Key Rotation Verification Without Decryption Using Convex Set Membership
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Solution Overview
Problem
Existing methods for verifying key rotation in cryptographic systems are insecure and computationally intensive, requiring decryption and access to plaintext, which poses security risks and inefficiencies, especially in large databases.
Innovation Solution
A method that uses a function family with a convex output space to verify key rotation without decryption by computing divergence between ciphertexts encrypted with different keys and employing a membership oracle to determine if they belong to the same convex set, thus validating the same plaintext without decrypting the ciphertexts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If decryption is used to verify key rotation, then verification accuracy is improved, but security is worsened and computational overhead increases
Solution Approach 1:
The patent introduces a membership oracle as an intermediary mechanism that verifies key rotation by checking whether ciphertexts belong to the same convex set without requiring decryption. This oracle acts as a mediator between the verification need and the encrypted data, providing accurate verification while maintaining security boundaries.
Solution Approach 2:
The patent replaces the mechanical decryption process with a mathematical verification approach using convex sets and membership oracles. Instead of mechanically decrypting and comparing plaintexts, the system uses mathematical properties of convex sets to verify key rotation, eliminating the security risks and computational overhead of decryption.
2Measurement precision
If decryption is used to verify key rotation, then verification accuracy is improved, but computational complexity is worsened
Solution Approach 1:
The patent extracts the essential verification property from the plaintext by using convex set membership. Instead of working with the entire plaintext data that requires decryption, the system extracts and verifies only the membership property in the convex set, significantly reducing computational complexity while maintaining verification accuracy.
Solution Approach 2:
The patent performs partial verification by checking only the convex set membership property rather than fully decrypting and verifying the entire plaintext. This partial action approach provides sufficient verification for key rotation while avoiding the excessive computational cost of complete decryption.
3Measurement precision
If decryption is used to verify key rotation, then verification completeness is improved, but information leakage is worsened
Solution Approach 1:
The membership oracle serves as a secure intermediary that provides verification completeness without exposing plaintext information. It mediates between the verification requirement and the encrypted data, ensuring that no information about the plaintext leaks during the verification process.
Solution Approach 2:
The patent converts the potential harm of information leakage into a benefit by using the mathematical structure of convex sets. The encryption process itself, which normally hides information, is leveraged to provide verification through membership testing, turning the secrecy property into a verification mechanism.
Data Source
AI summary
Key rotation verification without decryption is provided. Two ciphertext inputs encrypted from a plaintext input by an encryption function using different cryptographic keys are input, wherein the encryption function is selected from a function family having an output space of one or more convex sets. A divergence between the two ciphertext inputs is computed. A membership oracle is executed on the two ciphertext inputs, wherein the two ciphertext inputs are determined to be members of the same convex set of the one or more convex sets if the computed divergence satisfies a separation condition. The two ciphertext inputs are validated to both correspond to the same plaintext input, responsive to determining that the two ciphertext inputs are members of the same convex set, wherein the two ciphertext inputs do not correspond to the same plaintext input if the two ciphertext inputs are not members of the same convex set.