A "nonce" is an arbitrary number or string used only once within the context of a specific cryptographic scheme. Nonces are used e.g. in authentication protocols to prevent replay attacks, as well as in stream ciphers (including CTR mode) to avoid keystream reuse.

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What is a definition of a nonce?

Sometimes I read that nonce have to be a random number but imho it's wrong, nonce just should not repeat itself. You could increase in by 1 every time if you are sure it would never repeat.