What Does 6-of-10 Recovery Mean? The Math Behind YourKeep’s Default Architecture

When you protect an archive with YourKeep, the software generates 10 distinct fragment files and states that any 6 fragments are sufficient to restore 100% of your data.

To newcomers, this sounds like mathematical magic: How can you lose 4 entire files and still reconstruct every single byte of your original data without losing quality?

This guide explains the exact linear algebra and finite field mathematics behind the 6-of-10 threshold model.

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The Core Concept: Solving Linear Systems in Galois Fields

Imagine a simple algebra problem: If you are given the equation of a line ($y = mx + b$), you need exactly two points to determine the line completely. If you are given 5 points on that line, any 2 points will yield the exact same line, and the other 3 points are redundant.

Reed-Solomon erasure coding applies this concept to high-dimensional matrix algebra over Galois Fields ($ ext{GF}(2^8)$):

[ Master Encrypted File ] ──> Partitioned into 6 Data Blocks (D1, D2, D3, D4, D5, D6)
                                       │
                         Multiplied by Generator Matrix
                                       │
                      Produces 4 Parity Blocks (P1, P2, P3, P4)
                                       │
                      Total: 10 Fragments (F1 through F10)

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Why Any 6 Fragments Restore 100%

When you present any 6 fragments to YourKeep (for example: $F_1, F_3, F_5, F_7, F_8, F_{10}$), the recovery engine:

1. Extracts the corresponding 6 rows from the known Cauchy generator matrix.
2. Performs a matrix inversion over $ ext{GF}(2^8)$ to create a decoding matrix.
3. Multiplies the decoding matrix by the 6 retrieved fragment vectors.
4. Mathematically outputs the exact original data blocks $D_1$ through $D_6$ with zero loss.

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The Practical Superpower of 6-of-10

• Survives 4 Concurrent Failures: You can lose your local SSD, your Google Drive account, a damaged USB drive, and an unpaid S3 bucket all at the same time.
• Efficient Storage Footprint: The total storage expansion is only 1.67x (167%), compared to 3x or 4x for naive multi-copy backups.

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Conclusion

6-of-10 recovery replaces luck and corporate promises with rigorous mathematical certainty.