Questions tagged [cramer-shoup]

Cramer-Shoup asymmetric encryption (an extension of ElGamal)

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Is Cramer-Shoup Lite IND-CCA secure?

Recently, I studied about Cramer-Shoup encryption scheme. Then, I read a book which mentioned a simpler version of this scheme, the Cramer-Shoup Lite encryption scheme. I was wondering if there is ...
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Issues generating keys/cyclic group for Cramer-Shoup Cryptosystem with OpenSSL

I'm trying to implement a Cramer Shoup cryptography system in C but I've run into problems with generating the keys. From what I have found on the wiki and in other papers, to generate keys for Cramer ...
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ECCS: Elliptic Curve Cryptography Cramer Shoup

Introduction I know how to do Cramer-Shoup with cyclic groups. But how do I do it in elliptic curve cryptography (ECC)? Cramer-Shoup with cyclic groups Following was taken from Wikipedia: https://...
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Does Cramer-Shoup allow re-randomization?

Is it possible to re-randomize a ciphertext with the Cramer-Shoup System? I have some Cramer-Shoup ciphertexts and i want to re-randomize them, so they look different and are unlinkable to there ...
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Knowledge of discrete log is needed in the proof of Cramer-Shoup public key scheme?

In the proof of the Cramer-Shoup public key scheme [1], I understand that the adversary's view can be seen as equations such as $\log c = x_1 + w x_2, \log d = y_1 + w y_2$ and so on (equation 1 and 2 ...
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What's the proper way of fitting hash digest to encryption scheme?

I would like to know what is the proper way of fitting the hash digest to the prime in which the encryption scheme operates. regardless if the bits of the hash digest is larger or smaller than the ...
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Intuition for Cramer Shoup Encryption Scheme?

I was reading the Cramer Shoup CCA2 secure encryption scheme. The scheme is as follows. Public key = $(g_1, g_2, c, d, h, hk)$, where $c = g_1^{x_1}g_2^{y_1}$, $d = g_1^{x_2}g_2^{y_2}$, $h = g_1^z$, ...
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Why is the lite version of Cramer-Shoup not IND-CCA2 secure?

In the lite version of Cramer-Shoup we have a group $G$ with generators $g_1$ and $g_2$, private key $a_1, a_2, b_1, b_2$, and public key $A = g_1^{a_1} g_2^{a_2}$, $B = g_1^{b_1} g_2^{b_2}$. ...
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Can a Cramer-Shoup public key have two different private keys?

Since I am new to the Cramer-Shoup algorithm, I would like to know: Is it possible to have two different private keys for a public key due the key pair generation algorithm that Cramer-Shoup uses? I ...
The Full Cramer-Shoup Encryption scheme needs to choose six random numbers from $\mathbb{Z}_q$, which we denote them by $x_1,x_2,y_1,y_2,z_1,z_2$. Then the scheme hides these random numbers in the ...