Fundamental difference between Hashing and Encrypt

Question

I see a lot of confusion between hashes and encryption algorithms and I would like to hear some more expert advice about:

1. When to use hashes vs encryptions

2. What makes a hash or encryption algorithm different (from a theoretical/mathematical level) i.e. what makes hashes irreversible (without aid of a rainbow tree)

Here are some similar SO Questions that didn't go into as much detail as I was looking for:

What is the difference between Obfuscation, Hashing, and Encryption?
Difference between encryption and hashing

Answer 1

Symmetric Encryption:

Symmetric encryption may also be referred to as shared key or shared secret encryption. In symmetric encryption, a single key is used both to encrypt and decrypt traffic.

Asymmetric Encryption:

Asymmetric encryption is also known as public-key cryptography. Asymmetric encryption differs from symmetric encryption primarily in that two keys are used: one for encryption and one for decryption. The most common asymmetric encryption algorithm is RSA.

Compared to symmetric encryption, asymmetric encryption imposes a high computational burden, and tends to be much slower. Thus, it isn't typically employed to protect payload data. Instead, its major strength is its ability to establish a secure channel over a nonsecure medium (for example, the Internet). This is accomplished by the exchange of public keys, which can only be used to encrypt data. The complementary private key, which is never shared, is used to decrypt.

Hashing:

Finally, hashing is a form of cryptographic security which differs from encryption. Whereas encryption is a two step process used to first encrypt and then decrypt a message, hashing condenses a message into an irreversible fixed-length value, or hash. Two of the most common hashing algorithms seen in networking are MD5 and SHA-1.

Read more here:http://packetlife.net/blog/2010/nov/23/symmetric-asymmetric-encryption-hashing/

Answer 2

EncryptionThe Purpose of encryption is to transform data in order to keep it secret E.g (Sending someone a secret text that they only should able to read,sending passwords through Internet).

Instead of focusing the usability the goal is to ensure the data send can be send secretely and it can only seen by the user whom you sent.

It Encrypts the data into another format of transforming it into unique pattern it can be encrypt with the secret key and those users who having the secret key can able to see the message by reversible the process. E.g(AES,BLOWFISH,RSA)

The encryption may simply look like this FhQp6U4N28GITVGjdt37hZN

Hashing In technically we can say it as takes a arbitary input and produced a fixed length string.

Most important thing in these is you can't go from the output to the input.It prodeuce the strong ouptut that the given information has not been modified. The process is to takes a input and hash it and then send with the sender's private key once the receiver received they can validate it with sender's public key.

If the hash is wrong and did't match with hash we can't see any of the information. E.g(MD5,SHA.....)

Answer 3

A Hash function turns a variable-sized amount of text into a fixed-sized text.

Source: https://en.wikipedia.org/wiki/Hash_function

Lets see it in action. I use php for it.

HASH:

$str = 'My age is 29';
$hash = hash('sha1', $str);
echo $hash; // OUTPUT: 4d675d9fbefc74a38c89e005f9d776c75d92623e

DEHASH:

SHA1 is a one-way hash. Which means that you can't dehash the hash. However, you can brute-force the hash. Please see: https://hashkiller.co.uk/sha1-decrypter.aspx.

MD5, is another hash. A MD5 dehasher can be found on this website: https://www.md5online.org/.

An Encryption function transforms a text into a nonsensical ciphertext by using an encryption key, and vice versa.

Source: https://en.wikipedia.org/wiki/Encryption

--- Example: The Mcrypt extention in PHP ---

ENCRYPT:

$cipher = MCRYPT_RIJNDAEL_128;
$key = 'A_KEY';
$data = 'My age is 29';
$mode = MCRYPT_MODE_ECB;

$encryptedData = mcrypt_encrypt($cipher, $key , $data , $mode);
var_dump($encryptedData);

//OUTPUT:
string '„Ùòyªq³¿ì¼üÀpå' (length=16)

DECRYPT:

$decryptedData = mcrypt_decrypt($cipher, $key , $encryptedData, $mode);
$decryptedData = rtrim($decryptedData, "\0\4"); // Remove the nulls and EOTs at the END
var_dump($decryptedData);

//OUTPUT:
string 'My age is 29' (length=12)

--- Example: The OpenSSL extention in PHP ---

The Mcrypt extention was deprecated in 7.1. and removed in php 7.2. The OpenSSL extention should be used in php 7. See the code snippets below:

$key = 'A_KEY';
$data = 'My age is 29';

// ENCRYPT
$encryptedData = openssl_encrypt($data , 'AES-128-CBC', $key, 0, 'IV_init_vector01');
var_dump($encryptedData);

// DECRYPT    
$decryptedData = openssl_decrypt($encryptedData, 'AES-128-CBC', $key, 0, 'IV_init_vector01');
var_dump($decryptedData);

//OUTPUT
string '4RJ8+18YkEd7Xk+tAMLz5Q==' (length=24)
string 'My age is 29' (length=12)

Answer 4

Basic overview of hashing and encryption/decryption techniques are.

Hashing:

If you hash any plain text again you can not get the same plain text from hashed text. Simply, It's a one-way process.

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Encryption and Decryption:

If you encrypt any plain text with a key again you can get same plain text by doing decryption on encrypted text with same(symetric)/diffrent(asymentric) key.

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UPDATE: To address the points mentioned in the edited question.

1. When to use hashes vs encryptions

Hashing is useful if you want to send someone a file. But you are afraid that someone else might intercept the file and change it. So a way that the recipient can make sure that it is the right file is if you post the hash value publicly. That way the recipient can compute the hash value of the file received and check that it matches the hash value.

Encryption is good if you say have a message to send to someone. You encrypt the message with a key and the recipient decrypts with the same (or maybe even a different) key to get back the original message. credits

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2. What makes a hash or encryption algorithm different (from a theoretical/mathematical level) i.e. what makes hashes irreversible (without aid of a rainbow tree)

Basically hashing is an operation that loses information but not encryption. Let's look at the difference in simple mathematical way for our easy understanding, of course both have much more complicated mathematical operation with repetitions involved in it

Encryption/Decryption (Reversible):

Addition:

4 + 3 = 7  

This can be reversed by taking the sum and subtracting one of the addends

7 - 3 = 4     

Multiplication:

4 * 5 = 20  

This can be reversed by taking the product and dividing by one of the factors

20 / 4 = 5    

So, here we could assume one of the addends/factors is a decrpytion key and result(7,20) is an excrypted text.

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Hashing (Not Reversible):

Modulo division:

22 % 7 = 1   

This can not be reversed because there is no operation that you can do to the quotient and the dividend to reconstitute the divisor (or vice versa).

Can you find an operation to fill in where the '?' is?

1  ?  7 = 22  
1  ?  22 = 7

So hash functions have the same mathematical quality as modulo division and looses the information.

credits

Answer 5

A hash function could be considered the same as baking a loaf of bread. You start out with inputs (flour, water, yeast, etc...) and after applying the hash function (mixing + baking), you end up with an output: a loaf of bread.

Going the other way is extraordinarily difficult - you can't really separate the bread back into flour, water, yeast - some of that was lost during the baking process, and you can never tell exactly how much water or flour or yeast was used for a particular loaf, because that information was destroyed by the hashing function (aka the oven).

Many different variants of inputs will theoretically produce identical loaves (e.g. 2 cups of water and 1 tsbp of yeast produce exactly the same loaf as 2.1 cups of water and 0.9tsbp of yeast), but given one of those loaves, you can't tell exactly what combo of inputs produced it.

Encryption, on the other hand, could be viewed as a safe deposit box. Whatever you put in there comes back out, as long as you possess the key with which it was locked up in the first place. It's a symmetric operation. Given a key and some input, you get a certain output. Given that output, and the same key, you'll get back the original input. It's a 1:1 mapping.

Answer 6

Use hashes when you don't want to be able to get back the original input, use encryption when you do.

Hashes take some input and turn it into some bits (usually thought of as a number, like a 32 bit integer, 64 bit integer, etc). The same input will always produce the same hash, but you PRINCIPALLY lose information in the process so you can't reliably reproduce the original input (there are a few caveats to that however).

Encryption principally preserves all of the information you put into the encryption function, just makes it hard (ideally impossible) for anyone to reverse back to the original input without possessing a specific key.

Simple Example of Hashing

Here's a trivial example to help you understand why hashing can't (in the general case) get back the original input. Say I'm creating a 1-bit hash. My hash function takes a bit string as input and sets the hash to 1 if there are an even number of bits set in the input string, else 0 if there were an odd number.

Example:

Input    Hash
0010     0
0011     1
0110     1
1000     0

Note that there are many input values that result in a hash of 0, and many that result in a hash of 1. If you know the hash is 0, you can't know for sure what the original input was.

By the way, this 1-bit hash isn't exactly contrived... have a look at parity bit.

Simple Example of Encryption

You might encrypt text by using a simple letter substitution, say if the input is A, you write B. If the input is B, you write C. All the way to the end of the alphabet, where if the input is Z, you write A again.

Input   Encrypted
CAT     DBU
ZOO     APP

Just like the simple hash example, this type of encryption has been used historically.