I need to implement Blakley's Secret Sharing Scheme. I have read below mentioned two research papers but still unable to understand how to implement it.
- Safeguarding cryptographic keys
- Two Matrices for Blakley’s Secret Sharing Scheme
The following is the steps I have been able to understand.
- We chose positive integers $z$, $a$ and $b$.
- We chose a large $p$
A $(a+b+2)\times(b+2)$ matrix $M$ is created satisfying the following conditions:
- Random entry in each row is set to $1$.
- Another random entry in first row is set to $k$, chosen from $\mathbb F_p$.
- All other entries are filled with random values from $\mathbb F_p$.
After this some equation need to be formed and then solved for share.
I am unable to understand how shares are calculated and how can they be verified. Kindly help me understand the remaining process.