Shamir's Secret Sharing Online

Shamir’s Secret Sharing is a cryptographic technique invented by Adi Shamir in 1979. It allows a secret (password, private key, seed phrase, etc.) to be split into multiple parts called shares.

This tool provides a fully functional implementation of Shamir’s Secret Sharing. The implementation uses finite field arithmetic and polynomial interpolation exactly as specified by Shamir’s original scheme.

🔐 Shamir’s Secret Sharing

• Generate Shares
• Reconstruct Secret

{{ generatedShares.join('\n') }}

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We do not store, log any key you enter. This tool runs entirely over a secure HTTPS connection to keep your encryption key safe at all times.

Tool Documentation and Usage

Using this scheme, you can specify:

• Number of Shares (N) – Total shares to be generated
• Threshold (K) – Minimum number of shares needed to reconstruct the secret

Even if someone gets fewer than K shares, the secret cannot be recovered mathematically.

This makes SSS perfect for:

• Splitting crypto wallet keys
• Storing passwords securely
• Enterprise access control
• Multi-person authorization

2. Explanation of All Fields in the Form

🔹 Secret

This is the actual sensitive value you want to split. You can enter text, numbers, hex strings, binary, or encoded values depending on the selected mode.

🔹 Mode (UTF-8 / HEX / Binary)

Determines how the secret is interpreted and validated.

• UTF-8: Normal text input (passwords, phrases, etc.)
• HEX: Must be a valid hexadecimal string (0-9, A-F)
• Binary: Must contain only 0 and 1 characters

🔹 Number of Shares (N)

Total number of shares you wish to generate. Example: If N = 5, the tool will produce 5 independent shares.

🔹 Threshold (K)

Minimum shares required to rebuild the secret. If K = 3, any 3 of the total shares can recover the secret.

🔹 Share Outputs

After generation, each share contains two components:

• Index (X) – Position of the share
• Value (Y) – Computed polynomial output

Example share structure:

[1-fd34aa01], [2-09bc9932], ...

4. How to Read & Understand Generated Shares

Each share is unique, and no single share reveals anything about the secret. A typical generated share looks like this:

Share #1 → 1-8caff120934bd99a

Structure:

• 1 → X coordinate (share index)
• 8caff120934bd99a → Y value (polynomial output)

When K shares are combined, polynomial interpolation is performed to find:

S = f(0)

This tool performs the official Shamir’s Secret Sharing computation using:

• Finite field arithmetic (GF(256) or GF(2^8)) depending on mode
• Random polynomial generation:

  f(x) = S + a1x + a2x² + ... + a(k-1)x^(k-1)

• Evaluation of polynomial at x = 1...N
• Secure random coefficient generation
• Reconstruction using Lagrange interpolation

5. Advantages & Disadvantages

Advantages

• Mathematically secure – fewer than K shares reveal nothing
• Improves safety of passwords, crypto keys, and sensitive secrets
• Shares can be distributed among trusted people
• Simple, fast, and industry-approved cryptographic scheme

Disadvantages

• If all K threshold members lose their shares, the secret is unrecoverable
• Shares must be stored safely to avoid tampering
• Not suitable for extremely large secrets without encoding

Real-World Use Cases

• Splitting a crypto wallet private key among 3–5 people
• Storing an API key securely across multiple teams
• Multi-party recovery of master passwords
• Offline secure backup for seed phrases

7. Frequently Asked Questions (FAQ)