Key Schedule Using One-Way Functions to Break Correlations
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Solution Overview
Problem
Current cryptographic block ciphers are vulnerable to physical attacks, such as side-channel and fault attacks, which can recover the secret key due to correlations between the main key and round keys, making it possible to derive the main key from a single sub-key.
Innovation Solution
A sequence of sub-keys is generated from a main key using one or more one-way functions, ensuring each sub-key bit is set independently, reducing correlations and making it difficult to recover the main key from a single sub-key, with the main key being used only once to generate the sub-keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a traditional key schedule is used to generate round keys from the secret key, then the cryptographic operations can be performed efficiently, but the correlations between the secret key and round keys make the system vulnerable to side-channel and fault attacks
Solution Approach 1:
The patent introduces an intermediary mechanism (the specific key schedule algorithm with independent bit setting) between the secret key and round keys. This intermediary breaks the direct correlation path that attackers exploit, using one-way functions and independent bit assignment to decouple the relationship while still enabling efficient cryptographic operations
Solution Approach 2:
The key schedule divides the key generation process into independent segments where each bit of each round key is independently derived from specific bits of the secret key through one-way functions. This segmentation prevents attackers from exploiting correlations across multiple bits or words of the key material
2Device complexity
If the main key is used multiple times to generate sub-keys, then the key schedule can be simplified, but the vulnerability to side-channel attacks increases
Solution Approach 1:
The patent extracts the secret key from repeated operations by using it only once as input to the one-way functions. The extracted information is then transformed through multiple independent one-way function calls, each producing independent round keys without requiring repeated access to the secret key itself, thereby reducing side-channel exposure
3Reliability
If one-way functions are used to reduce correlations between keys, then resilience to attacks improves, but the computational complexity increases
Solution Approach 1:
The patent changes the parameters of the key generation process by using one-way functions with specific properties (collision-resistant, efficient evaluation). These parameter choices balance security requirements with computational efficiency, selecting functions that provide sufficient entropy expansion and correlation breaking while maintaining reasonable computational costs
Data Source
AI summary
Methods, system and devices are provided that generate a sequence of sub-keys for cryptographic operations from a main key. The main key is operated on only once to generate the sub-keys of the sequence, with a transformation comprising one or more one-way functions. The respective bit values of the sub-keys of the sequence are set using respective bit values of the one or more one-way functions. Advantageously, deriving sub-key bits from respective output bits of one or more one-way functions removes or at least reduces correlations between the main key and the sub-keys, as well as between sub-keys, making it harder or even impossible to recover the main key or other sub-keys from a single sub-key, for example as found using a side-channel attack. At the same time, by using the main key only once (rather than using the main key each time a sub-key is generated), the vulnerability of the main key to a side-channel attack is reduced, because the opportunities for recovering physical information that could lead to the discovery of the main key are reduced. Specific embodiments use parallel or chained execution of sub-functions to generate respective sub-keys. Other specific embodiments generate all sub-keys from a single one-way function in one go.