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Cryptographic Hash Functions

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  The cryptographic hash functions are well-known cryptographic primitives. They are widely used, either as stand-alone or as a building block in other, more complex constructions. Their applicability covers a wide area, some popular examples being password storage, electronic signatures, and blockchain. Please note that cryptographic hash functions must satisfy some (of the) security notions I will discuss later on, while non-cryptographic hash functions do not necessarily have to. Therefore, not all hash functions are cryptographically strong. Non-cryptographic hash functions are also valuable, e.g., in data structures. However, for simplicity, I will sometimes refer to cryptographic hash functions as simply  hash functions . As a note, there are also hash functions with a secret key , known as keyed hash functions. I will not refer to these keyed hash functions here; I will only explain the keyless (or unkeyed ) hash functions.   Cryptographic hash functions accept  binary inputs
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Perfect Secrecy and the One Time Pad (OTP)

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I have explained unconditional  (or  information-theoretical)  security in my previous post (see Unconditional vs. Conditional Security ). As I have mentioned there, we can refer to unconditional security in the context of various cryptographic primitives, among which the  encryption schemes (see Symmetric vs. Asymmetric Encryption ). An encryption scheme that is information-theoretically secure provides  perfect secrecy (see, e.g., [1]) ,  because the  ciphertext  perfectly  hides  the  plaintext.  In other words, the adversary has the same probability to correctly indicate the message  m  regardless if he/she knows the corresponding ciphertext  c.  Hence, the knowledge of the ciphertext gives no new information about the plaintext. We ignore the length of the message - which, of course, is exposed - and assume that all the possible messages are equally long. More rigorously, the  a-posteriori  probability  Pr[M=m/C=c]  to guess the plaintext  m  ( a - posteriori  in the sense that
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