White-box Cryptographic Key Protection via Random Bijections
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Solution Overview
Problem
Current digital rights management systems face challenges in securing cryptographic keys, as they can be compromised through reverse engineering or observation of memory access, especially in open CE platforms where users have control over hardware and software.
Innovation Solution
A method is presented to compute the outcome of an exponentiation without exposing the base or exponent, by establishing and providing specific values ωi and φi to a device, making it difficult for attackers to derive the cryptographic key, even if they can inspect or debug the entity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If cryptographic keys are stored in memory for decryption operations, then decryption functionality is enabled, but attackers can retrieve keys through memory observation
Solution Approach 1:
The patent introduces random bijections as intermediary transformations between the cryptographic key and the data structures used in decryption operations. These bijections act as mediators that allow decryption to proceed while preventing direct observation of the key in memory, as the key is never stored in its original form but rather transformed through multiple layers of random permutations.
Solution Approach 2:
The patent applies parameter changes by transforming the cryptographic key through random bijections that change the representation of key data at each processing stage. The key material is continuously transformed through different random permutations and compositions, ensuring that the same logical key value is represented by different parameter configurations in memory, thereby preventing key recovery through static analysis.
2Object-affected harmful factors
If white-box implementation is used to hide cryptographic keys, then key security is improved, but the system complexity increases
Solution Approach 1:
The patent segments the cryptographic key into multiple components that are processed through separate random bijections. Instead of applying a single complex transformation, the key material is divided and transformed through multiple simpler random permutation stages, making the overall system more manageable while maintaining security. Each segment is protected by its own random bijection layer.
Solution Approach 2:
The patent applies preliminary action by pre-computing and storing random bijections and their compositions before actual decryption operations. These random transformations are prepared in advance and integrated into the decryption algorithm structure, so that during runtime, the system only needs to execute predetermined transformation sequences rather than generating complex security measures on the fly.
3Object-affected harmful factors
If random bijections are used to encode cryptographic tables, then key derivation difficulty increases, but computational overhead increases
Solution Approach 1:
The patent applies partial action by using random bijections only where absolutely necessary for security-critical operations, rather than transforming all data uniformly. The random permutations are applied selectively to key-related data structures while leaving other non-critical data unchanged, thereby reducing overall computational overhead while maintaining security for the essential cryptographic operations.
Data Source
AI summary
A system for enabling a device to compute an outcome of an exponentiation Cx having a base C and/or an exponent x, the system comprising means for establishing a plurality of values λi; means for establishing a plurality of values ωi satisfying ωi=Cλ<sub2>i</sub2>; means for establishing a plurality of values φi satisfying that the sum of the values λiφi equals x; and an output for providing the device with the plurality of values φi. A device computes an outcome of the exponentiation Cx. The device comprises means for computing a product of the values ωi to the power of φi. The device is arranged for using the product as a result of the exponentiation Cx.