(or message authentication code), a short piece of information used to authenticate a message, and the algorithm to create and check such information, using a secret key.

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Cryptographic Primitive Method

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 ...
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HMAC ipad and opad choice

It is written in the HMAC paper that the $ipad=0x36$ and $opad=0x5c$ were chosen such that it maximize the Hamming-Distance of the part of the key used in the inner and outer part of the HMAC process. ...
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Attacking both authenticity and secrecy in authenticated encryption modes

looks like NIST only approved GCM mode for authenticated encryption and other modes don't have any approval or a good implementation available. Is that possible a weakness in $GHASH$ compromise ...
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Attacking multi block MAC constructions

For variable-length messages, there are three different ways to generate the tags. $Tag = MAC_k(\Sigma_i m_i)$. $t_i = MAC_k(m_i)$ and $Tag = (t_1, ..., t_l)$. $t_i = MAC_k(i||m_i)$ ...