Bijective Transformation for Cryptographic Data Masking
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Solution Overview
Problem
Existing methods for protecting sensitive data in electronic circuits from attacks like SPA, DPA, EMA, and DEMA require high-quality random number generators and memory for intermediate results, which are not always feasible.
Innovation Solution
A method using bijective transformation functions to mask secret data during cryptographic calculations, allowing the transformed data to be used in place of the secret data, without the need for random number generators or memory to store intermediate results, by applying a transformation function and its inverse to the data stream.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random numbers are used to mask cryptographic calculations, then security against statistical analysis attacks is improved, but device complexity increases due to requiring high-quality random number generators and additional calculation steps
Solution Approach 1:
The invention extracts the masking function from random number generation and implements it through a deterministic linear function f(x) = ax + b (mod p). This removes the need for random number generators while maintaining the security property of masking intermediate values against statistical analysis attacks.
Solution Approach 2:
The linear function f(x) = ax + b (mod p) acts as an intermediary transformation that masks the secret data during cryptographic operations. This intermediary function provides the necessary obfuscation without requiring random numbers, thereby reducing device complexity while maintaining security.
2Reliability
If random numbers are used to mask cryptographic calculations, then security is improved, but loss of time increases due to additional modular exponentiation calculations and multiplications
Solution Approach 1:
The invention extracts and eliminates the time-consuming random number generation and inverse calculation steps by using a deterministic linear function. This reduces the computational time while maintaining the security masking effect.
Solution Approach 2:
The linear function transformation uses computationally inexpensive operations (multiplication and addition modulo p) compared to modular exponentiation. This replaces expensive cryptographic operations with cheaper arithmetic operations, significantly reducing processing time.
3Reliability
If random numbers are used to mask cryptographic calculations, then security is improved, but loss of energy increases due to additional computational operations
Solution Approach 1:
The linear function transformation uses computationally inexpensive operations that consume minimal energy compared to modular exponentiation. This replaces energy-intensive cryptographic operations with low-energy arithmetic operations, reducing overall energy consumption while maintaining security.
4Reliability
If the transformation function is changed frequently to maintain security, then security against attacks is improved, but productivity decreases due to repeated transformation calculations
Solution Approach 1:
The linear function parameters (a, b, p) can be predetermined and stored, allowing the transformation to be applied efficiently without repeated setup. This preliminary preparation enables frequent transformation function changes without significant productivity loss.
Solution Approach 2:
The invention allows changing parameters (a, b, p) of the linear function to maintain security against attacks. These parameter changes are computationally inexpensive compared to changing the entire transformation structure, enabling frequent updates with minimal impact on processing speed.
Data Source
AI summary
A method of protecting a circuit from attacks aiming to discover secret data used during the execution of a cryptographic calculation by the circuit, by, executing a transformation calculation implementing a bijective transformation function, receiving as input a secret data, and supplying a transformed data, executing a cryptographic calculation receiving as input a data to process and the transformed data, and executing an inverse transformation calculation receiving as input the result of the cryptographic calculation, and supplying a result that the cryptographic calculation would have supplied if it had been applied to the data to process and directly to the secret data, the data to process belong to a stream of a multiplicity of data, the transformed data being supplied as input to the cryptographic calculation for all the data of the stream.