# Tagged Questions

A public-key cryptosystem based on squaring modulo the product of two primes, introduced in 1979 by Michael O. Rabin and proven to have security reducible to the hardness of integer factorization. It is similar to RSA but uses e=2.

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### Are there UFDs where the factorization problem is difficult but finding irreducibles is cheap?

Factorization of integers is hard, but finding irreducibles is expensive. Is there a ring where factorization is assumed hard but finding irreducibles is much cheaper than over $\Bbb Z$? It could ...
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### Residue requirements of Rabin-Williams primes?

I'm trying to determine the residue requirements of Rabin-Williams. An older copy of P1363's Public Key Cryptography states the following in Section 8.1.3.2 RW key pairs: An RW public key consists ...
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### Rabin/RSA four possible messages?

Given this encryption method: $$f_{N,e} : Z^{*}_{N} \to QR(N)^{*};\quad f_{N,e}(x) = x ^{2e} \bmod N$$ I need to show that, for any $x_{0} \in Z^{*}_{N}$, there are four elements $x \in Z^{*}_{N}$ ...
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### Rabin code same message sent with different $N$

I use Rabin code with modulus $N$. Now assume that Alice sends me a message $m$ $(1\le m\le N)$ encoded by Rabin code. Unfortunately after Alice sent me the text I lose the information about the ...