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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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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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 ...
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Secure(verifiable, delegated, outsourced) computation

Can we think "secure (verifiable, delegated, outsourced, 2-parties and multi-parties) computation" as a same single concept, or should we consider these secure protocols as different concepts? If ...
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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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80 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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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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68 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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106 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 ...
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CDH problem and Square-DH problem

CDH problem roughly says that choose $U=g^u, V=g^v$ uniformly at random from cyclic group $G$, it's hard to compute $CDH(U,V)=g^{uv}$. Square-DH problem roughly says choose $U=g^u$ uniformly at ...
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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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101 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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284 views

Security proofs for CBC mode

I'm looking for different approaches to proofs for the security of CBC mode encryption. What are the best sources of information about this subject?
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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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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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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 ...
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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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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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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.
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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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258 views

Relation between attack and attack model for signatures

I would like to know: What is the relationship between an attack and an attack model. For example, let $\Pi$ be the Lamport signature scheme. This signature has it's security based on the one-way ...
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72 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 ...
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207 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 ...
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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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349 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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What should I be aware of when implementing algorithms myself?

I plan to build my own crypto library. The project will be primarily for me to learn (and if useful for no other purpose, that is fine). In the past I have implemented a few hashes, and AES quite a ...
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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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102 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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Flaw in the security definition of *Stateful* Authenticated Encryption?

I'm in search of the correct definition of a stateful authenticated encryption scheme (sAE), and its related security notion. This has been treated several times in the academic literature, however, ...
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81 views

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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144 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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117 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 ...
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146 views

how much trust can we place in protocol verifiers? [closed]

I read many papers on authenticated key exchange protocols, and most security proofs are done by the authors. In this method, you can imagine that the efficiency is low. Moreover, even if you have ...
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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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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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210 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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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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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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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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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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Random oracle model proofs and programmability

Proving the security of a scheme with the random oracle model (ROM) involves two steps: first you prove that the scheme is secure in an idealized world where a random oracle exists, and then you ...
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Can anyone give an example where (asymmetric) crypto can go wrong due to selection of wrong groups?

Basically the title says it all. It would be great if someone could tell give an example using provable security. More information about groups can be found at: ...
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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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141 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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How can I tell how many bits of security a secure hash function has?

How can I tell how many bits of security a secure hash function has? For example, how would I calculate or tell how many bits of security a secure hash function with 160 bits output would have? ...
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357 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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191 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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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 ...
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Modular protocol design

What does modular protocol design mean? Why does TLS not have modular protocol design? What protocols have modular design? (IPSec, SSH)
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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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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 ...