Bitcoin on Nostr: If like me you're probably wondering: What’s the difference between 'Seed XOR' and ...
If like me you're probably wondering: What’s the difference between 'Seed XOR' and 'Shamir's Secret Sharing'?
Well, both seed XOR and Shamir’s Secret Sharing (SSS) are methods to split secrets, but they work differently and have distinct properties:
1. Mechanism:
• Seed XOR: This method involves the simple splitting of a secret into two parts using the XOR operation. Given a secret S and a random value R, you compute the value S XOR R to get T. Now, the two shares are R and T. To retrieve S, you’d XOR R and T again.
• Shamir’s Secret Sharing (SSS): SSS is based on polynomial interpolation over finite fields. The idea is to represent the secret as a coefficient in a polynomial and provide different points on that polynomial as shares. Using a sufficient number of these points (based on the degree of the polynomial), the secret can be reconstructed.
2. Number of Shares:
• Seed XOR: Typically creates two shares (though you could extend this idea to more).
• Shamir’s Secret Sharing: Can create any number of shares. You can specify a threshold, say k, such that any k shares are sufficient to reconstruct the secret.
3. Flexibility:
• Seed XOR: Less flexible. Always requires all the shares to reconstruct the original secret.
• Shamir’s Secret Sharing: More flexible. Allows you to specify how many shares (threshold) are needed to reconstruct the secret. For example, you could create 10 shares and set a threshold of 5, meaning any 5 out of the 10 shares can be used to reconstruct the secret.
4. Security:
• Seed XOR: Simple and based on the properties of the XOR operation. If you have one share, it reveals no information about the secret.
• Shamir’s Secret Sharing: More mathematically complex but offers strong security properties. Without a minimum number of shares (below the threshold), it’s computationally infeasible to retrieve the secret.
5. Applications:
• Seed XOR: More appropriate for simple, two-party secret splitting.
• Shamir’s Secret Sharing: Suited for scenarios where a secret needs to be split among multiple parties, and you want to ensure that only a certain number of them collaborating can recover the secret.
In essence, while both methods can be used to split secrets, Shamir’s Secret Sharing offers more flexibility and is appropriate for more complex use-cases.
Well, both seed XOR and Shamir’s Secret Sharing (SSS) are methods to split secrets, but they work differently and have distinct properties:
1. Mechanism:
• Seed XOR: This method involves the simple splitting of a secret into two parts using the XOR operation. Given a secret S and a random value R, you compute the value S XOR R to get T. Now, the two shares are R and T. To retrieve S, you’d XOR R and T again.
• Shamir’s Secret Sharing (SSS): SSS is based on polynomial interpolation over finite fields. The idea is to represent the secret as a coefficient in a polynomial and provide different points on that polynomial as shares. Using a sufficient number of these points (based on the degree of the polynomial), the secret can be reconstructed.
2. Number of Shares:
• Seed XOR: Typically creates two shares (though you could extend this idea to more).
• Shamir’s Secret Sharing: Can create any number of shares. You can specify a threshold, say k, such that any k shares are sufficient to reconstruct the secret.
3. Flexibility:
• Seed XOR: Less flexible. Always requires all the shares to reconstruct the original secret.
• Shamir’s Secret Sharing: More flexible. Allows you to specify how many shares (threshold) are needed to reconstruct the secret. For example, you could create 10 shares and set a threshold of 5, meaning any 5 out of the 10 shares can be used to reconstruct the secret.
4. Security:
• Seed XOR: Simple and based on the properties of the XOR operation. If you have one share, it reveals no information about the secret.
• Shamir’s Secret Sharing: More mathematically complex but offers strong security properties. Without a minimum number of shares (below the threshold), it’s computationally infeasible to retrieve the secret.
5. Applications:
• Seed XOR: More appropriate for simple, two-party secret splitting.
• Shamir’s Secret Sharing: Suited for scenarios where a secret needs to be split among multiple parties, and you want to ensure that only a certain number of them collaborating can recover the secret.
In essence, while both methods can be used to split secrets, Shamir’s Secret Sharing offers more flexibility and is appropriate for more complex use-cases.