# Questions tagged [bijection]

A bijection (or a bijective function) is a function $f$ from a set $X$ to a set $Y$ with the property that, for every $y$ in $Y$, there is exactly one $x$ in $X$ such that $f(x) = y$. It follows from this definition that no unmapped element exists in either $X$ or $Y$.

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### Does an binary elliptic curve like sect571r1 support a bijective asymmetric operation pair on bytes? If so, is there a self-contained example?

I'm wondering if a binary elliptic curve (such as sect571r1 aka B-571) supports pairs of asymmetric operations (for example, either sign/verify or encrypt/decrypt) on a fixed bit or byte input size in ...
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### Bijective function with unknown reciprocal function

I have a use case where I need to build a unique identifier for my users with the email address and the "family member number". However, the two personal informations used to build the ...
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### Proving that RSA encryption function with non-square free modulus is not a permutation

Here is a backgroung for the question on hand. While studying RSA I came up to the question about what happens if $p$ and $q$ involved in modulus computation are not actually primes? There is already ...
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### Is it reasonable to consider that an encryption scheme must be invertible?

I am in a dispute regarding a test question in an exam. The question is something like that: What would happen if one were to use RSA with $n=100$ and $e=13$ to encrypt a message $m$? a) You would be ...
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### Why $f(x)=x^e$ is a bijection i.f.f $e\in{\mathbf{Z^*_{\phi(N)}}}$?
I understand that if $e\in{\mathbf{Z^*_{\phi(N)}}}$ then $\gcd(e,\phi(N))=1$ and if $e\not\in{\mathbf{Z^*_{\phi(N)}}}$ than $\gcd(e,\phi(N))\neq{}1$. But I couldn't figure out why this implies ...