Abelian Ciphertext Metadata Encoding via Z Coordinate Segmentation

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Solution Overview

Problem

Elliptic Curve Cryptography (ECC) operations, particularly in projective coordinate representation, incur expensive modular inversions, and existing methods lack efficient mechanisms to embed metadata into ciphertext without altering its format or size.

Innovation Solution

Encoding metadata into projective coordinates of elliptic curve-based ciphertext by varying the Z value, allowing metadata representation without unique constraints, thus enabling key version management and attribute association within the same data structure as ciphertext.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of information

If metadata is embedded into ciphertext using existing methods, then metadata can be associated with ciphertext, but the format or size of ciphertext is altered

Engineering Contradiction:

Improvemetadata embeddingVSAvoidciphertext format

Core Design Contradiction:

Loss of informationVSShape

Solution Approach 1:

The ciphertext is segmented into projective coordinate components (X, Y, Z), where the Z coordinate is further segmented to embed metadata. This allows metadata to be embedded within the existing structure without altering the overall ciphertext format or size.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Metadata is embedded in the Z dimension of the projective coordinates, which is an existing dimensional component of the ciphertext structure. This approach adds information in another dimension without expanding the overall data structure.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Loss of information

If metadata is embedded into ciphertext, then key version management is enabled, but additional storage consumption occurs

Engineering Contradiction:

Improvekey version metadataVSAvoidstorage consumption

Core Design Contradiction:

Loss of informationVSQuantity of substance

Solution Approach 1:

The metadata and ciphertext are merged into a single data structure by embedding the metadata within the Z coordinate of the projective coordinates. This combining eliminates the need for separate storage of metadata, thus avoiding additional storage consumption.

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The Z coordinate of the projective coordinates serves multiple functions: it is part of the cryptographic structure and simultaneously serves as a container for metadata. This multi-functionality allows the same data structure to fulfill both cryptographic and information storage roles without increasing storage requirements.

Inventive Principle:

Principle #6Universality (Multi-functionality)

3Productivity

If ECC operations are performed in projective coordinate representation, then computational efficiency is improved, but expensive modular inversions are incurred

Engineering Contradiction:

Improvecomputational efficiencyVSAvoidmodular inversion cost

Core Design Contradiction:

ProductivityVSUse of energy by moving object

Solution Approach 1:

The metadata is embedded in the Z coordinate during the encryption process itself, before any decryption operations occur. This preliminary embedding ensures that when decryption happens, the metadata is already available in the correct format, eliminating the need for additional processing or expensive modular inversions to extract it later.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS11146397B2Encoding abelian variety-based ciphertext with metadata

Publication Date: 2021.10.12 MICRO FOCUS LLC

AI summary

A technique includes encrypting plaintext to provide a set of projective coordinates that represents a point of an abelian variety curve and represents ciphertext. The technique includes encoding the projective coordinates with metadata, which is associated with the ciphertext.