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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What is the “Random Oracle Model” and why is it controversial?

What is the "Random Oracle Model"? Is it an "assumption" akin to the hardness of factoring and discrete log? Or something else? And why do some researchers have a strong distrust of this model?
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Why does nobody use (or break) the Camellia Cipher?

If Camellia is of equivalent security and speed to AES, concerns arise. First of all, assuming the above, why is Camellia so rarely used in practice? Why aren't there any breaks in Camellia? Does ...
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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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995 views

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 ...
15
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245 views

Formal verification in cryptography

I have seen in some places that people use formal verification and/or computer-aided verification for cryptography (tools like ProVerif, CryptoVerif, etc.). How do these approaches work?
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What is the ideal cipher model?

What is the ideal cipher model? What assumptions does it make about a block cipher? How does it relate to assuming that my block cipher is a pseudo-random permutation (PRP)? When is the ideal ...
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Can you make a hash out of a stream cipher?

A comment on another question made me wonder about something: Assume you're on a rather constrained platform — say, a low-end embedded device — with no built-in crypto capabilities, ...
13
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1answer
190 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 more)...
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Practical differences between circuits and turing machines for cryptography

In formal cryptography, we model algorithms (mostly our adversaries) as (Probabilistic) Turing Machines or as boolean circuits. In our lecture on formal cryptography, we learned that circuits are more ...
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993 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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390 views

How did the Koblitz/Menezes papers affect the cryptography community?

Two highly-critical papers by Koblitz and Menezes (two well-regarded mathematicians who've contributed to the crypto community) were published years ago: Another Look at “Provable Security” in 2004, ...
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592 views

Is the inverse of a secure PRP, also a secure PRP?

If a block cipher is a secure PRP, is it's inverse a secure PRP as well? My intuition says yes but I'm not exactly sure. On a related note, if a block cipher is a secure sPRP, is it's inverse a ...
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474 views

Automated security protocol verification tool for eCK model

I want a tool that (runs on Win7 and) can perform automated verification of a protocol in the eCK security model as described in Microsoft Research's paper "Stronger Security of Authenticated Key ...
8
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3answers
168 views

How to prove the security of block ciphers

I see very often proofs of security for asymmetric crypto algorithms, for instance, using reductions to known hard problems, or game based proofs... In the field of protocols (like authentication) it ...
7
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2answers
1k 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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4answers
202 views

Why haven't we proven many things computationally secure yet?

Brute Force is infeasible for just about every algorithm we use today. Yet, attacks are feasible. This is because weaknesses keep coming up in our algorithms. Why? We have proven lower bounds for ...
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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 ...
7
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755 views

understanding forking lemma

Every time when I read a paper that has digital signature, when it comes to prove the security of a digital signature scheme, many chances that the author will use the forking lemma. The forking ...
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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 mentioned,...
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277 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 ...
7
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1answer
229 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 ...
7
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1answer
202 views

Is there a security proof for the Triple-DES construction in the ideal cipher model?

Suppose one has an ideal block cipher $E \: : \: \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^k \times \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^w \: \to \: \{0,\hspace{-0.04 in}1\hspace{-0.03 in}\}^w \;...
7
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1answer
177 views

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 ...
7
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1answer
468 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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4answers
455 views

Is there a proof for showing any cryptogram is crackable?

I commonly hear statements along the lines of "all cryptograms are crackable - it's only a matter of time". Is there a proof to show that any cryptogram is "crackable"? The proof may be of a more ...
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Is a book cipher provably secure?

I've seen ciphers (usually in spy drama shows) that involve taking a book and writing down an index to individual characters. Essentially it's a keyed substitution cipher, where the key is the name ...
6
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956 views

how to prove our algorithm is secure against chosen plaintext attack?

I am working on a topic in cryptography where I have tried to develop an encryption scheme. How could I prove mathematically that my algorithm is secure against chosen plaintext attacks?. Will it ...
6
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1answer
272 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 ...
6
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1answer
162 views

How to turn adversary against encryption of zeroes into adversary against random bits?

I recently read the article Nonce-Based Symmetric Encryption by Rogaway, where he presents two different notions of indistinguishability, which he calls ind$ and ind, respectively. Here's the ...
6
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1answer
137 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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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 ...
6
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2answers
220 views

Where is the proof of security of Diffie's cipher?

There is an apparently provably secure cipher that was proposed by Diffie, but enhanced by R.A. Rueppel. The scheme, which was mentioned in Applied Cryptography, works like this: Measure the length ...
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207 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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653 views

Goldreich-Goldwasser-Micali Construction

The Goldreich-Goldwasser-Micali construction allows to build a (cryptographically secure) pseudo-random function from of a (cryptographically secure) pseudo-random generator. More formally, let $G: \...
6
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1answer
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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0answers
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Explanation and proof of a well-know probabilistic lemma

Pointcheval and Stern in their paper on "Security proofs for Signature Schemes" state the following "well-known" probabilistic lemma: Let $A \subset X \times Y$, such that $\mathrm{Pr}[A(x, y)] \...
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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 PRF?...
5
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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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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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515 views

One-Way property of Random Oracle

I'm currently working on a proof in the Random Oracle model, and could not find the formal argument on why the random oracle is one-way (i.e. for an Oracle $O$, it is easy to calculate $x=O(n)$, but ...
5
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1answer
733 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 ...
5
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1answer
223 views

Proof that MACing a hash of the message is also a secure MAC

I found a theorem that says: Let $MAC = (S,V)$ be a MAC for short messages over $(K,M,T)$. Let $H: M^{big} → M$. Define $MAC^{big} = (S^{big},V^{big})$ over $(K,M^{big},T)$ as: $S^{big}(k,m) = S(k,H(...
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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 ...
5
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1answer
626 views

Proofs of security methodologies

I'm looking for course material on the subject of proofs, reductions, and games, as used to prove cryptographic schemes secure. What are the methodologies? What are the preferred ones? In what cases ...
5
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1answer
312 views

Unforgeability and type of adversary

When trying to prove security of asymmetric signature, for instance for existential (or strong) unforgeability against chosen messages attack, do we need to consider the signer as a possible adversary?...
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474 views

Exact mathematical definition of simulation based security?

I've been trying to understand cryptographic protocols and how to define their security. The problem is that while I can understand what the intuitive definition says, I have trouble understanding how ...
5
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103 views

Is the concept of provably secure hash the same as entropy smoothing hash functions?

Is the concept of provably secure hash the same as entropy smoothing hash functions? In the tutorial Sequences of Games: A Tool for Taming Complexity in Security Proofs V. Shoup shows us a proof of ...
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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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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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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, ...