ECDSA Signature Precomputation for Low Latency ITS

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Solution Overview

Problem

Existing Vehicle-Originating Broadcast (VOB) systems in Intelligent Transportation Systems face challenges in generating digital signatures for Basic Safety Messages within the stringent 40 ms time budget, which is not acceptable for low latency requirements, especially when using less powerful hardware in secure environments for ECDSA signature generation.

Innovation Solution

The proposed solution involves pre-computing portions of the ECDSA signature, such as using a dummy hash or setting the hash to zero, to optimize signature generation without modifying the existing ECDSA computing engine, allowing for completion of the signature outside the secure environment to meet the low latency requirements.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If ECDSA signature generation is performed in a secure environment with less powerful hardware, then security requirements are satisfied, but signature generation latency increases to unacceptable levels

Engineering Contradiction:

ImprovesecurityVSAvoidsignature generation latency

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent applies preliminary action by pre-computing the modular inverse of k (k^-1 mod n) before the actual signature generation. This pre-computed value is stored and reused during the signing process, eliminating the need to perform computationally expensive modular inversion operations during the time-critical signature generation phase, thus reducing latency while maintaining security

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent segments the signature generation process into distinct phases: a secure pre-computation phase where k^-1 is calculated and stored, and a faster signing phase where the pre-computed value is utilized. This segmentation allows computationally intensive operations to be separated from time-critical operations, resolving the contradiction between security requirements and latency constraints

Inventive Principle:

Principle #1Segmentation

2Reliability

If the minimum message interval is set to 40 ms as per security standards, then security compliance is achieved, but the effective signature generation latency remains unacceptably high

Engineering Contradiction:

Improvesecurity complianceVSAvoidmessage transmission rate

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

By pre-computing and caching the modular inverse k^-1 mod n before message signing, the system reduces the actual signing time to well below 10 ms. This allows the system to maintain the 40 ms security-compliant interval while having sufficient headroom to generate signatures much faster, effectively improving productivity without compromising security compliance

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS10135621B2Method to reduce the latency of ECDSA signature generation using precomputation

Publication Date: 2018.11.20 NXP BV

AI summary

In order to reduce latency of elliptical curve digital signature generation a portion of the digital signature is pre-calculated before receipt of the message hash using an unmodified ECDSA computing engine. After the message hash is received, the digital signature is completed without using the ECDSA computing engine. Applications include generating digital signatures for the safety messages in Intelligent Transport Systems.