Is there any cryptographic primitive bijective (one-to-one and onto) function for creating cryptographic tools like symmetric encryption/decryption, Hash code generator, MAC, HMAC and Random number generator?
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As CodesInChaos notes, a secure block cipher satisfies all the criteria in your question:
Indeed, insofar as there exists a "universal building block" in modern cryptography, block ciphers are it. Pretty much the only thing they cannot do is public-key cryptography.
That said, block ciphers certainly aren't the only possible building block. For example, a cryptographic hash or pseudorandom function can be used in the Feistel / Luby–Rackoff construction to construct a block cipher, which can then be used to construct all the other things described above.