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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Is Shamir's Secret Sharing Scheme insecure for larger field?

According to wikipedia, if you are using shamir's secret sharing scheme with a field of order $p$, "High values of $p$ are risky because Eve knows that the chance for $f(x)\pmod{p}=f(x)$ increases ...
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Permuted Hash Table

Suppose we have a hash table, $HT$, consisting of $100$ bins.The hash table uses a hash function $H$ that is public. We all know that given value $a$ we can compute the address in the hash by ...
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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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How to generate a random number so server cannot cheat?

Here is the protocol: Bunch of players connected to server. Server creates nonce and hashes it - send hash to clients as bit commitment. Clients make nonces and send hashes to server as their bit ...
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Why Generate Keys are inside game

I am studying reductions to prove security of crypto systems. Generally are used "games" for the proves. For example, the next image is extracted from the page 91 of the book Postquantum Cryptography. ...
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Is it okay to send an encrypted key using XSalsa20-Poly1305, and send subsequent messages using ChaCha20-Poly1305?

I am looking at a cryptographic protocol in a somewhat unusual environment: the communicating parties can share arbitrarily long secret keys over a secure channel. If forward secrecy is not required, ...
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LR-Oracle Experiment in Lindell and Katz

In reference to the LR-Oracle experiment in “Introduction to Modern Cryptography” (2nd edition) by Lindell & Katz, Definition 3.23 states a scheme $\pi = (Gen,Enc_K,Dec_K)$ is CPA secure for ...
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31 views

Why Boneh-Franklin BasicIdent IBE is not chosen-ciphertext secure? Why use random oracle?

I don't know why BasicIdent is not chosen-ciphertext secure. If there are anybody who knows well, please explain it to me with example. Moreover, I don't know random oracle and its usage for security ...
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Hamiltonicity proof of knowledge

I'm learning the POK notion and definitions and as a self exercise I wante to prove the statement that the Hamiltonicity protocol is a POK system with knowledge error $1/2$. So the question will be ...
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3answers
892 views

What are the differences between proofs based on simulation and proofs based on games?

what are the main pros and cons of proving the "security" of a crypto scheme under simulation proofs instead of game based proofs?
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1answer
44 views

Proven secure scheme under random oracle

Currently I am trying to understand random oracle model in order to make a small presentation about it but I seem to be very confused about it. Since it's an hypothetical model without a real life ...
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170 views

Construct IND-CPA secure encryption scheme by combining two given schemes

I have two encryption schemes $\Pi_0, \Pi_1$, at least one of them is IND-CPA secure but I don't know which one. The task is to construct a scheme $\Pi$ that is guaranteed to be CPA secure and to ...
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323 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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611 views

What does “Worst-case hardness” mean in lattice-based cryptography?

In the wiki page of Lattice-based Cryptography the "Worst-case hardness" is defined as below: Worst-case hardness of lattice problems means that breaking the cryptographic construction (even with ...
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1answer
79 views

Are those two distributions indistinguishable?

The Decision composite residuosity problem problem states that is impossible to distinguish between those two ensembles: $\{x^N \mod {N^2} | x \in \mathbb{Z^*_{N{^2}}}\}$ and $\{r \in ...
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HMQV and MQV group representation attack

Currently reading Krawczyk's HMQV paper https://eprint.iacr.org/2005/176 and trying to follow what he says about the group respetnation attack on MQV: It says that for any group of prime order $q$, ...
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1answer
1k views

What is it meant by a “hybrid argument”?

Can anyone explain (or point to a reference for) what a hybrid argument is in a security proof, and when it's convenient or preferable to use it? Among some of the places where I've seen it ...
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104 views

What is the difference between RCCA and CCA2?

Well, I know it's easy to tell CCA1 from CCA2, but I failed to find the difference between RCCA and CCA2. What is the difference?
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1answer
35 views

Generalization of the DL-assumption in bilinear group pair

When thinking about a pairing-based cryptographic scheme, I encountered the following problem. Let $e \colon G_1, G_2 \to G_T$ be a Type 3 pairing. Then: Given $P, zP \in G_1$ and $Q, zQ \in G_2$, ...
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108 views

Provable security of cryptographic hash functions

I am working on the following exercise question: Consider the following construction of a “keyed” hash function from Katz & Lindell (ex. 7.22 (1st ed.)/ 8.21(2nd ed.)). Gen : On input 1n ...
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Is a Mersenne-twister cryptographically secure if I truncate the output?

I want to create an online roulette game. Is it OK if the PRNG is seeded only once, when the user starts the game, or is it recommended to re-seed sometimes during game? Maybe just seeded once a day ...
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2answers
236 views

Can you help me understand PFS and wPFS?

Every time I encounter the concepts of PFS (perfect forward secrecy) and wPFS (weak perfect forward secrecy), I feel uncertain about them. My understanding is that: PFS ensures that, if the ...
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119 views

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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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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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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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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77 views

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 ...
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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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141 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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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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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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158 views

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 ...
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35 views

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 ...
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39 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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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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Are there any secure commutative ciphers?

This answer lists two commutative cipher algorithms - Pohlig-Hellman and SRA. However, they don't appear to be too secure. My question is, here there any commutative ciphers out there that are secure ...
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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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139 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 ...
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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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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: ...
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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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730 views

A block cipher with independent keys for each round

I want to modify a standard block cipher in the following way. I replace each round key by a key picked at random. Is this block cipher as secure as the original one ? Thank you. EDIT Some missing ...
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Is SipHash cryptographically secure?

I'm evaluating different hash algorithms for use in my application. One of the kind of algorithms I am looking at are cryptographically secure ones to protect against DOS attacks. SipHash seems ...
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Does unbalancing a feistel cipher always improve security? Does it improve security at all?

So according to Wikipedia unbalanced feistel ciphers provide greater provable security. Specifically, they state: The Thorp shuffle is an extreme case of an unbalanced Feistel cipher in which one ...
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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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128 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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Is $G$ a secure PRG?

Is the following function a secure PRG? Given $F$ is a secure PRG and $k$ is choosen random from key space $K$. $$G(x) = F(k,x) \oplus F(k,x \oplus 1^s)$$ My solution is $x \oplus 1^s = x'$ ...