What is One Way Function in Cryptography?

One-way functions in cryptography are easy to compute, whereas inverse functions are complicated to compute. There is no mathematical proof that one-way functions exist. The existence of such one-way functions is still a not-resolved question. Their existence indicates that the complexity classes are not equivalent. In this article, we will learn about the one-way function in cryptography, the trapdoor one-way function, the one-way hash function, and how the one-way functions work.

What is One Way Function in Cryptography?

A one-way function is a widely used mathematical function that is easier to compute in one direction. The forward direction of a function can be computed fast, while the inverse can take months. One-way functions in cryptography fulfill all conditions for one-way functions. It is easy to find their values using input data, but having merely a hash value prevents one from determining the original input sequence. A one-way hash function should be free of collisions. This means it can be extremely difficult to locate two sequences that give the same result. It converts input messages of different lengths into output sequences of fixed length. The output sequence is often referred to as a hash value. Hash values are frequently used to label input sequences, that is, to assign them unique values that identify them.

Trapdoor One Way Function

A trapdoor one-way function is easy to evaluate in one direction but difficult to compute in the opposite direction. When some additional information is revealed, such a function becomes a trapdoor one-way function.

In mathematical terms, if "f" is a trapdoor function, then there is some hidden information "t" that allows "x" to be easily computed given f(x) and "t". Consider the padlock and its key. To change the padlock from open to closed without using the key, simply push the shackle into the lock mechanism. The padlock can be readily opened, but the key is required. The key is the trapdoor, and the padlock performs the trapdoor function.

One Way Hash Function

One-way hash function algorithms provide security as their properties are one-way functions. Changing one bit of input data results in changing around half of the output bits. These are used to protect data from intentional or unintended changes.

It satisfies all of the requirements for one-way functions. It is simple to calculate their values using input data, but having merely a hash value prevents one from determining the original input sequence.

How Do One Way Functions Work?

• A one-way function mainly starts with a group of letters known as a key, which is then mapped to a hash of a specific length.
• Modern hashes have 128 bits or more, however, the hash value is shorter than the original string of characters.
• The hash value is often referred to as a message digest. When you scramble this message digest, it becomes unique each time.
• A one-way function should be free of collisions. This means it should be extremely difficult to locate two distinct sequences that give the same hash result.
• Furthermore, one-way functions are used to store data. Data can be accessed by locating hash values, and are stored in computer memory.

Types of One Way Functions in Cryptography

• Strong One-Way Function: A Strong One-Way function is easy to compute but can only be inverted with negligible probability on random input, or difficult to invert on all but a small number of inputs.

• Weak One-Way Function: A Weak One-Way function is easy to compute but difficult to invert for random inputs, or easy to invert for a significant fraction of inputs.

Why Use One Way Functions in Cryptography?

• One-way hash functions were first used in databases because it is faster to locate a short piece of information in a hash than a whole, long string of characters. Since their inception, one-way hash functions have become more popular in encryption.
• Hashing enables people to encrypt and decrypt digital signatures. The digital signature is converted into a hash value and transmitted to the recipient.
• After receiving the encrypted value, the computer generates the hash value using the same hash function.
• Then compares it to the message. If the two are the same, the message was delivered without mistakes.

Conclusion

In computer science, a one-way function is easy to compute in one direction but hard to reverse. This means you can quickly get the output from an input, but it's tough to figure out the input from the output. The terms "easy" and "hard" here refer to how quickly these tasks can be done by a computer, specifically relating to polynomial time problems. For a function to be considered one-way, it must be hard to reverse even if it's not one-to-one (where one input gives a unique output).

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Article Tags :

• Computer Networks
• cryptography