One-Bit MACs for XOR Key Integrity in Garbled Circuits
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Solution Overview
Problem
XOR encryption, widely used in cryptography due to its efficiency, is highly malleable and susceptible to malicious modification, particularly in large-scale private database systems where bit-flipping can occur undetected, and existing solutions are inefficient and costly in terms of circuit complexity and storage requirements.
Innovation Solution
Generating a separate one-bit message authentication code for each bit of the XOR encryption key using a unique identifier and a MAC key, allowing efficient verification within garbled-circuit secure computations to prevent malicious modification while minimizing storage needs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If XOR encryption is used for efficient cryptographic operations, then encryption efficiency is improved, but susceptibility to malicious modification increases
Solution Approach 1:
The patent introduces message authentication codes (MACs) as an intermediary mechanism to verify the integrity of XOR encryption keys. The MAC system acts as a mediator between the encryption operation and the verification process, allowing efficient XOR encryption to proceed while providing independent verification that the keys have not been maliciously modified. This resolves the contradiction by adding a separate verification layer without compromising the efficiency of the core encryption operation.
2Reliability
If traditional message authentication codes are applied to verify encryption keys, then protection against malicious modification is improved, but circuit complexity and storage requirements increase
Solution Approach 1:
The patent segments the verification process by generating separate one-bit MACs for each individual bit of the encryption key rather than using a traditional MAC that processes the entire key as a single unit. This segmentation allows the verification to be performed in parallel across multiple bits, significantly reducing the circuit complexity and storage requirements while maintaining comprehensive protection against malicious modification of any key bit.
Solution Approach 2:
The patent changes the parameter of the MAC output from traditional multi-bit codes to one-bit MACs. This parameter change fundamentally reduces the storage requirements and circuit complexity, as each bit of the encryption key is verified with a single bit rather than requiring storage and processing of multiple-bit authentication codes. The one-bit MAC approach maintains verification reliability while dramatically simplifying the implementation.
3Speed
If verification time is reduced to milliseconds, then operational speed is improved, but verification thoroughness may be compromised
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing the one-bit MACs for each bit of the encryption key before the actual verification is needed. During operation, the verification process simply compares the pre-computed MACs with freshly computed MACs from the received key, enabling millisecond-level verification without compromising thoroughness. The comprehensive verification is achieved because each key bit has its own pre-prepared authentication code ready for immediate comparison.
Data Source
AI summary
A message and an identifying parameter associated with the message are obtained. The message comprises a plurality of units. A plurality of one-unit message authentication codes is generated, wherein each one-unit message authentication code corresponds to a respective unit of the plurality of units of the message, and wherein each one-unit message authentication code is generated based on the identifying parameter associated with the message, a given one of the plurality of units, and the position of the given unit in the message. Verification of each unit of the message may then be efficiently performed inside a method of secure computation such as, by way of example only, a garbled circuit.