Modular Exponentiation Circuit Fault Injection Protection
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Solution Overview
Problem
Electronic circuits executing modular exponentiation operations are vulnerable to fault-injection attacks, particularly the C-Safe and M-Safe Error Attacks, which exploit the circuit's operations to deduce secret data by injecting faults during multiplication steps.
Innovation Solution
The method involves using two registers (R0 and R1) and a temporary register (T) to alternate the roles of the multiplier and multiplicand based on the exponent bit, ensuring that any fault injection affects the final result, thereby masking the attack's impact, and utilizing a temporary register to restore values before squaring operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard modular exponentiation algorithms are used, then calculation efficiency is maintained, but the circuit becomes vulnerable to fault-injection attacks that can reveal secret data
Solution Approach 1:
A third temporary register is introduced as an intermediary to store values during multiplication operations. This mediator register allows the circuit to perform secure modular exponentiation by temporarily holding operands and results, preventing fault-injection attacks from directly exposing secret data while maintaining the mathematical correctness of the computation.
Solution Approach 2:
The computation is divided into distinct phases (multiplication and squaring) that are executed alternately based on exponent bits. By segmenting the algorithm into discrete, controllable steps with clear state transitions, the circuit can implement security measures at each phase boundary without compromising overall efficiency.
2Loss of information
If fault injection is applied during multiplication steps, then secret data can be deduced through error analysis, but the calculation process is disrupted
Solution Approach 1:
The circuit performs preliminary validation checks and uses redundant register operations to cushion against potential fault-injection attacks. By anticipating possible attacks and preparing countermeasures in advance (such as verifying intermediate results and using temporary registers for additional validation), the system can detect and neutralize faults before they compromise secret data or calculation correctness.
Data Source
AI summary
A method of protecting a modular exponentiation calculation executed by an electronic circuit using a first register and a second register, successively comprising, for each bit of the exponent: a first step of multiplying the content of one of the registers, selected from among the first register and the second register according to the state of the bit of the exponent, by the content of the other one of the first and second registers, placing the result in said one of the registers; a second step of squaring the content of said other one of the registers by placing the result in this other register, wherein the content of said other one of the registers is stored in a third register before the first step and is restored in said other one of the registers before the second step.