Cryptography Hash Function __ Cryptography

What is a hash function. A hash function is a mathematical function that has the following three attributes:

Enter a string that can be of any size; it produces a fixed-size output; for a specific input string, the result can be calculated at a reasonable time. A string that corresponds to n bits whose hash value evaluates to O (n).

To make the hash function password safe, you need to attach the following three features: Collision resistance, stealth, puzzle friendly

Characteristic 1: Collision resistance

The collision here means that the same output is produced for two different inputs. If no one can find a collision for the hash function h (x), the function is said to have collision resistance.

Defined:


The hash function h takes the variable length block M as input, producing a fixed length hash value h = h (M).

M is the original image of H. Because H is a many-to-many mapping, there are multiple primitives for any given hash value H. If X≠y and H (x) =h (y) are met, it is called a collision.

Application: Information Digest

Used to verify the integrity of the data, that is, to determine whether the data has been tampered with.

Feature 2: Confidentiality

Defined:

The hash function h is secretive if: when its input r is chosen from a probability distribution of a higher order minimum entropy, the given H (r| | x) conditions down to determine that x is not feasible.

Application: Commitment

We call the promise of what we want to do. Here the promise is a digital process, the analogy is as follows: First select a number, put the number into the envelope, and then put the envelope on a table that everyone can see. After doing so, you can say that you have made a commitment to the numbers in the envelope, and before you open the envelope, even though you have made a promise, it is a secret for others. After that you can open the envelope and show the value of your commitment.

Feature 3: Puzzle friendly

Defined:

If for any n-bit output value y, assuming K selected from higher-order minimum entropy distribution, if a feasible method cannot be found, find x in a much smaller amount of time than 2 n times, guaranteeing H (k| | x) =y is established, then we call hash function h as a puzzle friendly.

Application: Search Puzzle

In this application, we'll build a search puzzle that is a mathematical problem that needs to be searched for a huge space to find a solution. There is no shortcut to the search puzzle, which means there is no other way to solve it than to search for a huge space.

Finally, you are welcome to scan the following two-D code to pay attention to my personal public number.