Tampering Detection via Ring Rq Vector Checksums
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Solution Overview
Problem
The existing checksum technique for tampering detection in secure computation has a probability of successful tampering that increases with the number of data pieces, making it inefficient as the number of data pieces grows.
Innovation Solution
A tampering detection device that divides N values into sets of q values, generating value vectors and using a specific checksum formula involving multiplication and addition to achieve a lower probability of successful tampering by uniformly mapping parameters from a ring R to Rq, where N and q are integers greater than or equal to 2, and ρ is a minimum integer greater than or equal to N/q.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the existing checksum technique is used for tampering detection, then the detection method can be efficiently applied to secure computation, but the probability of successful tampering increases as the number of data pieces increases
Solution Approach 1:
The invention divides N data values into multiple sets of q values each, creating value vectors. This segmentation transforms the single large checksum problem into multiple smaller vector-based checksum calculations, reducing the overall probability of successful tampering from N/|F| to N/pq while maintaining computational efficiency through structured vector operations
Solution Approach 2:
The invention changes the mathematical parameters by introducing a degree of field extension q and using uniform mapping from ring R to ring Rq. By transforming the checksum generation from operating over a single field F to operating over extended ring structures with parameters αijk, the system achieves lower tampering probability while preserving the efficiency needed for secure computation applications
Data Source
AI summary
The present invention can be efficiently applied to secure computation and can achieve a low probability of successful tampering. A tampering detection device includes a parameter storage storing parameters αijk for uniformly mapping from two elements of a ring Rq to one element of the ring Rq, a division part 12 dividing N values a0, . . . , aN−1 into sets of q values to generate value vectors A0, . . . , Aρ−1, a generation part 14 generating a checksum c, and a verification part 15 comparing a verification value generated by using the value vectors A0, . . . , Aρ−1 with the checksum c to determine whether or not any of the values a0, . . . , aN−1 has been tampered with. Here, N and q are integers greater than or equal to 2 and ρ is a minimum integer greater than or equal to N/q.