Elliptic Curve Cryptography Countermeasure Against Side-Channel Attacks
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Solution Overview
Problem
Elliptic curve cryptography is vulnerable to side-channel attacks, particularly the Big-Mac attack, which can reveal secret scalars by observing electrical consumption patterns, compromising the security of protected data.
Innovation Solution
A countermeasure method that modifies the coordinates of critical points during scalar multiplication operations by multiplying them with a predefined constant element c, chosen to prevent intervention during successive multiplications, and updates these coordinates using projective equivalence or isomorphism to maintain security without randomization, thus thwarting horizontal attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard ECSM operations are used, then cryptographic functionality is achieved, but the circuit becomes vulnerable to side-channel attacks through power consumption analysis
Solution Approach 1:
The patent modifies the coordinates of critical points by multiplying them with powers of a constant element c during each iteration of the scalar multiplication operation. This parameter transformation changes the actual values processed in the circuit without changing the mathematical result, thereby altering the power consumption pattern to prevent attackers from correlating consumption with secret scalar bits
Solution Approach 2:
The constant element c acts as an intermediary that transforms the coordinates of critical points. By introducing this intermediate transformation step, the patent decouples the relationship between the secret scalar and the actual values processed in the circuit, making power analysis attacks ineffective while preserving the correctness of the cryptographic operation
2Reliability
If randomization techniques are applied to counter side-channel attacks, then security is improved, but device complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-defining the constant element c and pre-calculating its powers before the scalar multiplication operation begins. This preparation eliminates the need for complex randomization mechanisms during execution, as the deterministic transformation with pre-computed powers achieves the same security goal with simpler implementation
Solution Approach 2:
The patent introduces dynamics by making the transformation factor variable across iterations - using different powers of c (c^i) in each iteration step. This dynamic transformation adapts the obfuscation strength throughout the computation process while maintaining a relatively simple implementation structure compared to full randomization approaches
Data Source
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AI summary
The subject of the invention is a countermeasure method for an electronic component implementing a public-key elliptic curve cryptography algorithm the elliptic curve E of which is defined over a body K, said method comprising an iterative scalar multiplication operation allowing a point [k]P to be obtained from a point P on the curve E and an integer k that must be kept secret, the electrical power consumption of the electronic component depending on the value taken by at least one point, which is said to be critical, used in said operation for iteratively determining the point [k]P. The method comprises: a step (500) of providing at least one power of an element c of K, which element is preset, constant, nonzero and different from one; a step of initialising (501) coordinates of at least one critical point to a preset value; and a step of implementing the operation of scalar multiplication (502), the coordinates associated with at least one critical point being modified in each iteration by multiplying at least one of the coordinates of this point by the at least one power of the element c obtained in the providing step (500).