combination of these specialized modules.
Solution Approach 2:
The patent utilizes parameter changes in the cryptographic primitives, particularly in the security parameters and circuit complexity parameters, to achieve somewhere statistical correlation intractability. By carefully selecting and adjusting these parameters, the system provides robust security against sophisticated attacks while controlling the complexity through parameter-based security reductions.
3Reliability
If fully homomorphic encryption is used to enable computations on encrypted data, then privacy preservation is improved, but the computational complexity increases
Solution Approach 1:
The patent applies partial homomorphic evaluation by performing computations only on the encrypted hash function outputs rather than all intermediate computations. This partial action approach maintains privacy preservation for the critical hash outputs while reducing the overall computational complexity by avoiding unnecessary encryption operations on all data processing steps.
Data Source
AI summary
The present disclosure provides a method for generating and evaluating a keyed hash function, the method comprising: receiving one or more integer parameters indicating a target input length n and a target output length m for the keyed hash function; receiving a target circuit-size parameter S, wherein the circuit-size parameter S is correlated to a security level of the keyed hash function; generating a hash key, the generated hash key comprising a ciphertext ct of a secret-key fully homomorphic encryption (FHE) scheme, wherein the ciphertext ct is generated by generating a secret key sk for a secret-key FHE scheme, generating the ciphertext ct as an encryption to sk of a message comprising sk concatenated with a string of S zero bits, and storing the ciphertext ct as the generated hash key; and computing a hash output based on the generated hash key ct and an input x.