Cryptography

Questions tagged [probabilistic-encryption]

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Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts.

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If a different plaintext may produce the same ciphertext, is the system perfectly secure?

Define the injective map $\phi: \Omega\rightarrow \mathbb{N}$, such that $\Omega=\mathcal{A}^n$ denotes the set of all strings of length $n\in\mathbb{N}^*$ from an alphabet $\mathcal{A}$ of elements $...
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Advantages and possible usages of encryption schemes with probabilistic decryption

We can define deterministic and probabilistic encryption; Deterministic $c = E(k,m)$, and Examples are textbook RSA, block ciphers in ECB mode. Deterministic encryption fails to achieve CPA security....
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Do probabilistic one-way functions imply deterministic one-way functions?

Suppose $f$ is a probabilistic one-way function. Then my question is, does there exist a construction of a deterministic one-way function $g$ based on $f$? Or is it possible that probabilistic one-...
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Why random number used in RSA padding but not in AES?

I noticed that people use a random number in the RSA-OAEP padding scheme to avoid deterministic encryption. But in pkcs#7 people just use the padding size rather than some random bits. Doesn't it make ...
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Probability of collision when we use a particular part of sha 256 hashed value

So I was supposed to use hash some co-ordinates and I was supposed to use k 3-wise independent hash functions in order for the mathematical explanations behind that algorithm to be hold. But after ...
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Laplace Inequality

I am trying to prove that if $r_i \sim Lap(0,1/\varepsilon)$ where $\varepsilon >0$ then: $$Pr[r_i \geq 1+r^*] \geq e^{-\varepsilon}Pr[r_i \geq r^{*}]$$. I know that for $r*>0$ it satisfies ...
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Understanding why Semantic Security implies Message Recovery Security

I am stuck in the proof where it says $$p_0=1/|M|$$ , I just do not understand how we can infer this equality. Also, am I right in understanding that B is defined as choosing his two messages at ...
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Is it possible to construct dataset for only another party to consult?

Is it possible to construct a dataset made of some kind of probabilistic encrypted indexes such that anyone can update the information contained in the set but only the one with a secret key could be ...
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102 views

Standard deviation of gaussian noise in FHEW scheme

I've got two questions regarding the paper FHEW: Bootstrapping Homomorphic Encryption in less than a second. First, the final error of a ciphertext after the refresh procedure is stated as following ...
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Question on nCPA Security and Uniform Permutations

I feel I am misunderstanding the idea of nCPA security and its relation to uniform permutations. In particular I've been reading the paper "Hoang, Morris Rogaway; An Enciphering Scheme Based on a Card ...
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107 views

Challenging Question for the Build a Secure MAC with Special Properties

We would like to ask you to give a construction for requested scheme which provides those properties or give a proof that is not achievable. [Note that unsuccessful attempts to build such a scheme ...
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Leak information (new setting)

This question is similar to Leak Information?, but with new settings. Let $a,b,c,d,e,f$ be selected at random from $\mathbb Z^*_q$. Also, let $r_1,r_2,r_3,z_1,z_2,z_3,p_1,p_2,p_3$ be selected at ...
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Leak Information?

Let a,b,c,d be selected at random from $\mathbb Z^*_q$. We pick values $r_1,r_2,r_3,z_1,z_2,z_3 \gets \mathbb Z^*_q$. Do $u_1,u_2$ that are computed as follows, leak information about values $a,b,c,d$...
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computational indistinguishable/distinguishable?

Let $a,b,c,d$ be selected at random from $Z_q$. Consider the following two distributions $X_1$ and $Y_1$: $X_1={(r_1\cdot a, r_2\cdot b, r_3\cdot c, (r_1+r_2-r_3)\cdot d)}$ where $r_1,r_2,r_3$ ...
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If a probabilistic encryption algorithm is used, how does decryption return the correct message?

Given a key $k$ and a plaintext $p$, a deterministic encryption algorithm will return a ciphertext $c_1$. In a second trial, I run the same key and plaintext $p$ through the encryption algorithm and ...
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527 views

Katz/Lindell Problem 2.2

2.2 Prove that, by redefining the key space, we may assume that $\text{Enc}$ is deterministic without changing $\text{Pr}[\text{Enc}_k(m)=c]$ for any $m, c$. After banging my head against this ...
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What is the advantage of a probabilistic PKC over a traditional PKC?

While reading through a textbook, I came across the idea of a probabilistic public key cryptosystem, which uses a probabilistic TM to generate the public encryption and private decryption algorithm; ...
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What's the difference between game-based and simulation-based security? [duplicate]

What's the difference between game-based and simulation-based security? When we use the simulation-based, how to construct the simulator based on the adversary?
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Understand LWE(Learning With Error) negligible error probability

According to Regev's paper, p15 Correctness. Note that if not for the error in the LWE samples, $b-⟨a, s⟩$ would be either 0 or ⌊ q ⌋ depending on the encrypted bit, and decryption would always be ...
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Thorp-Shuffle Coupling

My question is regarding the coupling of the Thorp-Shuffle, as described in Morris/Rogaway/Stegers, Thorp-Shuffle Encryption. On pages 7 to 9, they describe and implement a coupling. It's all fairly ...
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289 views

Using High Level Probability Theory (eg Markov Chain Mixing) in Cryptography/Cryptanalysis [closed]

I'm currently doing a PhD in probability theory, specifically (discrete space) Markov chains and their mixing properties. As well as my current main project, I'm looking to have a side project, eg to ...
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339 views

Probability of collision in PRF

My question is related to this: Collision-resistant Pseudorandom function Assume we have a pseudorandom function as follows: $PRF: \{0,1\}^{l}\times\{0,1\}^{t}\rightarrow\{0,1\}^{m}$, where $l$ is ...
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How can the identity $\textbf{Pr}[\textbf{y}=y|\textbf{x}=x] = \sum_{\lbrace K:x=d_K(y)\rbrace}\textbf{Pr}[\textbf{K}=K]$ be verified to hold?

How can the identity $\textbf{Pr}[\textbf{y}=y|\textbf{x}=x] = \sum_{\lbrace K:x=d_K(y)\rbrace}\textbf{Pr}[\textbf{K}=K]$ be verified to hold for any cryptosystem? In his book Cryptography, Theory ...
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How to sign low-entropy messages?

Suppose you would like to prove authenticity of messages where the message space is small. Suppose the meaning of the message depends highly on the context, e.g. on time but also on events that are ...
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1answer
582 views

Is there an additive homomorphic encryption that supports exponentation

For example say we have two numbers a and b. Now is there any partial homomorphic encryption scheme that allows to compute (a-b)^2 over the ciphertexts of a and b without round trips.
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setting the MGF hash to a different value other than the regular hash with openssl for PSS signatures

In PKCS1's Probabilistic Signature Mode you have the Hash and the MGF Hash. Both appear to be, by default, sha1, with the OpenSSL CLI client, however, I can change it to sha256 with the following: <...
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Why is Paillier Cryptosystem called probabilistic?

The definition of Paillier Cryptosystem says that it is a probabilistic asymmetric key algorithm for public key cryptography. Can some body explain why it is called "probabilistic"?
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What is the meaning of "probabilistic encryption algorithm"?

I am learning cryptography by myself, and I am not able to understand the meaning of "probabilistic encryption algorithm". How is it different from "deterministic encryption algorithm"? How can ...
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2answers
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Does $(u_1=r_1\cdot x,\ \ w_1=r_1\cdot z, \ \ u_2=r_2\cdot x,\ \ w_2=r_2\cdot z)$ Leak Information?

Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values. We compute ...
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1answer
266 views

Weakening of Paillier cryptosystem due to ciphertext equivalence and order in CryptDB

The Paillier cryptosystem is probabilistic in nature and IND-CPA secure. By design given two ciphertexts one cannot distinguish whether decrypting those two ciphertexts will result in same or ...
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1answer
230 views

Partial Homomorphic Schemes that are probabilistic

As mentioned in wikipedia there are many Partial Homomorphic Encryption(PHE) scheme like RSA, Elgamal, Pailler etc. Pailler encryption scheme seems to be probabilistic Are there any other PHE ...

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