Why the original value cannot be recovered from a given hash value?

A hash function is a mathematical function that takes input data (also known as the message or pre-image) and produces a fixed-length output called a hash value or digest. One of the main properties of a hash function is that it is designed to be a one-way function, meaning that it is computationally infeasible to recover the original input data from the hash value.

Examples:

Example 1: Let’s say we have a message “This is a secret message” that we want to hash using the SHA-256 algorithm. When we apply the SHA-256 algorithm to this message, we get the following hash value:

b60a6fa9d6d75cb724e556251ea7f14a3c3f3cf46284db2b6f051c21e3c3d521

Now, suppose an attacker obtains this hash value and tries to reverse-engineer the original message. The attacker might try various techniques, such as guessing the original message, using a precomputed list of possible messages with their corresponding hash values (known as a “rainbow table”), or brute-forcing the hash value by generating different messages and computing their SHA-256 hash values until a match is found.

However, due to the one-way nature of the SHA-256 algorithm, it’s very difficult (if not impossible) for the attacker to recover the original message from the hash value. In fact, the SHA-256 algorithm is designed to be so resistant to reverse-engineering that it’s considered practically impossible to find two different messages that produce the same hash value (a property known as “collision resistance”).

So, in this example, the original value (“This is a secret message”) cannot be recovered from the given hash value (“b60a6fa9d6d75cb724e556251ea7f14a3c3f3cf46284db2b6f051c21e3c3d521”).

Example 2: Let’s say we have a message “The quick brown fox jumps over the lazy dog” that we want to hash using the MD5 algorithm. When we apply the MD5 algorithm to this message, we get the following hash value:

9e107d9d372bb6826bd81d3542a419d6

Now, suppose an attacker obtains this hash value and tries to reverse-engineer the original message. The attacker might try various techniques, such as guessing the original message, using a precomputed list of possible messages with their corresponding hash values (known as a “rainbow table”), or brute-forcing the hash value by generating different messages and computing their MD5 hash values until a match is found.

However, due to the one-way nature of the MD5 algorithm, it’s very difficult (if not impossible) for the attacker to recover the original message from the hash value. In fact, the MD5 algorithm is no longer considered secure for cryptographic purposes due to its vulnerability to collision attacks. This means that an attacker may be able to find two different messages that produce the same MD5 hash value, which would allow them to bypass authentication or manipulate data.

So, in this example, the original value (“The quick brown fox jumps over the lazy dog”) cannot be recovered from the given hash value (“9e107d9d372bb6826bd81d3542a419d6”) using the MD5 algorithm.

There are several reasons why it is difficult or impossible to recover the original value from a given hash value:

• Irreversibility: Hash functions are designed to be one-way functions, meaning that given a hash value, it is computationally infeasible to determine the original input data that produced it. This is achieved by using complex mathematical algorithms and non-linear transformations to generate the hash value. Hash functions are designed to be deterministic, which means that for a given input data, the same hash value will always be produced. However, if the input data is even slightly modified, the resulting hash value will be completely different. This irreversibility makes hash functions useful for protecting sensitive data, such as passwords or credit card information.
• Collision Resistance: Hash functions are also designed to be collision-resistant, which means that it is difficult to find two different inputs that produce the same hash value. If a hash function is not collision-resistant, an attacker could deliberately create two different inputs that produce the same hash value, which could compromise the integrity and security of the data being protected. Hash functions that are commonly used in practice, such as SHA-256 or MD5, have been extensively tested to be collision-resistant and are considered secure.
• Fixed-length output: Hash functions produce a fixed-length output, which means that there are only a finite number of possible hash values for any given hash function. This means that there is a possibility of hash collisions, where two different inputs produce the same hash value. However, the probability of a hash collision is extremely low for commonly used hash functions, and the probability can be further reduced by using longer hash values.
• Loss of Information: Hash functions lose some information from the original input data in order to produce the fixed-length output hash value. This loss of information makes it impossible to recover the original input data from the hash value. In addition, many hash functions use key derivation functions to generate the hash value, which further complicates the process of recovering the original input data.
• Avalanche Effect: A good hash function should exhibit the avalanche effect, which means that a small change in the input data should result in a significant change in the hash value. This makes it difficult for an attacker to guess the input data by modifying the hash value. In other words, even a small change in the input data should cause a completely different hash value to be produced, which further obscures the relationship between the input data and the hash value.
• Salt: In some cases, a salt is added to the input data before hashing. Salt is a random value that is added to the input data, which makes it more difficult for an attacker to guess the input data by pre-computing a table of hash values for common input data. When salt is used, the attacker would need to pre-compute a table of hash values for every possible salt value, which significantly increases the computational effort required to guess the input data.
• Backward Compatibility: Sometimes, hash functions are updated or replaced with newer, more secure versions. In such cases, it is not always possible to recover the original input data from the old hash values, even if the hash function used is known. This is because the new hash function may use different algorithms and transformations that are not compatible with the old hash values.
• Speed: Hash functions are designed to be fast, which means that they can hash large amounts of data quickly. However, this also means that they sacrifice some security features, such as key stretching and iteration, which are used in slow hash functions to increase the computational effort required to guess the input data. The tradeoff between speed and security means that it is not always possible to recover the original input data from the hash value, even if the hash function used is known.
• Avalanche Effect Variations: In addition to the standard avalanche effect, some hash functions use variations of the avalanche effect, such as the double avalanche effect, to further enhance the security of the hash function. The double avalanche effect means that two independent hash functions are applied to the input data, and the resulting hash values are combined to produce the final hash value. This makes it even more difficult for an attacker to guess the input data from the hash value, as any changes to the input data will affect both hash functions, causing a significant change in the final hash value.
• Reversing Hashes is Computationally Infeasible: In order to recover the original input data from a hash value, an attacker would need to reverse the hash function. However, reversing a hash function is computationally infeasible, as it requires finding a pre-image of the hash value, which is an input that produces the hash value. The best-known method for finding pre-images is a brute-force search, which involves trying all possible input values until a match is found. For modern hash functions such as SHA-256, the number of possible input values is so large that a brute-force search is not feasible with current computing technology.
• Rainbow Tables: One common method for cracking password hashes is to use a pre-computed table of hash values known as a rainbow table. A rainbow table contains a large number of hash values and their corresponding input data and can be used to quickly look up the input data that produced a given hash value. However, the use of salt and other security measures can prevent the use of rainbow tables, as the attacker would need to create a separate rainbow table for each possible salt value.
• Multiple Inputs Produce the Same Hash: Hash functions are designed to produce a unique hash value for each input, but in some cases, multiple inputs may produce the same hash value. This is known as a hash collision. While hash collisions are rare for commonly used hash functions, they can occur in theory, and an attacker could potentially create two different input values that produce the same hash value. However, this is extremely difficult and requires significant computational resources.

The purpose of a hash function is to create a “fingerprint” of the input message that can be used to verify the integrity and authenticity of the message. Hash functions are commonly used in computer security to ensure that data has not been tampered with, as even a small change to the input message will result in a completely different hash value.

Because the output of a hash function is a fixed-size sequence of characters, it is theoretically impossible to reverse-engineer the original input message from the hash value. This is known as the “one-way” property of hash functions.

In other words, given a hash value, it is not possible to determine the original message that produced the hash value. This
fact that a hash function is designed to be a non-invertible function, meaning that it is computationally infeasible to find the original input message that corresponds to a given hash value. This property is important for ensuring the security of cryptographic protocols, as it prevents attackers from easily determining the original message by simply reversing the hash function.

Significance of hash value:

Hash value conversion can be significant in several ways depending on the context in which it is used. Here are a few examples:

• Data integrity: Hash values can be used to verify the integrity of data. By computing a hash value of a file or message before and after transmission, the recipient can ensure that the data has not been tampered with during transit. If the hash values match, then the recipient can be confident that the data has not been altered. Hash value conversion is essential here as it allows for the comparison of two fixed-length values, making the comparison process efficient.
• Password storage: When a user creates a password for an account, it is common practice to store a hash value of the password rather than the password itself. This is done for security reasons as it prevents a potential attacker from gaining access to the user’s password if the database is compromised. Hash value conversion is critical here as it ensures that the user’s password is not stored in plain text, which could be easily exploited.
• Digital signatures: Hash values are often used in digital signatures, which are used to authenticate the origin and integrity of a message. A digital signature involves hashing the message and encrypting the hash value with the sender’s private key. The recipient can then decrypt the hash value using the sender’s public key and verify that the hash value matches the message they received. Hash value conversion is essential here as it allows for the verification of the message without disclosing the sender’s private key.

Hash value conversion is a critical component of many security protocols and data integrity measures. It provides a way to efficiently compare and verify data without disclosing sensitive information.

Conclusion:

Overall, the main reason why it is difficult or impossible to recover the original value from a given hash value is that the hash function is designed to be a one-way function, meaning that it is irreversible and computationally infeasible to reverse-engineer the original input data from the hash value.