Elliptic Curve Scalar Multiplication Error Detection
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Solution Overview
Problem
Elliptic curve cryptography in electronic devices is vulnerable to attacks that cause faults during cryptographic calculations, making it difficult to detect and prevent the exposure of secret data, especially since current methods only detect errors at the end of the calculation process.
Innovation Solution
Implementing a method in electronic devices that detects the appearance of a point at infinity during intermediate calculations of scalar multiplication in elliptic curve cryptographic systems, activating an error signal if detected, and ensuring error detection only when the number of processed bits is lower than the rank of the most significant bit of the base point, thereby enabling early detection and prevention of fault injections.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If error detection is performed only at the end of cryptographic calculation, then device complexity is reduced, but security reliability deteriorates because secret data may be exposed during intermediate calculations
Solution Approach 1:
The patent implements error detection at intermediate stages of the scalar multiplication process, specifically after processing certain bits of the scalar number. This preliminary detection action occurs before the calculation is complete, allowing early identification of fault injections and preventing exposure of secret data, thus resolving the contradiction between early detection and calculation completion
Solution Approach 2:
The patent divides the scalar multiplication process into segments based on bit processing stages. Error detection is performed at specific segmentation points (after processing bits lower than the rank of the most significant bit of the base point order), allowing targeted detection without requiring continuous monitoring throughout the entire calculation, thereby balancing detection coverage with device complexity
2Reliability
If error detection is performed during intermediate calculations, then security reliability is improved, but calculation time increases due to additional detection steps
Solution Approach 1:
The patent applies partial error detection by monitoring only specific intermediate results during scalar multiplication, rather than continuously monitoring all calculation steps. The detection focuses on critical points where fault injections are most likely to expose secret data, performing detection on a partial basis that balances security improvement with minimal time overhead
Solution Approach 2:
The error detection mechanism leverages the existing calculation structure and intermediate results of the scalar multiplication process. Rather than adding completely independent detection circuits, the system uses the natural flow of computation and checks for anomalies (such as unexpected point values or calculation deviations) at predetermined stages, allowing the calculation process to serve its own detection needs
3Reliability
If fault injection detection is implemented, then security against attacks is improved, but ease of operation deteriorates due to additional monitoring requirements
Solution Approach 1:
The patent introduces an intermediary error detection mechanism that monitors intermediate calculation results without requiring direct intervention or complex user actions. The detection system acts as an intermediary layer between the cryptographic calculation and potential fault injections, automatically identifying anomalies and preventing attack success, thus improving security while maintaining ease of operation through automated monitoring
Data Source
AI summary
A method in an elliptic curve cryptographic system, the method being executed by an electronic device and including a multiplication operation of multiplying a point of an elliptic curve by a scalar number, the point having affine coordinates belonging to a Galois field, the multiplication operation including steps of detecting the appearance of a point at infinity during intermediate calculations of the multiplication operation, and of activating an error signal if the point at infinity is detected and if the number of bits of the scalar number processed by the multiplication operation is lower than the rank of the most significant bit of an order of a base point of the cryptographic system.