# Hash-Based Cryptosystems

Learn about the Lamport-Diffie one-time signature scheme (LD-OTS) and multi-time signatures in this lesson.

## We'll cover the following

## Overview

Hash-based cryptography makes use of cryptographic hash functions in order to provide digital signatures whose security relies on the collision resistance of the underlying hash function. The major advantage of these kinds of signature schemes is their flexibility since they can be constructed on any secure hash function. The most fundamental approaches are one-time signature (OTS) schemes, such as Lamport-Diffie signatures (LD-OTS) (

This means that each key can only be used once to sign one single message, thus a new public key must be published for each message to be signed. However, this disadvantage can be circumvented by applying Merkle authentication trees to one-time signature schemes. Its construction combines OTS with a binary hash tree structure that is applied to many OTS verification keys and publishing the root of the hash tree as a public key instead, thus transforming an OTS into a multi-signature scheme. We introduce the basics of these schemes in the next sections to get a first understanding of the basic construction of hash-based cryptosystems.

However, the original schemes are highly inefficient, but further enhancements to the basic algorithms brought significant improvements in key and signature sizes and optimized signature generation time. Recently,

## Lamport-Diffie one-time signatures

The **Lamport-Diffie one-time signature scheme (LD-OTS)** was introduced in this

$\varphi:\{0,1\}^{n} \rightarrow\{0,1\}^{n}.$

In practice, $\varphi$ is usually realized by a dedicated hash function, although the LD-OTS is secure even if $\varphi$ is not a collision-resistant function.

### Key generation, signature generation, and verification

A Lamport-Diffie signature consists of a one-way function

$\varphi:\{0,1\}^{n} \rightarrow\{0,1\}^{n}$

together with a cryptographic hash function

$H:\{0,1\}^{*} \rightarrow\{0,1\}^{n}.$

According to Buchmann (

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