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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Random Coin Flip

Quoting an old question: Consider the following protocol for two parties A and B to flip a fair coin (more complicated versions of this might be used for Internet gambling): A trusted ...
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Brute force attack multiple stream cipher

Assume that a scheme used to secure a specific system $Π=(Gen,Enc,Dec)$ which is thought have indistinguishable multiple encryption in the presence of an eavesdropper. For any adversary $A$ that can ...
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273 views

Simulation-based proofs and universal composability proofs

I recently read Ran Canetti's famous UC paper but I'm still trying to wrap my head around the concepts. I think this answer has me confused a bit, particularly where it says The stand-alone ...
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Proving for a single input vs several inputs. Is there any difference?

I am working on a new protocol for pattern matching. While defining the ideal functionality, it is possible to say: Alice sends $p$ and Bob sends $T$ to the ideal functionality. i.e. searching for ...
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Can several run of a semi-honest protocol be used to infer malicious security?

In the ideal world, $A$ sends several inputs $x_1,...,x_\lambda$ to the functionality and $B$ sends input $y$. Functionality sends $f(x_1,y),...,f(x_\lambda,y)$ to $A$ and nothing to $B$. Suppose ...
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What is the difference between “securely realizes” and “securely implements”?

In some security proofs it is stated that "a protocol securely realizes an ideal functionality" while in some others "a protocol securely implements an ideal functionality". Is there a meaningful ...
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Is it possible for a simulator to always abort?

In this paper of J. Baron, et al. (PDF), simulator always aborts the ideal functionality before client outputs its pattern-matching result obtained from the ideal functionality. (See bottom of page 30,...
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175 views

Why is only one oracle + challenge-response phase sufficient for IND-CPA security?

The CRYPTUTOR wiki from UIUC uses the following definition of the IND-CPA game: We (privately) choose a key K according to the key generation algorithm: K $\gets \mathsf{KeyGen}$. We (...
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Salary Negotiation Problem

Imagine Alice is applying for a new job. Alice has an idea of the minimum salary that she is willing to accept—let's call this value A. Bob, the hiring manager for ...
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230 views

Why is “semantically secure” important for cryptosystems?

The first question: what is the exact definition of semantically secure? Basically, a cryptosystem is semantically secure if given the public key and the ciphertext, an adversary cannot learn any ...
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Difference between oracle behavior and real execution

Suppose that there is a place in a security proof where the behavior of an oracle differs from the corresponding real execution (for example, the decryption oracle rejects certain types of ciphertexts ...
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How is “post-quantum security” proven/shown?

Due to growing concerns over the threat of quantum computing to asymmetric cryptography (RSA, ECC, etc), a number of "quantum resistant" replacements have been proposed (SPHINCS, McBits, and many more)...
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Deriving a Set of Seeds from a Seed

I need a set of seeds $S=\{s_1,..., s_n\}$, for pseudo-random function where seed $s_i$ is used to generate a set of pseudo-random values. Obviously I need to be able to regenerate the sets of pseudo-...
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What level of security is provided when a Feistel Cipher is used as a round function of another Feistel Cipher?

Recently, I was reading: Are there any specific requirements for the function F in a Feistel cipher?, and the answer posted mentions a Feistel Cipher named Turtle, which uses a four-round Feistal ...
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41 views

Proving the security of a one-way function with partially known input

Let's say we have a construction like in this question: We have a OWF $h(.)$, a secret salt TXT, and a counter starting at 1, and we compute ...
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Perfect Secrecy of AES file Encryption

Why does AES file encryption not ensure perfect secrecy? I understand that $\Pr[E(K,M_1)=C_1] = \Pr[E(K,M_2)=C_2]$ given $M1\neq M2$ holds for perfect secrecy of a scheme. However, this seems to hold ...
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How can IND-CPA encryption be identity revealing?

This is problem 10 of Chapter 4 "Symmetric Encryption" (pdf) from Lecture notes by Bellare and Rogaway: An IND-CPA secure encryption scheme might not conceal identities, in the following sense: ...
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Do random oracles are called even by honest users in the PAK protocol [BMK00]?

In the full-length proof of PAK scheme, the authors made extensive use of random oracles to extract (guessed) password from the messages generated by the real world adversary for the ideal world ...
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(Uniformly) Random Value when an element is picked with $\frac{1}{p-1}- \frac{1}{(p-1)^2}\ $ probability

Let's $\mathbb{F}_p$ be a finite field where $p$ is a large prime number(e.g. 256-bit) I know if the probability that an element picked from the field is $\frac{1}{p-1}$ we say the element is picked ...
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How To prove Any Change to $v=a\cdot y+b$ maks $y=(a)^{−1}\cdot (v−b)$ Uni. random value [closed]

This question is related to data integrity. Let a finite field be $\mathbb{F}_p$, where $p$ is a prime number. I have a fixed value $y$ and two uniformly random values $a$ and $b$. Hypothesis: $a,...
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159 views

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 Diffie-...
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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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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 chooses a ...
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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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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 |k|...
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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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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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83 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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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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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 ...