Fundamental difference between Hashing and Encryption algorithms

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

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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

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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

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Use hashes when you only need to go one way   For example  for passwords in a system  you use hashing because you will only ever verify that the value a user entered  after hashing  matches the value in your repository   With encryption  you can go two ways  hashing algorithms and encryption algorithms are just mathematical algorithms   So in that respect they are not different -- its all just mathematical formulas   Semantics wise  though  there is the very big distinction between hashing  one-way  and encryption two-way    Why are hashes irreversible   Because they are designed to be that way  because sometimes you want a one-way operation

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Cryptography deals with numbers and strings  Basically every digital thing in the entire universe are numbers  When I say numbers  its 0  amp  1  You know what they are  binary  The images you see on screen  the music that you listen through your earphone  everything are binaries  But our ears and eyes will not understand binaries right  Only brain could understand that  and even if it could understand binaries  it can   t enjoy binaries  So we convert the binaries to human understandable formats such as mp3 jpg etc  Let   s term the process as Encoding  It   s  two way process and can be easily decoded back to its original form   Hashing  Hashing is another cryptography technique in which a data once converted to some other form can never be recovered back  In Layman   s term  there is no process called de-hashing  There are many hash functions to do the job such as sha-512  md5 and so on    If the original value cannot be recovered  then where do we use this  Passwords  When you set up a password for your mobile or PC  a hash of your password is created and stored in a secure place  When you make a login attempt next time  the entered string is again hashed with the same algorithm  hash function  and the output is matched with the stored value  If it   s the same  you get logged in  Otherwise you are thrown out   Credits  wikimedia By applying hash to the password  we can ensure that an attacker will never get our password even if he steal the stored password file  The attacker will have the hash of the password  He can probably find a list of most commonly used passwords and apply sha-512 to each of it and compare it with the value in his hand  It is called the dictionary attack  But how long would he do this  If your password is random enough  do you think this method of cracking would work  All the passwords in the databases of Facebook  Google and Amazon are hashed  or at least they are supposed to be hashed   Then there is Encryption  Encryption lies in between hashing and encoding  Encoding is a two way process and should not be used to provide security  Encryption is also a two way process  but original data can be retrieved if and only if the encryption key is known  If you don   t know how encryption works  don   t worry  we will discuss the basics here  That would be enough to understand the basics of SSL  So  there are two types of Encryption namely Symmetric and Asymmetric encryption   Symmetric Key Encryption  I am trying to keep things as simple as I could  So  let   s understand the symmetric encryption by means of a shift algorithm  This algorithm is used to encrypt alphabets by shifting the letters to either left or right  Let   s take a string CRYPTO and consider a number  3  Then  the encrypted format of CRYPTO will be FUBSWR  That means each letter is shifted to right by 3 places  Here  the word CRYPTO is called Plaintext  the output FUBSWR is called the Ciphertext  the value  3 is called the Encryption key  symmetric key  and the whole process is a cipher  This is one of the oldest and basic symmetric key encryption algorithm and its first usage was reported during the time of Julius Caesar  So  it was named after him and it is the famous Caesar Cipher  Anyone who knows the encryption key and can apply the reverse of Caesar   s algorithm and retrieve the original Plaintext  Hence it is called a Symmetric Encryption   Asymmetric Key Encryption  We know that  in Symmetric encryption same key is used for both encryption and decryption  Once that key is stolen  all the data is gone  That   s a huge risk and we need more complex technique  In 1976  Whitfield Diffie and Martin Hellman first published the concept of Asymmetric encryption and the algorithm was known as Diffie   Hellman key exchange  Then in 1978  Ron Rivest  Adi Shamir and Leonard Adleman of MIT published the RSA algorithm  These can be considered as the foundation of Asymmetric cryptography   As compared to Symmetric encryption  in Asymmetric encryption  there will be two keys instead of one  One is called the Public key  and the other one is the Private key  Theoretically  during initiation we can generate the Public-Private key pair to our machine  Private key should  be kept in a safe place and it should never be shared with anyone  Public key  as the name indicates  can be shared with anyone who wish to send encrypted text to you  Now  those who have your public key can encrypt the secret data with it  If the key pair were generated using RSA algorithm  then they should use the same algorithm while encrypting the data  Usually the algorithm will be specified in the public key  The encrypted data can only be decrypted with the private key which is owned by you   Source  SSL TLS for dummies part 1   Ciphersuite  Hashing Encryption   WST  https   www wst space ssl-part1-ciphersuite-hashing-encryption

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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

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A Hash function turns a variable-sized amount of text into a fixed-sized text     Source  https   en wikipedia org wiki Hash function    Hash functions in PHP  A hash turns a string to a hashed string  See below    HASH    str    My age is 29    hash   hash  sha1    str   echo  hash     OUTPUT  4d675d9fbefc74a38c89e005f9d776c75d92623e   Passwords are usually stored in their hashed representation instead as readable text  When an end-user wants gain access to an application protected with a password then a password must be given during authentication  When the user submits his password  then the valid authentication system receives the password and hashes this given password  This password hash is compared to the hash known by the system  Access is granted in case of equality   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    To hamper brute-force attacks on hashes a salt can be given   In php you can use password hash   for creating a password hash   The function password hash   automatically creates a salt  To verify a password on a password hash  with a salt  use password verify        Invoke this little script 3 times  and it will give you everytime a new hash  password    1234      hash   password hash  password  PASSWORD DEFAULT      echo  hash      OUTPUT    2y 10 ADxKiJW Jn2DZNwpigWZ1ePwQ4il7V0ZB4iPeKj11n iaDtLrC8bu    2y 10 H8jRnHDOMsHFMEZdT4Mk4uI4DCW7 YRKjfdcmV3MiA WdzEvou71u    2y 10 qhyfIT25jpR63vCGvRbEoewACQZXQJ5glttlb01DmR4ota4L25jaW   One password can be represented by more then one hash  When you verify the password with different password hashes by using password verify    then the password will be accepted as a valid password      password    1234       hash     2y 10 ADxKiJW Jn2DZNwpigWZ1ePwQ4il7V0ZB4iPeKj11n iaDtLrC8bu     var dump  password verify  password   hash         hash     2y 10 H8jRnHDOMsHFMEZdT4Mk4uI4DCW7 YRKjfdcmV3MiA WdzEvou71u     var dump  password verify  password   hash         hash     2y 10 qhyfIT25jpR63vCGvRbEoewACQZXQJ5glttlb01DmR4ota4L25jaW     var dump  password verify  password   hash         OUTPUT   boolean true   boolean true   boolean true         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    Encryption in PHP  Let s dive into some PHP code that handles encryption    --- The Mcrypt extention ---  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         y  q            p     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    --- The OpenSSL extention ---  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

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Encryption and hash algorithms work in similar ways   In each case  there is a need to create confusion and diffusion amongst the bits   Boiled down  confusion is creating a complex relationship between the key and the ciphertext  and diffusion is spreading the information of each bit around   Many hash functions actually use encryption algorithms  or primitives of encryption algorithms   For example  the SHA-3 candidate Skein uses Threefish as the underlying method to process each block   The difference is that instead of keeping each block of ciphertext  they are destructively  deterministically merged together to a fixed length

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when it comes to security for transmitting data i e Two way communication you use encryption All encryption requires a key  when it comes to authorization you use hashing There is no key in hashing  Hashing takes any amount of data  binary or text  and creates a constant-length hash representing a checksum for the data  For example  the hash might be 16 bytes  Different hashing algorithms produce different size hashes  You obviously cannot re-create the original data from the hash  but you can hash the data again to see if the same hash value is generated  One-way Unix-based passwords work this way  The password is stored as a hash value  and to log onto a system  the password you type is hashed  and the hash value is compared against the hash of the real password  If they match  then you must ve typed the correct password   why is hashing irreversible    Hashing isn t reversible because the input-to-hash mapping is not 1-to-1  Having two inputs map to the same hash value is usually referred to as a  hash collision   For security purposes  one of the properties of a  good  hash function is that collisions are rare in practical use

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Well  you could look it up in Wikipedia     But since you want an explanation  I ll do my best here   Hash Functions  They provide a mapping between an arbitrary length input  and a  usually  fixed length  or smaller length  output   It can be anything from a simple crc32  to a full blown cryptographic hash function such as MD5 or SHA1 2 256 512   The point is that there s a one-way mapping going on   It s always a many 1 mapping  meaning there will always be collisions  since every function produces a smaller output than it s capable of inputting  If you feed every possible 1mb file into MD5  you ll get a ton of collisions    The reason they are hard  or impossible in practicality  to reverse is because of how they work internally   Most cryptographic hash functions iterate over the input set many times to produce the output   So if we look at each fixed length chunk of input  which is algorithm dependent   the hash function will call that the current state   It will then iterate over the state and change it to a new one and use that as feedback into itself  MD5 does this 64 times for each 512bit chunk of data    It then somehow combines the resultant states from all these iterations back together to form the resultant hash   Now  if you wanted to decode the hash  you d first need to figure out how to split the given hash into its iterated states  1 possibility for inputs smaller than the size of a chunk of data  many for larger inputs    Then you d need to reverse the iteration for each state   Now  to explain why this is VERY hard  imagine trying to deduce a and b from the following formula  10   a   b   There are 10 positive combinations of a and b that can work   Now loop over that a bunch of times  tmp   a   b  a   b  b   tmp  For 64 iterations  you d have over 10 64 possibilities to try   And that s just a simple addition where some state is preserved from iteration to iteration   Real hash functions do a lot more than 1 operation  MD5 does about 15 operations on 4 state variables   And since the next iteration depends on the state of the previous and the previous is destroyed in creating the current state  it s all but impossible to determine the input state that led to a given output state  for each iteration no less    Combine that  with the large number of possibilities involved  and decoding even an MD5 will take a near infinite  but not infinite  amount of resources  So many resources that it s actually significantly cheaper to brute-force the hash if you have an idea of the size of the input  for smaller inputs  than it is to even try to decode the hash    Encryption Functions  They provide a 1 1 mapping between an arbitrary length input and output   And they are always reversible   The important thing to note is that it s reversible using some method   And it s always 1 1 for a given key   Now  there are multiple input key pairs that might generate the same output  in fact there usually are  depending on the encryption function    Good encrypted data is indistinguishable from random noise   This is different from a good hash output which is always of a consistent format   Use Cases  Use a hash function when you want to compare a value but can t store the plain representation  for any number of reasons    Passwords should fit this use-case very well since you don t want to store them plain-text for security reasons  and shouldn t    But what if you wanted to check a filesystem for pirated music files   It would be impractical to store 3 mb per music file   So instead  take the hash of the file  and store that  md5 would store 16 bytes instead of 3mb    That way  you just hash each file and compare to the stored database of hashes  This doesn t work as well in practice because of re-encoding  changing file headers  etc  but it s an example use-case    Use a hash function when you re checking validity of input data   That s what they are designed for   If you have 2 pieces of input  and want to check to see if they are the same  run both through a hash function   The probability of a collision is astronomically low for small input sizes  assuming a good hash function    That s why it s recommended for passwords   For passwords up to 32 characters  md5 has 4 times the output space   SHA1 has 6 times the output space  approximately    SHA512 has about 16 times the output space   You don t really care what the password was  you care if it s the same as the one that was stored   That s why you should use hashes for passwords   Use encryption whenever you need to get the input data back out   Notice the word need   If you re storing credit card numbers  you need to get them back out at some point  but don t want to store them plain text   So instead  store the encrypted version and keep the key as safe as possible    Hash functions are also great for signing data   For example  if you re using HMAC  you sign a piece of data by taking a hash of the data concatenated with a known but not transmitted value  a secret value    So  you send the plain-text and the HMAC hash   Then  the receiver simply hashes the submitted data with the known value and checks to see if it matches the transmitted HMAC   If it s the same  you know it wasn t tampered with by a party without the secret value   This is commonly used in secure cookie systems by HTTP frameworks  as well as in message transmission of data over HTTP where you want some assurance of integrity in the data   A note on hashes for passwords   A key feature of cryptographic hash functions is that they should be very fast to create  and very difficult slow to reverse  so much so that it s practically impossible    This poses a problem with passwords   If you store sha512 password   you re not doing a thing to guard against rainbow tables or brute force attacks  Remember  the hash function was designed for speed   So it s trivial for an attacker to just run a dictionary through the hash function and test each result   Adding a salt helps matters since it adds a bit of unknown data to the hash   So instead of finding anything that matches md5 foo   they need to find something that when added to the known salt produces md5 foo salt   which is very much harder to do    But it still doesn t solve the speed problem since if they know the salt it s just a matter of running the dictionary through   So  there are ways of dealing with this   One popular method is called key strengthening  or key stretching    Basically  you iterate over a hash many times  thousands usually    This does two things   First  it slows down the runtime of the hashing algorithm significantly   Second  if implemented right  passing the input and salt back in on each iteration  actually increases the entropy  available space  for the output  reducing the chances of collisions   A trivial implementation is   var hash   password   salt  for  var i   0  i  lt  5000  i          hash   sha512 hash   password   salt       There are other  more standard implementations such as PBKDF2  BCrypt   But this technique is used by quite a few security related systems  such as PGP  WPA  Apache and OpenSSL    The bottom line  hash password  is not good enough   hash password   salt  is better  but still not good enough     Use a stretched hash mechanism to produce your password hashes     Another note on trivial stretching  Do not under any circumstances feed the output of one hash directly back into the hash function   hash   sha512 password   salt    for  i   0  i  lt  1000  i          hash   sha512 hash       lt -- Do NOT do this      The reason for this has to do with collisions   Remember that all hash functions have collisions because the possible output space  the number of possible outputs  is smaller than then input space   To see why  let s look at what happens   To preface this  let s make the assumption that there s a 0 001  chance of collision from sha1    it s much lower in reality  but for demonstration purposes    hash1   sha1 password   salt     Now  hash1 has a probability of collision of 0 001    But when we do the next hash2   sha1 hash1    all collisions of hash1 automatically become collisions of hash2   So now  we have hash1 s rate at 0 001   and the 2nd sha1   call adds to that   So now  hash2 has a probability of collision of 0 002    That s twice as many chances   Each iteration will add another 0 001  chance of collision to the result   So  with 1000 iterations  the chance of collision jumped from a trivial 0 001  to 1    Now  the degradation is linear  and the real probabilities are far smaller  but the effect is the same  an estimation of the chance of a single collision with md5 is about 1  2128  or 1  3x1038    While that seems small  thanks to the birthday attack it s not really as small as it seems    Instead  by re-appending the salt and password each time  you re re-introducing data back into the hash function   So any collisions of any particular round are no longer collisions of the next round   So   hash   sha512 password   salt   for  i   0  i  lt  1000  i          hash   sha512 hash   password   salt       Has the same chance of collision as the native sha512 function   Which is what you want   Use that instead

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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        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     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     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     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

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My two liners    generally Interviewer wanted the below answer  Hashing is one way   You can not convert your data  string from a hash code  Encryption is 2 way - you can decrypt again the encrypted string if you have the key with you

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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 sent secretly 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 produces the strong output that the given information has not been modified    The process is to take 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

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You already got some good answers  but I guess you could see it like this  ENCRYPTION  Encryption has to be decryptable if you have the right key  Example  Like when you send an e-mail  You might not want everyone in the world to know what you are writing to the person receiving the e-mail  but the person who receives the e-mail would probably want to be able to read it  HASHES  hashes work similar like encryption  but it should not be able to reverse it at all  Example  Like when you put a key in a locked door the kinds that locks when you close them   You do not care how the lock works in detail  just as long as it unlocks itself when you use the key  If there is trouble you probably cannot fix it  instead get a new lock  like forgetting passwords on every login  at least I do it all the time and it is a common area to use hashing       and I guess you could call that rainbow-algorithm a locksmith in this case  Hope things clear up

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