Lamportaikaleimat

Lamportaikaleimat, known in English as Lamport signatures, are a hash-based digital signature scheme introduced by Leslie Lamport in 1979. They are among the earliest public-key signature schemes and are designed as a one-time signature system.

Key generation and signing: The private key consists of 2n random values, where n is the length of the hash output (for example, 256 bits for SHA-256). The public key is the set of hashes of these values. To sign a message, the signer hashes the message to produce a bit string of length n. For each position i, the signer reveals one of the two corresponding private values depending on the i-th bit of the hash: reveal x_i if the bit is 0, or x'_i if the bit is 1. Verification checks that the hashes of all revealed values match the public key.

Security and use: The scheme’s security rests on the preimage resistance of the underlying hash function. A critical limitation is that a Lamport key pair is intended for a single use; reusing a key compromises all signatures produced with it. Consequently, signatures are large, and substantial private-key material must be kept secure, making practical deployment limited. Despite this, Lamport signatures are valued for their simplicity and for illustrating hash-based, post-quantum cryptographic principles.

Extensions and related schemes: To improve efficiency and practicality, variants such as Winternitz One-Time Signatures (WOTS) were developed, and iterative schemes like XMSS and XMSS^e extend the one-time idea to multiple-signature families while preserving hash-based security.

Applications: Primarily educational and research contexts, where they demonstrate principles of hash-based cryptography and serve as building blocks for more modern post-quantum signature frameworks. See also: hash-based cryptography, Lamport signatures, Winternitz OTS, XMSS.