Question

Can you “decrypt” a hash of a message to get the original message? Explain your answer

Short answer

You cannot decrypt a hash back to the original message due to the one-way nature of hash functions.

Step-by-step solution

Understanding Hash Functions

A hash function takes an input (or message) and converts it into a fixed-size string of characters, which is typically a seemingly random sequence of numbers and letters. The output is called a hash, hash value, or message digest.

Properties of Hash Functions

A crucial property of hash functions is that they are one-way functions. This means it is computationally infeasible to reverse the process, i.e., to derive the original input from its hash value.

Irreversibility of Hashes

Due to the one-way nature of hash functions, there is no algorithmic method available to reverse the hashing process to retrieve the original message from the hash.

Understanding Collisions and Birthday Paradox

While it is possible for different messages to produce the same hash (called a collision), this does not imply decryption. Finding such a collision is extremely unlikely and computationally intense, leveraging the ‘Birthday Paradox’ to exploit hash functions’ weaknesses.

Conclusion

Decrypting a message from its hash is not feasible as hash functions are designed to ensure that their output doesn't reveal any information about the input, under security assumptions typical with well-designed hash functions.

Key concepts

One-way Functions

Hash functions are a fascinating aspect of cryptography, primarily because they behave as one-way functions. This means they convert a message into a hash value, but going back from the hash value to the original message is practically impossible. One-way functions are designed to provide an irreversible encryption process because:

• The operation's nature makes guessing the original input extremely difficult if not practically impossible.
• There's no straightforward way or efficient method that reverses this hashing process.

This one-way characteristic is known as being computationally infeasible. Even if you had vast computational resources, the time and effort required to reverse a hash to find the original input would be astronomical. In cryptography, these functions serve as a backbone for secure data transmission, ensuring that sensitive information remains protected during transactions.

Hash Collisions

Although hash functions are adept at securing data, they are not entirely invincible. A phenomenon known as hash collision occurs when two different inputs produce the same hash value. This might sound like a flaw, but hash functions are designed to minimize such instances. The interesting part is that a collision doesn't mean we can uncover the original messages.

• Instead, they arise because the hash values are typically shorter than the possible number of unique inputs, like fitting infinite possibilities into a finite range.
• Creating a collision isn't as straightforward as it sounds; it requires immense processing power and time.

Despite theoretical vulnerabilities, this complexity keeps hash collisions from being a significant risk in everyday applications. Security-conscious algorithms ensure it remains practically unfeasible to exploit these situations.

Message Digest

A hash function transforms an input into a fixed-length string of characters known as a message digest. This digest serves as a unique identifier for the data, somewhat like a digital fingerprint. Understanding message digests can be broken down into:

• Consistency: A specific input will always yield the same message digest.
• Uniqueness: Ideally, different inputs should produce different digests.
• Efficiency: Generating a digest is quick and resource-light.

This makes message digests fundamental in verifying data integrity. They provide confidence that a message hasn't been altered, making them crucial in signature validations and password storage. The property of having fixed-length outputs ensures that even if the input size changes, the digest remains predictable and manageable.

Birthday Paradox

The Birthday Paradox is a fascinating probability theory that significantly impacts hash functions. It states that in a group, the chances of two people sharing a birthday are surprisingly high when considering average expectations. This paradox extends to hash functions:

• The more hash values created, the higher the chance of encountering a hash collision.
• Surprisingly, not every collision requires a complete scan of all inputs, parallel to how not every person needs to be compared to identify shared birthdays.

In practice, this means that as you hash more data, the probability increases that two different inputs will eventually share the same hash value, akin to the birthday paradox. It guides developers to choose sufficiently large hash sizes, maintaining security and reducing collision chances effectively.