Post-Quantum Electronic Signatures Using an Infinite Hash Chain

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Solution Overview

Problem

Conventional electronic signature methods, such as RSA and DSA, are vulnerable to quantum computing, and hash-based signature (HBS) algorithms face limitations like finite key pair usage, increased message length, and inefficient verification due to expanding tree hierarchies.

Innovation Solution

A method using an infinite hash chain to generate multiple public key-private key pairs, with verification factors derived from a hash chain, ensuring constant verification values and secure, post-quantum electronic signatures without tree expansion limits.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Duration of action of moving object

If the tree hierarchy is expanded to increase the number of signature algorithm uses, then the number of applications increases, but the length of electronically signed message increases and verification efficiency decreases

Engineering Contradiction:

Improvenumber of signature algorithm usesVSAvoidlength of electronically signed message

Core Design Contradiction:

Duration of action of moving objectVSLength of stationary object

Solution Approach 1:

The patent segments the verification process by introducing incremental verification factors that allow verification to proceed step-by-step through the hash chain, rather than requiring all verification values to be present simultaneously. This enables the system to support unlimited signature uses while keeping individual message lengths constant, as only the current verification factor needs to be transmitted with each signed message.

Inventive Principle:

Principle #1Segmentation

2Duration of action of moving object

If the tree hierarchy is expanded to increase the number of signature algorithm uses, then the number of applications increases, but verification efficiency decreases due to increased computational load

Engineering Contradiction:

Improvenumber of signature algorithm usesVSAvoidverification efficiency

Core Design Contradiction:

Duration of action of moving objectVSProductivity

Solution Approach 1:

The patent applies preliminary action by pre-computing and storing the entire infinite hash chain in the verifier's memory during initialization. This allows the verification process to simply look up pre-computed verification factors rather than performing complex hierarchical computations, dramatically improving verification efficiency while supporting unlimited signature uses.

Inventive Principle:

Principle #10Preliminary action

3Device complexity

If a finite number of one-time public key-private key pairs are determined according to the hierarchical depth of the tree structure, then the structure is manageable, but the number of applications of signature algorithm is finite

Engineering Contradiction:

Improvetree structure manageabilityVSAvoidnumber of signature algorithm uses

Core Design Contradiction:

Device complexityVSDuration of action of moving object

Solution Approach 1:

The patent transforms the static, finite tree structure into a dynamic, unlimited hash chain structure. Instead of being constrained by a fixed hierarchical depth, the system uses a sequential hash chain that can be extended indefinitely. The verifier maintains the entire chain dynamically, allowing unlimited signature algorithm applications while keeping the structure manageable through sequential rather than hierarchical organization.

Inventive Principle:

Principle #15Dynamics

4Reliability

If all hash values assigned to tree nodes are calculated and stored in advance, then electronic signature verification can be performed, but computational and memory loads increase

Engineering Contradiction:

Improveelectronic signature verification capabilityVSAvoidcomputational and memory load

Core Design Contradiction:

ReliabilityVSQuantity of substance

Solution Approach 1:

The patent extracts only the essential verification factor from the complete hash chain structure and transmits it with each signed message. Instead of requiring all tree node hash values to be present, the system extracts and transmits only the current verification factor (a single hash value from the chain), dramatically reducing the quantity of data that needs to be transmitted and processed while maintaining verification reliability.

Inventive Principle:

Principle #2Taking out (Extraction)

Data Source

PatentUS12592830B2Method, apparatus, and system for post-quantum electronic signature based on infinite hash function

Publication Date: 2026.03.31 IND ACADEMIC COOP FOUND YONSEI UNIV

AI summary

The present disclosure relates to a method and apparatus for electronic signature and, more particularly, to a method and apparatus for performing safe, post-quantum electronic signature using infinite continuity of a hash function and one-time key pairs. A method for electronic signature using a computing device according to one embodiment of the present disclosure comprises obtaining a message to be electronically signed; obtaining a plurality of public keys generated by a key generation algorithm, and based on the plurality of public keys, generating a signature verification value for the message, wherein the signature verification value includes at least one verification factor generated based on the different public keys or a value obtained by merging the different public keys.