Merkle-Signature-Scheme

The Merkle-Signature-Scheme (MSS) is a cryptographic method for digital signatures that was invented by Ralph Merkle in the late 1970s. This scheme leverages the concept of hash trees, also known as Merkle Trees, to provide a method of signing an unlimited number of messages using a limited number of one-time signature keys.

History and Development

• Ralph Merkle first proposed the idea of the Merkle Tree in 1979, which laid the groundwork for the Merkle-Signature-Scheme.
• The MSS was detailed in Merkle's 1979 paper titled "Secrecy, Authentication, and Public Key Systems," which was part of his Ph.D. dissertation at Stanford University.
• The scheme was further refined in the 1990s as part of the efforts to develop post-quantum cryptography, where it gained attention for its potential resistance to quantum computing attacks.

How It Works

The Merkle-Signature-Scheme operates as follows:

1. Key Generation: A large number of one-time signature key pairs are generated. Each public key is hashed and combined in a tree structure (Merkle Tree), where the leaves are the hashes of the public keys, and each internal node is the hash of its children.
2. Signature:
   • When signing a message, one of the one-time private keys is used to sign it.
   • The corresponding public key and a path through the Merkle Tree (authentication path) that proves the public key's inclusion in the tree are included with the signature.
3. Verification:
   • The verifier uses the authentication path to reconstruct the root hash of the Merkle Tree.
   • If the reconstructed hash matches the known root hash, and the signature verifies under the one-time public key, the signature is accepted as valid.

Advantages

• Quantum Resistance: Unlike RSA or ECC, the Merkle-Signature-Scheme is considered resistant to attacks by quantum computers.
• Unlimited Signatures: While each one-time key can only be used once, the structure of the Merkle Tree allows for a theoretically unlimited number of signatures by using different keys.

Limitations

• Key Management: The requirement to manage many one-time keys can be cumbersome.
• Signature Size: Signatures are significantly larger than those from traditional schemes because of the need to include the authentication path.

Applications and Implementation

While not widely used in mainstream cryptographic applications due to its complexity and key management issues, MSS has found niche applications:

• In systems requiring long-term security where keys need to be generated and stored securely for future use.
• As part of hybrid cryptographic schemes where quantum-resistant signatures are needed alongside traditional ones.

Sources:

• Stanford University's Crypto Corner
• RFC 8391: XMSS: eXtended Merkle Signature Scheme

Related Topics

• Hash-based-Signatures
• Post-Quantum-Cryptography
• Merkle-Trees
• One-Time-Signatures