Merkle-Damgard Scheme in Cryptography

Pre-requisites: Cryptography and its Types

MD scheme(discovered by Ralph Merkle) is used to build collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. It is used in algorithms like SHA-1, SHA-256, etc.

This scheme can be divided into two stages:

Stage 1: Design a fixed-length, collision-resistant compression function.

Collision-Resistant Compression Function

Stage 2: Design a CRHF H for arbitrary length messages, using ‘h’.

1. Encode the input M(with length L) for H_MD to make the encoded message, a multiple of l bits. If L is already a multiple of l bits, then add an additional dummy block.

 Original Message || Padding length            

2. The message is then considered as t-blocks each of n bits, i.e: M₁, M₂…….M_t. Apply function h iteratively over the blocks of M and the previous outcome of h(i.e H_1, H₂…….H_MD)

F(H_i-1, M_i) = H_i

3. Before starting iteration, an initial vector(H₀) is used.

4. The digest H_MD created after t^th iteration is the compressed hash value of the original message.

Security Characteristics

• The second preimage attack is more efficient for long messages, as compared to brute force.
• Multi-collision is present.
• Given a hash of message X, it is easy to find the value of X+Y (padding on X).

Advantages of Merkle-Damgard Scheme in Cryptography

• Simplicity: The Merkle-Damgard scheme is relatively simple to understand and implement. The scheme uses a compression function that takes in a fixed-size block of data and outputs a fixed-size hash value. This compression function is applied repeatedly to the input data in a block-by-block manner until the entire message is processed.
• Collision resistance: The Merkle-Damgard scheme provides a high degree of collision resistance, which means that it is difficult to find two different input messages that produce the same hash value. This is achieved by incorporating a one-way compression function that reduces the input message to a fixed-size output, making it difficult to derive the original input from the hash value.
• Incremental hashing: The Merkle-Damgard scheme supports incremental hashing, which means that it can process large input messages in smaller chunks. This is useful in situations where the entire message is not available at once or where the message is too large to be processed in one go.
• Efficiency: The Merkle-Damgard scheme is computationally efficient, which means that it can process large amounts of data quickly. The scheme’s simple design and incremental hashing capabilities contribute to its efficiency.
• Proven security: The Merkle-Damgard scheme has been extensively studied and analyzed by cryptographers, and it has stood up to rigorous analysis. While no cryptographic scheme is completely immune to attacks, the Merkle-Damgard scheme is considered to be a strong and secure construction.

Disadvantages of Merkle-Damgard Scheme in Cryptography

• Length extension attacks: One of the primary weaknesses of the Merkle-Damgard scheme is its susceptibility to length extension attacks. An attacker can use the hash value of a message and the length of the message to generate a new message with the same hash value, which can compromise the security of the system.
• Limited security: While the Merkle-Damgard scheme is considered to be a strong construction, it has some limitations in terms of security. For example, it is vulnerable to collision attacks, where an attacker can find two different input messages that produce the same hash value.
• Inefficient padding: The Merkle-Damgard scheme requires padding of the input message to ensure that it is a multiple of the block size. This padding can be inefficient and may result in a significant increase in the size of the message.
• Sequential processing: The Merkle-Damgard scheme processes the input message in a sequential manner, which can limit its parallelism and make it vulnerable to side-channel attacks.
• Complexity of compression function: The compression function used in the Merkle-Damgard scheme can be complex and difficult to analyze. This can make it challenging to ensure that the function is secure and free from vulnerabilities.