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The SHA-1 Hash Function

In this blog post, we are going to explore a core concept of the “Git” Technology :

the SHA-1 Hash function.

Briefly, any file in a computer can be thought of as a series of bytes, each of which is 8 bits. If  you put these bytes from left to right, all files can be thought of as very large numbers represented in binary (base-2) format. Cryptographers have come up with a very interesting function called SHA-1 which has the following curious property: any binarynumber, up to 264 bits, can be rapidly mapped to a 160 bit (20 byte) number that we can visualize as a 40 character  long number in hexadecimal (base-16) format. Here is an example using node’s crypto module:

sha-1-hash-function

The point is that, even binary numbers which are very close,  map to completely different 20 byte SHA-1 values, which means SHA-1(x) is very different from most “normal” functions like cos(x)

SHA-1 Hash function

Because a hash can be assumed to map 1-to-1 to a file, rather than conveying the full file’s contents to distinguish it, you can just use the hash. Indeed, you can just use a hash to uniquely identify any string of bits less than 264 bits in length.

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