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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246 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?
2
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0answers
20 views

What is bounded-retrieval model?

What is bounded-retrieval model in cryptography? How is it related (or apply) to leakage-resilient cryptography?
3
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1answer
64 views

Parameterizing adversaries with security parameters

In many cryptographic games, the adversary doesn't seem to be parameterized by the security parameter.‡ Are such games equivalent to variants in which the adversary is parameterized by the security ...
2
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1answer
141 views

Difference left-or-right CPA security, IND-CPA security

I am trying to understand the notion of left-or-right-CPA (LOR-CPA) security for private-key encryption schemes introduced in my lecture. If I understood it correctly so far, the only difference to ...
0
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0answers
55 views

Security Proof in Fuzzy Identity Based Encryption?

Been having a great deal of difficulty understanding the use of simulators to prove security of ABE schemes so I though I would start from the first ABE paper (Fuzzy Identity Based Encryption) to try ...
4
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1answer
72 views

Enhance security by combining bits of 4 different hashes

Assuming that performances do not matter, is there any real benefit in terms of security (in general) in combine hashes in this way: hash functions: ...
2
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1answer
60 views

How to prove a lemma that is based on phi-hiding assumption?

Assume that the $\phi$-hiding assumption is true, i.e. that for a composite number $m$, a PPT adversary A cannot distinguish between a prime $p_0$ that divides $\phi(m)$ and another prime $p_1$ that ...
2
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1answer
68 views

Are the following schemes based on a pseudo-random permutation secure?

I am currently working on the following task: Let F be a pseudorandom permutation. Consider the encryption scheme for the message space $\{0, 1\}^n$ defined as follows: $Gen(1^n)$ chooses ...
0
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1answer
96 views

How are security proofs done in ABE Schemes?

I have been studying several ABE schemes and I understand the security assumptions and the several types of security models used for the security game between the Challenger and the Adversary. What ...
4
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0answers
110 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
270 views

Security proof in pairing based cryptography

Let : $G_{0}$ and $G_{1}$ be two multiplicative cyclic groups of prime order $p$, $g$ be a generator of $G_{0}$ and $e$ be a bilinear map, $e : G_0 \times G_0 → G_1$ and let $𝐶_{1} = 𝑔^{𝛽𝑠_{1}...
6
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1answer
957 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 ...
3
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0answers
45 views

What is the restriction on $k$, for the $k$th composite residuosity problem to be hard?

The paper “Residuosity Problem and Its Applications to Cryptography” considers the exponent to be an odd integer. When $k = 2$, it is called the quadratic residuosity problem (mod $n$, where $n$ is ...
5
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1answer
71 views

How many blocks can securely be encrypted with XTS

I could not find in the NIST recommendations on XTS how many blocks can securely be encrypted with XTS-AES. Through the recommendations, I've found: The length of the data unit for any instance ...
3
votes
1answer
62 views

How can I convert a mathematical formula into a logical formula?

I'm using cryptominisat2.9.6 to solve equation set (including more than 160 equations). There are 160 variables in total, which are as follows: $x_0,x_1,x_2,...,x_{78},x_{79},y_0,y_1,y_2,..,y_{78},y_{...
1
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0answers
98 views

Simulation-Based Proof: When a Secret Key is Involved

Assume we have a protocol in which a party receives an encrypted random polynomial. The polynomial is encrypted using his public key. We want to construct a simulator for this party (so this party ...
2
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1answer
307 views

An example of of an information theoretically secure protocol that is not cryptographically secure

Does there exist a protocol $\pi$ for some functionality $F$ which is information theoretically secure protocol that is not cryptographically secure for some threshold number of corrupt parties? ...
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 ...
1
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2answers
82 views

Is a PRF applied to a secure MAC also a secure MAC?

Suppose I apply a PRF to a secure MAC. Do I still have a secure MAC?
11
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2answers
102 views

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 ...
3
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2answers
77 views

Why is it allowed to Generate Keys inside the game?

I am studying reductions to prove security of crypto systems. Generally "games" are used for the proofs. For example, the next image was extracted from the page 91 of the book Post-Quantum ...
2
votes
1answer
61 views

A confusion on the proof of Yao's theorem (Yao 82)

I'm reading the proof of Yao's theorem on Boaz Barak's lecture, the main part of the proof is the following claim: My question is: How can we say "without loss of generality" here? Since $H^...
5
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4answers
1k 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?
2
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1answer
182 views

What is the meaning of IND-CCA secure under standard model? [duplicate]

I notice that in many research papers (viz. "Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption" by Cramer and Shoup) the authors showed that their ...
0
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0answers
29 views

How is Extended Euclidean Algorithm related to Approximate-GCD problem?

I had a doubt regarding the connection between the Extended Euclidean Algorithm and the Approximate-GCD problem. Are there any relations? i.e., the hardness of A-GCD is derived from EEA. Is there any ...
3
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1answer
78 views

How to prove hardness of approximate-GCD problem?

I am trying to prove the security of my system using the hardness assumption of the approximate-GCD problem using contradiction, i.e. If the attacker is able to break in our scheme, then attacker ...
11
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1answer
999 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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2answers
92 views

How to show that this modification of CBC-MAC is insecure?

I'm working on some cryptography problems, found this and I'm not sure how to solve it: Modify CBC-MAC so that all blocks $t_1,\dots,t_l$ are output rather than just $t_l$ and prove it is not ...
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0answers
22 views

Should we use exponent 3 in RSA-OAEP?

As I understand it the proof that RSA-OAEP is secure in the random oracle model is much tighter for exponent 3. Does that mean that exponent 3 should be chosen?
3
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1answer
175 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 $1^...
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0answers
29 views

Is original DSA a TEGTSS-I scheme?

Brickell et al. define TEGTSS-I scheme in paper "Design validations for discrete logarithm based signature schemes" In this paper original DSA is generalized as DSA-I variant where $r = g^k \bmod p \...
6
votes
0answers
57 views

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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18 views

Finding missing probabilities for formal proofs

In formal proofs, you often need to use probabilities to show that the Advantage of an algorithm is negligible. In proofs by contradiction, these probabilities are often tied to probabilities of other,...
2
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2answers
100 views

Shannon theorem of perfect secrecy

From the class: Shannon Theorem: For a perfect encryption scheme, the number of keys is at least the size of the message space (number of messages that have a non-zero probability). Proof: ...
3
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1answer
73 views

Does concatenation of two pair computational indistinguishable distributions still indistinguishable?

Let $X,X',Y,Y'$ be some distribution ensembles such that $X\sim X'$ and $Y\sim Y'$, where $\sim$ means computational indistinguishable. Define $(X,Y)$ be the distribution ensemble over $\{0,1\}^{2n}$ ...
6
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5answers
3k views

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 ...
3
votes
1answer
55 views

Selective and existential unforgability of signature schemes

I understand that one can define EUF-CMA of a signature scheme is terms of a game where the adversary is allowed to query signatures on messages of his choosing, and at the end of the game he must ...
7
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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 ...
3
votes
1answer
75 views

How can I formally verify fuzzy commitment scheme based security protocol?

I am currently working on designing a security protocol which involves usage of fuzzy commitment schemes, for. eg Reed-Solomon codes which allows us to tolerate a certain level of error. I was ...
5
votes
1answer
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 ...
3
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1answer
53 views

Difference between Constructor and Destructor terms

I was thinking that in the formal model (or symbolic model?) the destructor terms were used to model processes that could abort generating some errors or something like that. But then, I realized that ...
-1
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1answer
453 views

Prove that the affine cipher over Z26 has perfect secrecy if every key is used with equal probability of 1/312

Prove that the affine cipher over Z26 has perfect secrecy if every key is used with equal probability of 1/312. Just some guidance/help with this problem would be greatly appreciated not sure how to ...
5
votes
1answer
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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0answers
64 views

Is $E_{k}(x) = F_{k}(x) \oplus F_{k}( \bar x)$ PRF?

$E_{k}(x) = F_{k}(x) \oplus F_{k}( \bar x)$ and F is PRF which maps $\left \{0,1 \right \}^n \times \left \{0,1 \right \}^n $ to $\left \{0,1 \right \}^n$. Let two messages $m_{0} = 0^l $ and $m_{1} ...
3
votes
1answer
50 views

About the necessity simulators set adversary random-tape

In the ideal/real proof paradigm we sometimes find simulators with the capacity of set adversary random tape. My question: when do we have to consider the necessity of simulators set adversary random-...
1
vote
1answer
38 views

Create a potential input for sha-256 hash given a substring of input?

Let's say I'm given a specific SHA-256 hash. Further assume that the SHA-256 input, that yielded this hash contained a known sub-string. Is there a way to find the input (containing the specific ...
4
votes
1answer
430 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 its security based on any one-way ...
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0answers
26 views

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

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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0answers
29 views

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 $H(a)=j$...
2
votes
2answers
262 views

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 ...