Elliptic Curve Cryptography Scalar Multiplication Side-Channel Countermeasure
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Solution Overview
Problem
Conventional approaches to countermeasures for simple side-channel attacks in elliptic curve cryptography are not sufficiently optimized, impacting the performance of the system by making observable information dependent on the secret scalar, which can be exploited for timing or power consumption attacks.
Innovation Solution
Implementing an elliptic curve cryptographic scheme that uses Jacobian projective coordinate representation for scalar multiplication, where each iteration performs either doubling or mixed addition of points, with a dummy operation that has a computational cost of one operation, and transforming the result to affine coordinates, making the operations indistinguishable in terms of time and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional scalar multiplication algorithms are used in ECC, then the cryptographic scheme is efficient and fast, but the execution time and power consumption depend on the secret scalar d, making the system vulnerable to simple side-channel attacks
Solution Approach 1:
The patent changes the operational parameters by introducing dummy operations that modify the execution profile of the scalar multiplication algorithm. Specifically, it adds extra operations (such as extra point additions or dummy scalar multiplications) that change the timing and power consumption characteristics without affecting the cryptographic correctness, thereby decoupling the observable side-channels from the secret scalar d
Solution Approach 2:
The patent introduces intermediary dummy operations as mediators between the actual cryptographic computation and the external observer. These dummy operations act as a buffer that masks the true computational path, making it impossible for an attacker to directly observe the relationship between execution characteristics and the secret scalar through operations like point doubling or addition
2Reliability
If dummy operations are added to countermeasure simple side-channel attacks, then security is improved, but the computational cost and execution time increase
Solution Approach 1:
The patent applies partial dummy operations rather than complete masking for all operations. Instead of adding dummy operations for every single computational step, it strategically inserts them at specific points in the algorithm (such as after certain iterations or under specific conditions), providing sufficient security against simple SCA while minimizing the impact on overall execution speed
Solution Approach 2:
The patent segments the scalar multiplication algorithm into distinct phases or iterations, applying dummy operations selectively to certain segments rather than uniformly across the entire computation. This segmentation allows the system to balance security requirements with performance constraints by concentrating countermeasures where they are most effective
Data Source
AI summary
There is provided an elliptic curve cryptographic scheme for permitting secure communications between two or more cryptographic correspondent devices, with a simple side-channel attack countermeasure. The cryptographic scheme includes: transforming a point to Jacobian projective coordinates; constant-time scalar multiplication of the point by a parameter; and transforming the resultant of the scalar multiplication to affine coordinates. The scalar multiplication including: performing iteratively to the value of the parameter either one of: doubling of the point and multiplying any two random field elements; or mixed addition of the point.