# Questions tagged [rabin-cryptosystem]

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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### Why did Rabin use $x(x + b)$ instead of just $x^2$ in the original paper?

Encryption in the original Rabin scheme took a message $x$ and computed $x(x + b) \bmod n$, where $0 \le b \lt n$ and $n$ is the product of two secret primes $p$ and $q$. The private key is defined as ...
101 views

### 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 ...
36 views

### 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 ...
288 views

### 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 ...
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### Encoding function for ISO 9796-2

I try to reproduce the analysis conducted in this presentation by R. Lifchitz. Namely, data signed by an 1024-bit key $n$ (Rabin scheme) and following ISO/IEC 9796-2. From what I understand, for a ...
48 views

### 1-out-of-2 Oblivious Transfer Security

Just started reading Oblivious Transfer. I am searching for a proof of security based on RSA implementation but I can't find anything simple to understand. Can someone direct/show me to an easy to ...
436 views

### Rabin cryptosystem with 1 mod 4

We have p and q which are distinct primes congruent to 1 mod 4. Then we have n = p*q. Do you know any algorith for calculating square roots for the decryption in this case? I'm asking for some ...