Quasi-Cyclic LDPC Coding for Secure Error-Correcting Communication

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Solution Overview

Problem

Existing secure communication methods fail to effectively combine cryptographic encoding and low-density parity check (LDPC) encoding to enhance privacy, as eavesdroppers can exploit error correction capabilities to break encryption.

Innovation Solution

The method involves generating pseudorandom seed values to initialize pseudorandom number generators, creating binary root matrices, and using these to generate quasi-cyclic LDPC codes that intertwine with cryptographic codes, making it difficult for eavesdroppers to perform error correction and cryptanalysis simultaneously.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If cryptographic encoding and LDPC encoding are combined to enhance privacy, then security is improved, but eavesdroppers can exploit error correction capabilities to break encryption

Engineering Contradiction:

ImprovesecurityVSAvoidvulnerability to cryptanalysis

Core Design Contradiction:

ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The patent merges cryptographic encoding and LDPC encoding into a unified hybrid encoding scheme where both functions are performed simultaneously through a single encoding process, making it difficult for eavesdroppers to separate and exploit either function independently

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The encoding process is segmented into distinct cryptographic and error correction components that are interleaved at the bit level, creating a structure where error correction bits are cryptographically protected and cryptographic bits have embedded error correction, preventing attackers from isolating vulnerable components

Inventive Principle:

Principle #1Segmentation

2Reliability

If error correction capabilities are provided to handle channel errors, then communication reliability is improved, but eavesdroppers can use these capabilities to perform cryptanalysis

Engineering Contradiction:

Improvecommunication reliabilityVSAvoidaid to eavesdropper

Core Design Contradiction:

ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The patent introduces cryptographic encoding as an intermediary layer between the message and error correction encoding, where the cryptographic transformation obscures the structure of the message before error correction is applied, preventing eavesdroppers from using error correction algorithms to recover the original message structure

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

Cryptographic encoding is performed as a preliminary action before error correction encoding is applied to the message bits, establishing a secure foundation that protects the message structure from being exploited by subsequent error correction processes performed by eavesdroppers

Inventive Principle:

Principle #10Preliminary action

3Ease of manufacture

If encryption and error correction are separated, then implementation is simplified, but security is compromised as eavesdroppers can exploit error correction

Engineering Contradiction:

Improveimplementation simplicityVSAvoidsecurity

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The patent combines encryption and error correction into a single hybrid encoding process that can be implemented as one unified algorithm, maintaining implementation simplicity while achieving both security and error correction goals simultaneously through integrated processing steps

Inventive Principle:

Principle #5Merging (Combining)

4Reliability

If cryptographic codes and error correction codes are intertwined, then privacy is enhanced, but device complexity increases

Engineering Contradiction:

ImproveprivacyVSAvoidencoding complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent employs dynamic encoding where the specific encoding parameters and transformations are determined by pseudorandom sequences generated from shared secret keys, allowing the encoding structure to adapt dynamically while maintaining a consistent underlying algorithm that can be efficiently implemented

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The patent changes encoding parameters such as the specific permutation patterns and mixing operations based on the shared secret key, allowing the same basic encoding algorithm to produce different secure encodings for different communication sessions without increasing the fundamental complexity of the encoding mechanism

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS11265012B1Methods of secure communication using low-density parity check coding

Publication Date: 2022.03.01 GOVERNMENT OF THE UNITED STATES AS REPRESENTED BY THE DIRECTOR NAT SECURITY AGENCY

AI summary

A method of transmitting a message includes, for each data block, generating a root matrix using a generator, generating a quasi-cyclic matrix H using the root matrix, encoding the block using H to create a codeword, and transmitting the codeword. The root matrix includes three submatrices: an identity matrix in an upper-left-hand portion of the root matrix, an identity matrix in a lower-left-hand portion of the root matrix, and a circulant matrix in a right-hand portion of the root matrix. The circulant matrix equals the sum of an identity matrix and an identity matrix with rows shifted once to the right. Generating H includes expanding the root matrix by replacing 0 elements in the root matrix by a square matrix of 0 elements and replacing 1 elements in the root matrix by a shifted diagonal matrix. Non-zero elements of the diagonal matrix are selected from GF(q) based on the generator.