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Is there a cryptographic primitive process/method for creating cryptographic tools like symmetric encryption/decryption, Hash code generator, MAC generator and Random number generator?

 Or

Is it possible to create cryptographic tools like symmetric encryption/decryption, Hash code generator, MAC generator and Random number generator using the same cryptographic primitive process/method?

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I can't quite undestand what you mean by 'cryptographic primitive process'? I think you should clarify your question a bit. –  Rami Luisto Jan 24 '13 at 9:10

2 Answers 2

Hi,

from any blockcipher (for example as Threefish as mentioned by Gro-Tsen) you can build various other primitives. This is heavily related to their mode of operation. You can find basic pointers in wikipedia's article on block ciphers.But usually one uses dedicated algorithms for different problems like encryption, hashes, etc..

However there are other much more general approaches, for example many primitives can be seen as instances of sponge constructions. But it is hard to guess what you are looking for.

Also 'cryptographic primitive' is more an idea rather than a fixed notion. It is distinguishes 'cryptographic algorithms' from 'cryptographic schemes'. There is a beautiful paper from U.Maurer: Constructive cryptography about 'pasting' primitives.

All this said, it seems to be a question for crypto.stackexchange. Also you should provide more background in what (and why) your are interested.

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The Threefish block cipher, for example, is well equipped to do all the things you mention (it's a symmetric cipher which was built for the purpose of creating the Skein hash function, a SHA-3 finalist; the Skein paper explains how it can easily be used as a MAC and RNG).

That being said, I don't think MathOverfow was the right place to ask this particular question.

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Thanks for the response. –  Auth Jan 24 '13 at 15:04
    
Let me modify my question, i.e. is there a cryptographic primitive one-to-one function for creating the above mentioned tools like symmetric encryption/decryption, Hash code generator, MAC generator and Random number generator? –  Auth Jan 24 '13 at 15:12

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