Cryptographic Device Fault Injection Protection via Group Segmentation
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Solution Overview
Problem
Existing cryptographic systems are vulnerable to fault injection attacks, which exploit modular operations in RSA and ECC algorithms, compromising the security of cryptographic operations by allowing attackers to infer secret keys or system parameters.
Innovation Solution
A cryptographic device and method that transform modular operations by determining intermediary and final groups, mapping the base to auxiliary elements and bases within these groups, and performing elementary operations to execute modular operations in a way that randomizes results, making it difficult for attackers to extract sensitive information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If modular operations are performed directly in RSA or ECC algorithms, then cryptographic operations can be executed efficiently, but the system becomes vulnerable to fault injection attacks that allow attackers to infer secret keys or system parameters
Solution Approach 1:
The cryptographic operation is segmented into multiple independent modular operations performed in different finite groups. Instead of executing a single modular operation directly, the patent divides the computation into several operations with different bases and exponents, where each operation contributes to the final result through a combination function. This segmentation ensures that a fault in one operation does not compromise the entire system, as the other operations remain intact and can be combined to produce the correct result.
Solution Approach 2:
The patent introduces intermediary computational elements (multiple bases and exponents) that act as mediators between the input and output of the cryptographic operation. These intermediary elements obscure the direct relationship between the secret key and the final result, making it difficult for attackers to infer secret parameters even if they can observe or inject faults into the intermediate computations. The combination function serves as an intermediary that integrates the results of multiple modular operations.
2Reliability
If multiple modular operations are performed in different finite groups, then security against fault injection attacks is enhanced, but the computational complexity and execution time increase
Solution Approach 1:
The patent applies local quality by performing modular operations with different characteristics in different finite groups. Each modular operation is tailored to specific local requirements (different bases, exponents, and groups), which provides security diversity. This allows the system to optimize each individual operation for its specific context while maintaining overall security, rather than using a uniform approach that would be either less secure or less efficient.
Solution Approach 2:
The patent merges the results of multiple modular operations performed in different finite groups through a combination function. This merging process integrates the computational work from multiple operations into a single final result. By carefully designing the combination function, the patent ensures that the merged result provides the desired cryptographic security while avoiding redundant computations, thus balancing security enhancement with execution efficiency.
Data Source
AI summary
There is provided a device for protecting the execution of a cryptographic operation from attacks, the cryptographic operation being implemented by a cryptographic algorithm, the cryptographic operation comprising at least one modular operation between a main base (m) representing a data block and at least one scalar (d) in at least one finite starting group. The device is configured to determine at least one intermediary group (E′) different from the at least one starting group (E), the number of intermediary groups being equal to the number of starting groups E. The device is further configured to determine at least one final group (E″) from the at least one starting group E and the at least one intermediary group E′. The base m being mapped to an auxiliary element (x) in the at least one intermediary group and to an auxiliary base (m″) in the at least one final group E″. The device performs a first elementary operation in each final group (E″i), the first elementary operation consisting in executing the modular operation between the auxiliary base (m″) and an auxiliary scalar (da) in each final group E″, which provides at least one result, the auxiliary scalar (da) being determined from the auxiliary element (x) and from the main scalar (d). The device further performs a second elementary operation in each starting group E, the second elementary operation consisting in executing the modular operation between an additional auxiliary base and an additional auxiliary scalar d′b in each starting group, at least one of the additional auxiliary base and of the additional scalar being derived from the result of the first elementary operation.