Challenge-response authentication is a family of protocols in which one party presents a question ("challenge") and another party must provide a valid answer ("response") to be authenticated.

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Challenge-response based on public-key decryption, why send public key

Quoting the handbook of applied cryptography, chapter 10.3.3 (i): Identification based on PK decryption and witness. Consider the following protocol: $A \leftarrow B: h(r), B, P_A(r,B)$ ...
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Challenge–response authentication which can be done in head?

Say we have door where you have to say a password to pass. If theres someone standing nearby he would hear the password and could also use it. So therefore the doorman gives you a different number ...
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A rudimentary challenge–response authentication based on dot products in $\mathrm{GF}(2)^k$

We are building a rudimentary challenge–response authentication protocol based on dot products in $\mathrm{GF}(2)^k$. Assume a user has a password $\mathbf{p} \in \mathrm{GF}(2)^k$. When logging in, ...