Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build 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 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 X number of computer operations, then if it can be broken with significantly less than X operations, that cryptographic primitive is said to fail. 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:
Cryptographic primitives are similar in some ways to programming languages. A computer programmer rarely invents a new programming language while writing a new program; instead, they will use one of the already established programming languages to program in.
Cryptographic primitives are one of the building blocks of every crypto system, e.g., TLS, SSL, SSH, etc. Crypto system designers, not being in a position to definitively prove their security, must take the primitives they use as secure. Choosing the best primitive available for use in a protocol usually provides the best available security. However, compositional weaknesses are possible in any crypto system and it is the responsibility of the designer(s) to avoid them.
Cryptographic primitives, on their own, are quite limited. They cannot be considered, properly, to be a cryptographic system. For instance, a bare encryption algorithm will provide no authentication mechanism, nor any explicit message integrity checking. Only when combined in security protocols, can more than one security requirement be addressed. For example, to transmit a message that is not only encoded but also protected from tinkering (i.e. it is confidential and integrity-protected), an encoding routine, such as DES, and a hash-routine such as SHA-1 can be used in combination. If the attacker does not know the encryption key, he can not modify the message such that message digest value(s) would be valid.