Elliptic Curve Coefficient Randomization for Side-Channel Resistance
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Solution Overview
Problem
Existing elliptic curve cryptosystems face significant side-channel leakage issues during scalar point multiplication, which can be exploited by attackers to recover secret keys, and current countermeasures do not adequately protect against leakage of elliptic curve coefficients, leading to vulnerabilities in power and timing information.
Innovation Solution
The introduction of elliptic curve coefficient randomization, which involves generating a randomization numerical input to compute a new, substantially equivalent elliptic curve representation, thereby masking computations and reducing side-channel leakage with minimal overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If elliptic curve arithmetic is implemented without countermeasures, then computational efficiency is maintained, but side-channel leakage occurs enabling secret key recovery
Solution Approach 1:
The patent introduces a randomization coefficient as an intermediary element that masks the relationship between intermediate computation values and secret keys. This coefficient acts as a mediator that transforms the computation to hide side-channel leakage while maintaining cryptographic correctness, resolving the contradiction between security improvement and complexity increase
Solution Approach 2:
The patent changes the parameter space by introducing randomization coefficients that transform the elliptic curve arithmetic operations. By varying these coefficients randomly, the computation maintains equivalent cryptographic results while obscuring the timing and power consumption patterns that would otherwise leak secret information
2Reliability
If existing countermeasures are applied, then some side-channel protection is achieved, but leakage of elliptic curve coefficients remains vulnerable
Solution Approach 1:
The randomization coefficient serves as a mediator that specifically addresses coefficient leakage by introducing an additional layer of obfuscation in the computation. This intermediary element ensures that even if intermediate values are observed, the original coefficient values cannot be recovered, eliminating the information loss vulnerability
Solution Approach 2:
The patent applies preliminary randomization of coefficients before they are used in the elliptic curve arithmetic operations. This preliminary action prevents coefficient leakage from occurring in the first place by ensuring that the coefficients are already obscured by randomization when the computation begins
3Reliability
If randomness is added to elliptic curve arithmetic, then side-channel leakage is suppressed, but computational overhead increases
Solution Approach 1:
The patent changes the computational parameters by using field multiplication with randomization coefficients, which is a standard operation in elliptic curve cryptography. By framing the solution in terms of existing efficient field operations rather than introducing new computational primitives, the patent achieves side-channel protection without significant productivity loss
Solution Approach 2:
The patent applies randomization only to the coefficient values rather than the entire computation space. This partial action provides sufficient side-channel protection by randomizing only the critical leakage points while avoiding the excessive computational overhead that would result from randomizing all operation parameters
Data Source
AI summary
A computer processing system that includes an elliptic curve computational unit in a computer processing device operably configured to perform an elliptic curve arithmetic operation with a sequence of field operations, receive an elliptic curve numerical input that includes at least one elliptic curve coefficient of an elliptic curve that is operably utilized in the elliptic curve arithmetic operation,receive an elliptic curve coefficient randomization numerical input that is operably configured for use in the elliptic curve arithmetic operation, compute a new and substantially equivalent elliptic curve representation for the elliptic curve coefficient of the elliptic curve by performing a field operation with the elliptic curve numerical input and the elliptic curve coefficient randomization numerical input, and utilize the new and substantially equivalent elliptic curve representation in the sequence of field operations, and having an arithmetic output port operably configured to output a numerical result therefrom.