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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CCA security in double encryption [duplicate]

my friend and I are trying to reach out a convenient security solution for CCA when we encrypt the message m two times, first for m to get c and then for c to get C(so it is one inside other). I have ...
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115 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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1answer
63 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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1answer
55 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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46 views

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 ...
2
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1answer
63 views

Gap problem for Learning With Errors

Informally, a "Gap" problem is the one that arises when solving the computational (or search) version using an oracle for the decisional version. For example, the Gap Diffie-Hellman Problem (GDH) is ...
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1answer
99 views

To prove $r \cdot f_1 +f_2 \cdot (s+1)$ is secure

We define the polynomials $r, f_1,f_2,s \in R[x]$. Where $r$ is a random degree 1 polynomial and $s$ is a random polynomial such that: $degree(s)=degree(f_1)=degree(f_2)$, let $R$ be $\mathbb{Z}_p$ ...
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1answer
84 views

Why is this cryptosystem insecure?

Can someone help me see the flaw in this cryptosystem? Note: This is homework and it is due today at 1:30pm. An answer before that is not expected; I'd just like to understand what the flaw is. ...
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1answer
72 views

Why does NTRUEncrypt lack a formal security proof?

Is there any particular reason why NTRUEncrypt lacks a formal security proof? That is, a demonstration that it achieves certain security notion (e.g. IND-CPA). I know there is a provable-secure ...
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1answer
50 views

Key escrow on indistinguishability games

Does it mean that when PPT attacker is breaking an indistinguishable based (equivalent with semantic security) game with non negligible probability that he is able to infer the secret keys either on ...
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1answer
109 views

Is this chat protocol safe?

I am in the design phase of a secure chat application at the moment. I am trying to make this as secure as possible. The Serverprovider should not have access to the messagedata. So my idea was the ...
2
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50 views

Bridging the gap between security proofs and “real-world” security

I've been studying cryptography for a little while. I understand fairly well the nuts and bolts of security proofs, but I'm having trouble reconciling the formal statements of security in these proofs ...
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1answer
112 views

Is this modified Schnorr signature scheme secure?

Signing Let y = g^x, which is your public/private keypair. Let r = g^v, for random v Let c = H(M) Let z = (v + cx) mod q The signature is the pair (r,z) Verifying g^z = ry^c mod p We further ...
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61 views

Privacy-Preserving Protocols and Proofs of Security

While dabbling in privacy-preserving protocols (mainly using Semi-Homomorphic Encryption) and coming up with miscellaneous ideas for comparison tests or other similar primitives, based on obfuscation ...
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1answer
100 views

How to prove Security of Onion Layers of encryption?

CryptDB has Onion layers of Encryption to provide wider functionality from weaker forms of encryption. How do we prove such things are indeed secure ? Intuitively It seems ok. Are there any parallels ...
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30 views

Hard problems in composite order group even when factorization is known

Composite discrete log problem has been proved to be reducible to hardness of factorization and discrete log on the prime factor groups. Are there any problems apart from that in composite order ...
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35 views

What is the restriction on k, for the kth composite residuosity problem to be hard

This paper considers the exponent to be an odd integer. When k = 2, it is called the quadratic residuosity problem (mod n where n is composite) which is hard and can be solved if the factorization of ...
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1answer
174 views

Proof for composed signatures

Assumes that we have 3 signature algorithms, $S^A$ with key pair $(sk^A,pk^A)$, $S^B$ with key pair $(sk^B,pk^B)$,$S^C$ with key pair $(sk^C,pk^C)$. We denote by $\epsilon$, $\epsilon'$ and ...
4
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1answer
82 views

OCB and GCM security

Is OCB as secure as GCM or CCM ? Since OCB design is quite different from GCM and CCM, I was wondering if the security properties of these latters are satisfied by OCB, as well. Thank you.
3
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210 views

Security equivalent to Diffie–Hellman problem?

I've been doing the security proof for one of my Theorem. Basically, given $g^a$, $g^b$, $g^{cb}$, $g$ and $c$ as known values. Is the problem of computing $g^{acb^{-1}}$ equivalent to the Diffie ...
4
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1answer
62 views

Are HMACs based on hashes with larger bit-lengths also more secure?

When doing encrypt-then-mac, I can choose to use a hmac as the MAC. For example, I could use a hash like SHA-256 or SHA-512 (by using it as a keyed hash) to create that HMAC. Does it increase ...
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1answer
117 views

Use ElGamal to solve Diffie-Hellman problem

Say we are able to decrypt a Elgamal ciphertext $c$ using only the public key. Apparantly it is now possible to solve the Diffie-Hellman problem (given $g^a, g^b$ calculate $g^{ab}$). How? I know how ...
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2answers
374 views

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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1answer
73 views

Protocol composition [closed]

I have been trying to wrap my head around different definitions of protocol security (stand alone, sequential composition, parallel composition, universal composition) and how the proofs of any of ...
4
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2answers
153 views

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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2answers
124 views

Reductionist proofs of decisional problems to computational

Are they any reductionist proofs where an attacker $\mathcal{I}$ for a well established computationally "hard" problem $\mathsf{Π}$ is employing an attacker $\mathcal{A}$ who we assume is able to ...
5
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1answer
146 views

What is the “artificial abort” technique?

In the security proof of Brent Waters's paper Efficient Identity-Based Encryption Without Random Oracles, he uses a novel “artificial abort” step on page 6. At this point the simulator is still ...
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103 views

Is it possible to construct a secure block cipher of size $2n$ given a secure block cipher of size $n$?

Given, say, the Blowfish block cipher, which is considered secure but only has a 64-bit block size, can we construct a secure block cipher of 128-bit block size? Say we run the key through two KDFs, ...
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1answer
29 views

Is the CONF key sharing Problem equivalent to discrete log problem?

If there a proof in the literature which says the CONF Problem is equivalent to solving the discrete log ? Let $g$ be a generator of a cyclic group $\mathbb{G}$ of prime order $q$ CONF problem: ...
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84 views

Is less security required for a short stream cipher than for the AES enciphering of very long messages? [closed]

Criticisms of a cipher system such as 'the ciphertext from one message must be indistinguishable from the ciphertext of a second message" surely only apply when there are very large amounts of ...
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1answer
75 views

Exchanging Keyspace and Message space in PRF

Suppose there is a secure PRF $F: K \times X \to Y$. Then is $F': X \times K \to Y$, defined by $F'(x,k):=F(k,x)$, a secure PRF? In my opinion it should be because exchanging the keyspace with ...
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1answer
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Showing that security of a elgamal invariant is insecure

Original Elgamal signature is defined $S(m, \alpha) = (r, s)$, where $$r = g^k \bmod p$$ $$s = (m – r*α)k^{-1} \bmod (p – 1)$$ more information on Elgamal signature can be found here. Variant ...
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229 views

security in the standard model → random oracle model?

Can a protocol proved secure in the standard model be considered secure in the random oracle model?
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84 views

Times of nested algorithms in proofs of security

Proofs of security may be constructed such that an adversary $A$ is used to construct an adversary $A'$. The reduction/algorithm which uses $A$ has to perform a number of computations in order to ...
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1answer
136 views

Security proof of FO(Fujisaki-Okamoto) hybrid encryption

The proof of FO hybrid encryption is hard to understand. $\:$ Especially, how does the challenger respond to the decryption queries when the challenger can only have some encryption queries? Can ...
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Looking for a detailed example of proof by reduction

I'm looking for a very detailed example of proof by reduction. Say we have two or three protocols (that have been proven secure) and we construct a new protocol. We want to provide a proof of security ...
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194 views

Is a random oracle controled by the challenger?

When proving a Crypto scheme security under random oracle model, is the random oracle always controlled by the challenger? What if the Hash is only used by the adversary?
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1answer
113 views

Rock-paper-scissors over network, how to protect from cheating server?

I'm trying to design cryptographic protocol to play Rock-Paper-Scissors with two parties, neither trusting each other, nor trusting server they use for communication, so game is 'provably fair'. So ...
4
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1answer
147 views

Would a symmetric cipher with a keylength a big as the data length be information theoretically secure?

One-Time-Pad is information theoretically secure as long as the random number stream is evenly long or longer than the data stream it encrypts, for a "decyphered" message could have been any message ...
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596 views

Is this a pseudo random function (PRF)? F(k,x) = f(k,x) - f(k,x-1)

I have a question about Pseudo Random Functions. Let $f:\{0,1\}^m \times \{0,1\}^n → \{0,1\}^n$ be a secure PRF. Define $F(k,x) = f(k,x) - f(k, x-1 \bmod 2^{n}) \bmod 2^{n}$. Is $F$ is a secure ...
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1answer
89 views

Modular protocol design

What does modular protocol design mean? Why does TLS not have modular protocol design? What protocols have modular design? (IPSec, SSH)
3
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1answer
148 views

Proofs by reduction and times of adversaries

I have some difficulties to understand, when we construct a reduction, how we determine the time for the constructed adversary to break a target security property. In general these details are not ...
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2answers
376 views

Signature based on public key cryptography and forgery

In the definition of existential unforgeability, there is no detail about the following questions. In general, can we suppose that a signer is also a possible adversary ? When generating a signature, ...
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1answer
568 views

Perfect Secrecy -> One Time Semantic Security -> Secure PRG

I think I have some sense of what Perfect Security means, and even Semantic Security, but I am struggling with randomness, so I'm going to ask a question about CSPRG's (Cryptographically Secure PRG's) ...
2
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2answers
228 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 ...
4
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1answer
142 views

Reason for difference in assumptions for practical private-key and public-key crypto

Theoretical cryptography tells us that everything in the world of private-key cryptography (CCA-secure symmetric encryption, message authentication codes, etc.) can be built from one-way functions and ...
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135 views

Can you prove the existance of a PRG $G$ s.t. for each even $k$: $G(k)=G(k+1)$?

In one of the exercises in [KL] Book I need to tell whether an encryption scheme is secure under an eavesdropper of only one message. Given a PRG $G: \{0,1\}^n \rightarrow \{0,1\}^{n+1}$. The ...
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Is it feasible to break an encrypted and later encoded message?

A message is sent from a person to another. The plain message is first encrypted, even with a weak algorithm - say, DES. Then, the encrypted message is encoded with a simple substitution, which is ...
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221 views

Chance in cryptography

I was just thinking about my own chance and the way chance can defeat even the most advanced algorithm. My thought was : you can make a strong session id, but what if by chance, a hacker set this ...
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92 views

A confusion about HMQV?

As the full version of HMQV is very long, I will give a graph of it below \begin{array}{@{}l@{}c@{}l@{}} \hat{A} && \hat{B} \\ (a,A=g^a)&&(b,B=g^b) \\ x\in_R[1,q-1],\quad X=g^x ...