Combination-Based Broadcast Encryption for Collusion Resistance
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Solution Overview
Problem
Existing broadcast encryption methods, such as the Fiat algorithm, are insecure against collusion attacks and inefficient, as they rely on difficult prime factorization and require excessive key management and decryption operations, especially when multiple users collude.
Innovation Solution
A combination-based broadcast encryption method that assigns each user a unique base group generated from coprime integers, using random numbers for security, and calculates a group key using inverse-base parameter values to ensure only privileged users can decrypt the session key, thereby enhancing security against collusion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Fiat algorithm is used for broadcast encryption, then encryption can be performed, but the system is insecure against collusion attacks
Solution Approach 1:
The patent segments the broadcast encryption system into distinct components: base groups assigned to users, secret information derived from these base groups, and inverse-base parameters. Each user receives a unique base group formed by combining a subset of integers, creating segmented key material that prevents collusion attacks while simplifying overall key management structure.
Solution Approach 2:
The patent performs preliminary actions by pre-assigning base groups to users before any broadcast encryption occurs. Each user's base group is pre-calculated as a combination of integers, and secret information is pre-derived from these base groups. This preliminary setup eliminates the need for complex runtime key management and provides built-in collusion resistance.
2Loss of energy
If traditional broadcast encryption methods are used, then encryption is possible, but transmission and storage overheads are excessive
Solution Approach 1:
The patent changes the fundamental parameters of broadcast encryption by using base groups formed from integer combinations rather than traditional prime factorization. This parameter change reduces the size of transmitted data (inverse-base parameters) and stored secret information while maintaining strong security properties that resist collusion attacks.
3Productivity
If Fiat algorithm is used, then broadcast encryption can be implemented, but decryption operations are inefficient
Solution Approach 1:
The patent extracts the computationally intensive prime factorization step from the decryption process. Instead of requiring users to perform difficult prime factorization during decryption, the system pre-computes base groups and secret information, extracting only the necessary inverse-base parameters for transmission. This dramatically improves decryption efficiency while reducing operational complexity.
Data Source
AI summary
A combination-based broadcast encryption method includes: assigning by a server a base group of different combinations to each user; producing and sending secret information for each user by using as a base the base group allocated to each user; producing and sending an inverse-base parameter value through calculations with integers used to produce the base group and key value information of one or more privileged users; and deriving a group key by using the key value information of the privileged users, encrypting a session key by using the derived group key, and sending the encrypted session key to each user. Accordingly, each user is assigned a different base through a combination, thereby having security against collusion attacks.