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.

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Why is this authentication procedure using Rabin crypto not useful?

A friend asked me the following, pointing out that the method is not very useful (my problem is I do not see why it is not good): Consider a person A which chooses $n$ as the public key for the ...
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543 views

Identification of correct plaintext after decryption in Rabin cryptosystem

In the Rabin cryptosystem, decrypting a message can produce four different outputs, of which only one is the correct plaintext. How can one know which of the outputs is the correct one?
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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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135 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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122 views

Pseudo Random Generator (PRG) from Rabin function

I'm trying to make a PRG using the Rabin function. The code (in Java) I wrote to implement the function is: ...
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189 views

Is Rabin's cryptosystem secure against known-plaintext attacks?

I've bee learning about Rabin's cryptosystem, and I already know that Rabin's cryptosystem is vulnerable to a chosen-ciphertext attack, but I was wondering, is it also vulnerable against ...
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68 views

Why isn't Rabin-Williams cryptosystem widely used?

I think we all know RSA. And of course we also know DJB (a.k.a. Daniel J. Bernstein). Now some already have noticed that he has an opinion towards cryptographic questions. In his 2008 paper on ...
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23 views

Why does P1363 require RW signature with $0 ≤ s < n/2$?

I'm using an older copy of P1363 Public Key Cryptography was used below. It may (or may not) reflect the current state of affairs. P1363 has the following requirement in section 8.2.8 IFSP-RW, p. 45: ...
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42 views

Tweaked Square Roots and Rabin-Williams

I'm reading Bernstein's RSA signatures and Rabin–Williams signatures: the state of the art. In section 6, Bernstein states: Recall that Rabin’s system needed to try several values of r, on ...
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1answer
55 views

Rabin-Williams, blinding and size of Integer r?

I was reading the paper Breaking the Rabin-Williams digital signature system implementation in the Crypto++ library. The library uses blinding, but it was not enough to stop key recovery. But my ...
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171 views

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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188 views

Solving a quadratic equation for a variant of Rabin

My understanding of Rabin We have $p$ and $q$ which are distinct primes congruent to $3 \pmod 4$. Then we have $n = pq$. Encryption is done as $e(m) = m^2 \pmod n$, where $m$ is our message. ...
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How to prove the hardness of Rabin's function?

I am unable to prove the following theorem: If for a $1/(\log(n))$ fraction of the quadratic residues $q\pmod n$ one could find a square root of $q$, then one could factor $n$ in random polynomial ...
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72 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 ...
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198 views

How does knowing the factorization of N can help to obtain the secret?

Assuming $x=a^2 \pmod n$ and knowing $x$, $p$, $q$ how is it possible to obtain $a$?