Authenticated Error-Correcting Codes for Adversarial Channels
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Solution Overview
Problem
Existing error correcting codes, such as Reed-Solomon codes, face inefficiencies in encoding and decoding times, especially over adversarial channels, where selective corruption can prevent decoding, and there is a need for secure authenticated codes that can withstand computationally bounded adversarial channels.
Innovation Solution
The development of authenticated error correcting codes using Luby Transform (LT) codes, Raptor codes, and block codes that incorporate pseudo-random number generators (PRNGs) and message authentication codes (MACs to securely encode and decode messages, ensuring resilience against adversarial corruption while maintaining linear or quasi-linear time complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Reed-Solomon codes are used for error correction, then strong error correcting capacity is achieved, but encoding time becomes quadratic in input size
Solution Approach 1:
The patent segments the encoding process into two distinct stages: first applying an authenticated code to provide security and error detection, then applying an erasure code for efficient decoding. This segmentation allows each code to operate optimally within its strength, avoiding the quadratic complexity of Reed-Solomon while maintaining strong error correction through the combination of authentication and erasure correction capabilities.
2Loss of time
If fountain codes are used to achieve linear time encoding and decoding, then encoding speed is improved, but security against adversarial channels is lost
Solution Approach 1:
The patent merges two previously separate cryptographic functions into a unified code construction: authenticated codes (for security and error detection) and erasure codes (for efficient decoding). This merging creates a hybrid system that achieves both linear-time encoding/decoding from the erasure code component and security against computationally bounded adversaries from the authenticated code component, resolving the contradiction between speed and security.
3Reliability
If authenticated codes are added to provide security against adversarial channels, then security is improved, but device complexity increases
Solution Approach 1:
The patent introduces an intermediary authentication layer that sits between the message and the erasure code. This intermediary authenticated code verifies the integrity of encoded symbols and provides security guarantees, while the underlying erasure code handles the complex decoding operations. The intermediary structure simplifies the overall system by separating security concerns from decoding complexity, making each component more manageable.
Data Source
AI summary
Methods and apparatus are provided for encoding and decoding via authenticated error correcting codes, such as secure LT codes, secure Raptor codes, block codes and/or rateless codes. Encoded symbols are generated via an authenticated error correcting code by applying a Luby Transform (LT) code to a plurality of message symbols to produce one or more intermediate symbols using a pseudo random number generator (PRNG) to select the plurality of message symbols to combine to produce the intermediate symbols; encrypting the intermediate symbols to produce encrypted symbols; computing an authentication value, such as a message authentication code (MAC), over one or more of the one or more encrypted symbols; and appending the authentication value to the corresponding encrypted symbols to form the encoded symbols. Block scalable and random scalable constructions are also provided, as well as decoding techniques for all of the constructions.