A primitive or protocol with provable security is accompanied by a mathematical proof that shows how to reduce the security claims about the protocol to a set of assumptions.

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Proving security of TLS handshake with ProVerif

Background For my dissertation I am working on an application protocol for which I require a TLS session. I am looking to achieve Perfect Forward Secrecy, which means I have selected ephemeral ...
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60 views

Indistinguishability game hop

I am trying to prove that changing an input in a security game from a randomly permuted set to a set that is permuted using a pseudorandom permutation (PRP) results in a negligible distinguishing ...
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91 views

Simulation Based Proof: How the Corrupted Party's Input is Given To Simulator

Imagine we have a 3-party protocol, including client $A$,client $B$ and a server. In this protocol client $B$ encrypts its input under its public key and sends it to the server. The server performs ...
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CPA-security of a pseudorandom permutation encryption scheme

Let $F$ be a pseudorandom permutation, and define a fixed-length encryption scheme $(Gen, Enc, Dec)$ as follows: on input $m \in$ $\{0,1\}^{n/2}$ and key $k \in \{0,1\}^n$, algorithm Enc ...
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64 views

Simulation Based Proof: What Can / Can not Simulator Do?

I have seen some examples in "Foundation of cryptography" and "Efficient two party computation", in which simulator can do some things that in the real world model the parties cannot do, for instance: ...
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Simulator in Private Outsourced Computation over Outsourced Datasets

Please, consider two honest parties $A$ and $B$ outsourced their private data to a malicious server $S$. So the parties store their data in the server. Then at a later point in time they want to ask ...
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106 views

How to prove that a function is not pseudorandom?

I am currently enrolled in a cryptography course, which uses the book by Katz and Lindell. I'm struggling with the exercies which ask for proofs, like the following one: Let G(k) be a PRG with ...
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71 views

What does “simulator” and “interactive” mean in a cryptographic credential system's definition of security?

Definition 1 on Page 7 of “An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation” by Camenisch and Lysyanskaya, uses the term “simulator” in defining the ...
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81 views

Simulation based proofs: Simple examples

I am aware that,(in theory) in order to proof that a scheme is secure using simulation based proof we replace an adversary in real world with a simulator in ideal world. Then we try to show that their ...
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47 views

Does anyone still use BAN or GNY logic in practice?

I want to implement a simple protocol, and I'd like to verify it through BAN or GNY logic. I would assume that if these logics are still used that there would be some programs available that would ...
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146 views

Easy explanation of “IND-” security notions?

There are many schemes that can advertise themselves with certain security notions, usually IND-CPA or IND-CCA2, for example plain ElGamal has IND-CPA security but doesn't provide IND-CCA security. ...
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96 views

Simulation aborted because the adversary doesn't use the random oracle

I'm trying to construct a proof for an encryption scheme in the Random Oracle model. This encryption scheme is like a PKE scheme but with an additional function that kind of "alters" ciphertexts ...
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69 views

On Proving That a Primitive Does Not Exist

In the paper of Hsiao and Reyzin, Section $1.4$: Note that to show that no general reduction from $P$ to $Q$ exists requires proving that $Q$ does not exist Since the statement is about trying ...
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42 views

Definition of indistinguishable schemes

Let $\mathsf{Exp}_{A,\Pi}(\lambda)$ be some indistinguishability experiment that finally outputs 1 if A outputs $b'$ that satisfies $b' = b$, otherwise 0. Then the textbooks often define the security ...
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Secret key and Decryption oracle in the revised Fujisaki-Okamoto transformation

Recently, Fujisaki and Okamoto provided a revised version of the Fujisaki-Okamoto transformation [1], a generic transformation for achieving IND-CCA2 security in the Random Oracle model. This new ...
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81 views

Is it possible to encrypt a message's destination as well as its content?

I have imagined a way to break through any kind of censorship but since I don't have enough professional knowledge of cryptography I don't know whether it is feasible or not. If there is a method ...
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38 views

Anyone familiar with domain of hash functions in bilinear pairing based system?

I need a clarification regarding domain of hash functions. I have defined a bilinear pairing based system as follows: Let G1 and G2 be cyclic multiplicative groups of prime order p generated by g1 ...
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71 views

Correctness in Multi-party Computation: Real/Ideal Paradigm in Malicious case

I need to know: 1- What does exactly correctness mean in this context? 2- How is correctness implied in malicious model? 3- If the correctness means " the adversary cannot cause the output to be ...
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65 views

What should I think about these unique certificate serial numbers [closed]

I was looking at the serial numbers of the certificates for www.google.com and wordpress.com. Wordpress was listed by openssl as: 04:0B:D4:F8:25:88:C5 This serial is listed as the serial for both ...
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173 views

Building a combined encryption scheme from two encryption schemes that's secure if at least on of them is secure

Any thoughts on how this can be done? Let $\Pi_1 = (\mathrm{Gen}_1, \mathrm{Enc}_1, \mathrm{Dec}_1)$ and $\Pi_2 = (\mathrm{Gen}_2, \mathrm{Enc}_2, \mathrm{Dec}_2)$ be two encryption schemes for ...
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72 views

Computational indistinguishability with Example

Based on computational indistinguishability definition no PPT algorithm can distinguish $X$ from $Y$, where $X=\{X_n\}_{n \in N}$ and $Y=\{Y_n\}_{n \in N}$ are ensembles of probability ...
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75 views

Negilible Function $\frac{1}{n!}$

Is $\frac{1}{n!}$ a negligible function where $n$ is a security parameter? Application: I have a vector of n>100 elements. I permute it and give it to an adversary. The adversary can break it if it ...
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32 views

Outsourced Multiparty computation proof in Ideal world

I need to know in an outsourced two party computation where honst $A$ and $B$ outsource their private and secure data to a malicious server, why we need to design a simulator that interacts with an ...
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48 views

Role of trusted party in the Ideal model in Malicious case

Imagine there is a protocol supporting outosurced multi party computation. There are three parties involved in the protocol: client $A$, client $B$ and a server. Client $A$ and $B$ send their private ...
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54 views

Malicious party security model: When one party is corrupted at a time

Consider we have three parties,namely client $A$, client $B$ and a server. Client $B$ and the server can be malicious, but we do not allow the adversary to simultaneously corrupt the server and ...
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Permuted vectors

Consider we have two vectors $v_1, v_2$ of size $n$, and each vector contains $n$ elements. We permute the vectors as: $\pi (k_1,v_1), \pi (k_2,v_2)$. Where $\pi (k_i,v)$ denotes a permutation of a ...
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How to securely map an element from an smaller domain to the other element in a large domain

Problem: I have a small sized domain, say s-bit. It's clear that the probability for an adversary to guess an element is $ \frac{1}{2^s}$. I need to make the probability negligible. However, I need to ...
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86 views

Is MCrypt's 8-bit OFB mode secure?

I just stumbled across a Stack Overflow post which points out that the libmcrypt library (notably used in PHP) implements a somewhat unusual set of block cipher modes: it calls the usual CFB and OFB ...
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43 views

why are both ipad and opad required for HMAC? [duplicate]

I was reading about HMAC and why it is crucial to avoid security issues with normal prepending / appending the secret k to a message (issues due to merkel damagard construction). I am not familiar ...
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96 views

RFID Protocol Cryptanalysis

Assume we have the following scheme for RFID: TAG & READER both have initially k keys. Every session the TAG computes $k_i$=F($k_{i-1})$ where F is a function which computes XOR of previous key ...
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Fault-based transition for crypto proof (a la Shoup) with big probability of fault - does it work?

background In [Shoup2004], Victor Shoup synthesizes the 'sequence of games' technique for proving security properties: Roughly it consists in a sequence from game_0 to game_n, game_0 consisting in ...
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uniform vs. non-uniform PPT

I'm trying to understand PPT and in particular what the differences are in uniform and non-uniform PPT's. First, this is how I see it: A Probabilistic Polynomial-Time algorithm A is an algorithm that ...
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193 views

Why are twofish or other algorithms not NIST approved, are they still safe?

NIST has a total of 3 approved block ciphers on their website: AES, TDES and skipjack. I get why those are on there (though personally I find TDES a bit iffy) but from my understanding Twofish and ...
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Is the reduction from left-or-right IND-CPA to real-or-random IND-CPA tight?

A modern trend in cryptography consists of defining security as rigorously as possible, and then designing schemes which are secure according to those definitions. Proving security comes in the form ...
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164 views

How to compare between two cryptographic algorithms in terms of security? [closed]

How to compare between two cryptographic algorithms (e.g. SHA-1 and SipHash) in terms of security? That is, how could one prove that algorithm X is more secure than algorithm Y?
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Hash “Preimage by product” resistance

Let H() be a hash function that achieves collision resistance as well as first and second preimage resistance. Let's equip the output set of H of a multiplicative group structure, more precisely a ...
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99 views

Counter Mode (CTR) and mult-CPA

I am not sure if Counter Mode (CTR) encryption is mult-CPA (chosen-plaintext attack) secure or not.
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136 views

Hash function as secure as one-time pad?

We know that the one-time pad is provably secure as a cipher to encrypt some data. Is there an algorithm which does the same just as a hash function? Can we get a provably secure hash function? Maybe ...
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Given $g^a, g^b, g^c, g^{1/b}$, is it hard to distinguish $e(g, g)^{abc}$ from a random value?

where $g$ is a group element in bilinear group $\mathbb{G}$. I understand it is very similar to the conventional DBDH problem, but $g^{1/b}$ is also known, possibly making it easier? Does anyone know ...
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135 views

Definition of the Decryption oracle

In the context of public-key encryption, what would be a formal definition of the decryption oracle? I know the informal definition (i.e., a function that is available to the adversary and that ...
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93 views

Formal security of recycled random blinding in a Paillier scheme

This question is a follow-up/variant on a previous question. Supposing that we are trying to generate a large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the ...
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360 views

Why is EdDSA collision-resilient with SHA-512?

In the Bernstein et al. paper about EdDSA, the authors claim EdDSA is resilient against collisions (i.e. it can still be secure even if the hash function used isn't collision-resistant), drawing on a ...
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197 views

Variant of the Decisional Bilinear Diffie Hellman problem

I am working on a cryptographic scheme and I need to rely on the following problem, which I have nicknamed the "Hybrid Decisional Bilinear Diffie Hellman (hDBDH)" problem: Let $e: \mathbb G_1 ...
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111 views

Hardness of problem related to bilinear pairings

Let $e: \mathbb G_1 \times \mathbb G_1 \rightarrow \mathbb G_T$ be an efficient bilinear pairing. Note that the pairing is symmetric (i.e., Type 1). The problem is, given $g \in \mathbb G_1$ and ...
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115 views

Size of a MAC for a quickly checked message?

Let suppose that we have to check a message that was written one second ago. The message is discarded immediately after having being checked. What "minimal" size for such a MAC is secure ? Thank you. ...
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Encrypting decryption key

What's that property called when a scheme is secure even if you encrypt the decryption key? Some schemes have problems when your plaintext is the decryption key (or just the key if symmetric).
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203 views

Secure double encryption using CPA and CCA

Do you mind if you give me any hints, links or ideas about how to improve the security of double regular encryption and decryption, by using CPA game and CCA game, it sounds interesting question, and ...
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104 views

Why is proving “parties' views are simulatable” enough in semi-honest model?

To prove a protocol is secure in semi-honest model, we have to prove: the view of each party, on each possible pair of inputs, can be efficiently simulated based solely on its own input and and ...
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119 views

Requirement for the length of a HMAC tag?

I've seen NIST requirements about key length. What about the output lengths ? Is 112 bits enough for the HMAC output length ? Can we truncate the tag to keep only 112 bits ? Thank you
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Efficient proof of knowledge using Wegman-Carter hash

A verifier wants to ensure, with only little exchange of data with other systems, that a large block of data $M$ that the verifier holds is also available to some other system(s). It is not an ...