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Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions. When creating cryptographic systems, designers use cryptographic primitives as their most basic building blocks. Because of this, cryptographic primitives are designed to do one very specific task in a precisely defined and highly reliable fashion. Since cryptographic primitives are used as building blocks, they must be very reliable, i.e. perform according to their specification. For example, if an encryption routine claims to be only breakable with number of computer operations, and it is broken with significantly fewer than operations, then that cryptographic primitive has failed. If a cryptographic primitive is found to fail, almost every protocol that uses it becomes vulnerable. Since creating cryptographic routines is very hard, and testing them to be reliable takes a long time, it is essentially never sensible (nor secure) to design a new cryptographic primitive to suit the needs of a new cryptographic system. The reasons include: The designer might not be competent in the mathematical and practical considerations involved in cryptographic primitives. Designing a new cryptographic primitive is very time-consuming and very error-prone, even for experts in the field. Since algorithms in this field are not only required to be designed well but also need to be tested well by the cryptologist community, even if a cryptographic routine looks good from a design point of view it might still contain errors. Successfully withstanding such scrutiny gives some confidence (in fact, so far, the only confidence) that the algorithm is indeed secure enough to use; security proofs for cryptographic primitives are generally not available. Cryptographic primitives are similar in some ways to programming languages.

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In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to conventional data compression algorithms, which instead can be inverted exactly (lossless compression) or approximately (lossy compression) to the original data.

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