Elliptic Curve Cryptography Side-Channel Protection
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Solution Overview
Problem
Existing cryptographic data processing methods on elliptic curves are vulnerable to side-channel attacks, particularly due to variations in operation types that can be observed, such as energy consumption patterns, which can reveal sensitive information.
Innovation Solution
The method involves determining a second point on an elliptic curve using a set of operations that include squaring operations, which are faster than multiplications, while maintaining a periodic repetition of operation types to obscure the specific operations being performed, thereby reducing the time for implementing operations on the elliptic curve without compromising the ability to repeat predefined types of operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If operations on elliptic curves are implemented with varying operation types (multiplications, additions) to perform cryptographic calculations, then cryptographic functionality is achieved, but the varying operation types create observable patterns that make the system vulnerable to side-channel attacks
Solution Approach 1:
The patent applies periodic action by organizing cryptographic operations into atomic blocks that repeat a fixed sequence of operation types (multiplication, addition, opposition, addition) regardless of the actual cryptographic operation being performed. This periodic repetition masks the true operation sequence from side-channel observers, as the observable pattern remains constant while the underlying cryptographic logic varies.
Solution Approach 2:
The patent changes the parameter of operation type sequence from variable to fixed/periodic. By transforming the operation sequence into a predetermined periodic pattern, the patent eliminates the information leakage that would otherwise occur through observation of operation type variations, thereby resolving the vulnerability to side-channel attacks.
2Reliability
If dummy operations are added to create periodic repetition of operation types to prevent side-channel attacks, then security against side-channel attacks is improved, but the computational time increases due to additional operations
Solution Approach 1:
The patent makes the atomic block universal by designing it to serve multiple cryptographic operations (both point doubling and point addition) through the same sequence of operation types. This multi-functionality eliminates the need for separate operation sequences for different cryptographic primitives, reducing overall computational overhead while maintaining security.
Solution Approach 2:
The patent changes the operational approach from using operation-specific sequences to a unified periodic sequence. By transforming the operation sequence into a fixed periodic pattern that works for multiple cryptographic operations, the patent reduces the total number of operations needed while maintaining side-channel protection.
3Ease of operation
If standard multiplication operations are used for all Galois field operations, then operational flexibility is maintained, but computational speed decreases compared to using squaring operations
Solution Approach 1:
The patent applies local quality by optimizing specific operations within the atomic block. When the operands are identical (as in certain steps of the cryptographic algorithm), the patent uses squaring operations which are computationally faster than general multiplication. This localized optimization maintains operational flexibility while improving speed where applicable.
Data Source
AI summary
The method involves determining a point i.e. scalar product, on an elliptic curve represented using three elements e.g. jacobian projective coordinates, of a Galois body from another point i.e. integer, on the elliptic curve represented using other three elements e.g. jacobian projective coordinates. An assembly of successive operations is implemented, where a sequence of the operations forms a periodic repetition of multiple types of operations including a multiplication, addition and squaring in the body. An independent claim is also included for an electronic entity for cryptographic processing of data.