Randomized Modulus for Side Channel Attack Prevention in IC Cards
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Solution Overview
Problem
Existing semiconductor devices for primality determination in RSA encryption are vulnerable to side channel attacks due to the leakage of prime numbers during power residue calculation, as the power consumption patterns reveal the prime number values, especially when incremental generation methods are used.
Innovation Solution
Randomizing the modulus in power residue calculations by using a product of a prime number candidate and a random number as the modulus, thereby making the power consumption independent of the prime number candidate, preventing leakage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If incremental prime number generation is used to improve efficiency, then productivity is improved, but security is worsened due to power consumption patterns revealing prime number values
Solution Approach 1:
The patent changes the parameter of the modulus used in power residue calculation from the prime number candidate itself to a randomized value. By randomizing the modulus parameter, the power consumption pattern no longer directly reveals the prime number candidate, thus preventing side channel attacks while maintaining the efficiency of incremental generation
Solution Approach 2:
The patent introduces a randomized modulus as an intermediary between the prime number candidate and the power residue calculation. This intermediary masks the direct relationship between the prime number and the calculation process, preventing attackers from inferring prime number values through power consumption analysis
2Reliability
If the exponent is randomized to disturb power consumption, then security is improved, but leakage cannot be completely prevented because the modulus is not randomized
Solution Approach 1:
The patent extends randomization from just the exponent parameter to include the modulus parameter as well. By randomizing both parameters involved in the power residue calculation, the patent achieves complete masking of power consumption patterns, preventing any information leakage about the prime number candidate
3Object-affected harmful factors
If the modulus is randomized using an arbitrary random number, then power consumption is disturbed, but the result of power calculation changes and primality determination fails
Solution Approach 1:
The patent changes the modulus parameter to a randomized value while systematically adjusting the exponent parameter to compensate. This coordinated parameter change ensures that the power residue calculation result remains valid for primality determination while the power consumption pattern is sufficiently disturbed to prevent side channel attacks
Data Source
AI summary
In power residue calculation in the primality determination, in addition to the conventional randomization of an exponent, a modulus is also randomized. A random number generated by a random number generator is set to a randomizing number, and is input to a modulus generator and an exponent generator. The modulus generator and the exponent generator randomize a prime number candidate P using the randomizing number to generate a randomized modulus R1 and exponent R2. Using the randomized modulus R1 and exponent R2, the power residue calculation for primality determination is executed, and based on the result, the primality of the prime number candidate P is determined. The power consumption during the primality determination of a semiconductor device becomes noncorrelated with a value of a prime number candidate to be determined, and the leakage of a prime number due to side channel attacks can be prevented.