Questions tagged [security-definition]

Questions about formal definitions of "security" for various cryptographic schemes (e.g. perfect secrecy, semantic security, ciphertext indistinguishability, etc.)

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Difference between an authentication scheme and a identification scheme in ZK proofs?

I know that a signature scheme is the "strongest" level of security, and correct me if I'm wrong, but that should be basically just a identification scheme where you can also sign a message ...
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50 views

KPA-Security definition

In cryptography there are 4 basic attack classifications: Ciphertext-Only Attack Known-Plaintext Attack Chosen-Plaintext Attack Chosen-Ciphertext Attack In Katz & Lindell's textbook (2nd edition)...
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Exact security requirements for extendable output functions (XOF)?

In the FIPS202 document "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions" an extendable-output functions is defined as: An extendable-output function (XOF) is a ...
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47 views

Reference for a formal definition of universal forgery and EUF-CMA

In many papers, I see EUF-CMA and SUF-CMA referenced as a canonical term used, but I did not find a reference paper/book that ...
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Besides block-cipher which other methods can only be computed step-by-step even with known secret (but fast per step) and can be inverted?

Depending at the cryptographic function used applying it $i$-times to a given input can be computed in different complexity classes (based at their input size). $$f^i(m_0) = c_i$$ For example for most ...
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46 views

How can a concatenation of $N$ block-cipher with known keys be more secure?

General problem / Intro: encrypting the (computable) relation in between two random numbers which are members of a as small as possible set while anything except the order of execution is known to the ...
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93 views

Superscript vs subscript notation in cryptographic formulation

I'm currently reading this paper [PDF]. On page 4, I bumped into these notations : \begin{equation} \text { Experiment } \operatorname{Exp}_{\mathcal{F} \mathcal{E}, A}^{\text {ind-mode }}(k) \text { :...
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74 views

Can a block-cipher considered secure if a bit-change of the input leads to a 50% chance change for every single output bit? -> round number?

Block-cipher use self-inverse ($f(f(x)) = x $) operations which then will be applied to the plaintext and most likely contain some constants which can be based at a key. To get security such ...
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2 different definitions of Special Soundness

There are 2 different definitions of special soundness in the literature: (1) can be found in Damgard: We say that a Sigma-protocol $\Pi$ satisfies special soundness, if there exists a PPT extractor $\...
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64 views

The security of DDH with multiple instances?

Let $G$ be a finite group of prime order $p$, and $g$ a generator of $G$. The standard DDH is hard to distinguish two distributions $$ \{ (g, g^a, g^b, g^{ab}) : a, b \leftarrow \mathbb{Z}_p\} \text{ ...
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42 views

Is it allowable to put a restriction on the length of the plaintext used in the known-plaintext attack?

The definition of the known-plaintext attack: I have a plaintext and I can encrypt it to have its ciphertext, then I use this pair to break the cipher. The question: The only thing I further assume is ...
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114 views

MPC Definitions: UC-Security vs. Real-Ideal Simulation?

I consider the "standard" definition of maliciously-secure 2PC to be the simulation-based, ideal–real-world indistinguishability definition of e.g. Lindell's How to Simulate It [Lin17, ...
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Encrypting random coins used for the encryption itself

Circular security notions for PKE schemes capture the security of (PKE) schemes when encrypting the secret decryption key. Is there an analogous notion but for encrypting the randomness used for the ...
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46 views

Shamir secret sharing in automated verification tools

Can Shamir secret sharing scheme (SSS) be verified using automated verification tools such as AVISPA? I read in the HLPSL manual that we cannot use arithmetic or relative operations such +,-,< ......
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106 views

Statistical security parameter -> information theoretically secure

If a cryptographic protocol has a computational security parameter and a statistical security parameter, does this mean it is only computationally secure instead of information-theoretically secure? I ...
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Uniform vs Non-uniform Attackers

There is a concept of attackers gaining some information before attacking a system and those attackers being called non-uniform attackers. How do the security proofs for cryptographic primitives in ...
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91 views

What do the "adversary state" and "internal coins" mean?

I was reading papers about searchable symmetric encryption these days and in the security definition part the author mentioned: where state is a polynomially bounded string that captures A1’s state, ...
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61 views

Why require that public and private key each have length at least the security parameter?

In Jonathan Katz and Yehuda Lindell's Introduction to Modern Cryptography (3rd edition), the key generator of e.g. signature has The key-generation algorithm $\mathsf{Gen}$ takes as input a security ...
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If a different plaintext may produce the same ciphertext, is the system perfectly secure?

Define the injective map $\phi: \Omega\rightarrow \mathbb{N}$, such that $\Omega=\mathcal{A}^n$ denotes the set of all strings of length $n\in\mathbb{N}^*$ from an alphabet $\mathcal{A}$ of elements $...
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Prove that secure authenticated encryption system composed with itself is secure

Suppose $(E,D)$ provides authenticated encryption with key space $K$. Define $(E',D')$ with key space $K^2$ as follows: $$ E'((k_1,k_2),m) = E(k_2,E(k_1,m)) \\ D'((k_1,k_2),c) = \begin{cases} D(k_1,E(...
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Distributional Virtual Black Box security

Can anyone clearly explain the difference between these two notions of obfuscation security: VBB security and D-VBB Security. VBB Security: An obfuscated program is no better than just a black box ...
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53 views

Reduction to the discrete log problem

Let $G$ be a group of prime order $p$ and generator $g$. Let $msk_i = (x_i, y_i) \in Z_p^2$ be two master secret keys and $mpk_i = (g^{x_i}, g^{y_i})$ the corresponding master public keys, $i \in [0, ...
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50 views

Question about game based security

When a game between an adversary $A$ and a challenger $CH$ is used in the security model of a scheme, and oracles are defined, does the adversary only have access to those oracles in the attack or ...
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How to compare two post quantum digital signature schemes in terms of latency?

I want to compare two digital signature schemes of different nature. One is Hash-based (Winternitz one time signature scheme) and the other is lattice-based (Dilithium Crystals). What about be an ...
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How to evaluate number of security bits of a signature scheme?

I am trying to evaluate the effective security levels that a digital signature scheme (namely post-quantum digital schemes like WOT-S (Winternitz one time signature scheme) and Dilithium Crystals). ...
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36 views

show that key recovery is not possible in a computationally secure system

(G, E, D) is a computationally secure encryption scheme over the message space $\{0,1\}^n$. Show that the probability that a PPT adversary can recover the key after seeing the encryption of a random (...
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42 views

what's the reason of the notational difference between statistical and computational indistinguishabilities?

Statistical: $|\Pr[E_K(m_0)\in T]-\Pr[E_K(m_1)\in T]|\leq\epsilon$ Computational: $|\Pr[A(E_K(m_0))=1]-\Pr[A(E_K(m_1))=1]|\leq\epsilon(n)$ What is the $1$ doing there? Why isn't it $Pr[A(E_K(m_0))\in ...
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113 views

What is Black-Box Obfuscation?

I understand black-box obfuscation at some intuitive level as- "an adversary can learn nothing more from an obfuscated program/circuit/function than he or she can from a black-box access to the ...
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141 views

Does CCA-security implies CPA-security

While reading Katz & Lindell's textbook (2nd edition) if found three main security definitions: ING-EAV-Security, ING-CPA-Security and ING-CCA-Security. (From this forum I know there are more, but ...
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54 views

Question on the disprove of CCA security

I have a question on the disprove of the CCA-security given in Katz & Lindell's textbook (2nd edition) in chapter 3.7 on page 97. It works like this: Consider our construction based on PRFs: $\...
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131 views

How does the security of Elliptic curve compare to normal discrete logarithm?

Intro: EC are often compared with RSA but how about a more safe version of the discrete logarithm? All 3 can be reduced to the problem: $$b = g^a \mod{P}$$ In RSA $P$ is a product of two primes. To ...
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103 views

Combined scheme security proof

Let CS be a combined scheme of $n$ public key subschemes. CS is composed of two algorithms Setup and KeyGen, that all the subschemes share, plus all the other algorithms of each subscheme. Suppose ...
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85 views

Clarification of Advantage vs Probability/Success of an Adversary

In cryptography, for a polynomial time-bounded adversary $\mathcal{A}$, given a scheme $\Pi$, the success or probability of succeeding $\mathcal{A}$ is the likelihood for $\mathcal{A}$ to break $\Pi$, ...
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191 views

An exercise to show that CBC Chain is insecure

The CBC-Chain mode of operation is a CBC variant in which the IV that is used for the very first message to be encrypted is randomly selected, whereas the IV used for each subsequent encrypted message ...
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Question about IND-CCA security

We are given the following securitygame $G^{\text{LOSTNAME}}$: Generate $k \leftarrow \{0,1\}^{\kappa}$ uniformly at random Choose $h \leftarrow \{0,1\}$ uniformly random Create decryption oracle $\...
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80 views

GetModulus negligible probability

I have this textbook definition, I shall include below. GenModulus denotes a ppt algorithm that, on input $1^n$, outputs $(N, p, q)$ where $N = p\,q$ and (except with negligible probability) $p$ and $...
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207 views

How long would it take all of the supercomputers or cloud computing on Earth to bruteforce a significantly long password?

I was arguing with a colleague who thinks that SHA256 (password + 64 character static salt) is "insecure." My argument is that nothing in cryptography is "secure," it's all a ...
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How to formally define the security of Random Oblivious Transfer

Assume that there is a protocol $(A,B)$ such that receives no input and satisfies: $A$ - outputs two random bits $x_0, x_1 \in \{0,1\}$ $B$ - outputs a random bit $b \in \{0,1\}$ and also outputs $x_b$...
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Alternatives to simple bit-measured security for ciphers

For a cryptographic primitive, we usually see the security level measured in bits, where n-bit security means that the attacker would have to perform $2^n$ operations to break it. For key-derivation ...
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Not understanding deterministic authenticated encryption (DAE) security definition

I have a question regarding the security definition of deterministic authenticated encryption (DAE) as defined by Bellare and Shrimpton. Their definition is reproduced below, and my question pertains ...
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153 views

Bits of security vs collision resistance?

I have been doing some research on security, and I am confused on the bits of security vs collision resistance, and I was wondering if someone could clarify my understanding. For instance, if you have ...
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90 views

What are the “costs” to find a pre-image, weak collision, or strong collision?

For a secure, n-bit hash function, what are the “costs” to find a pre-image, weak collision, or strong collision?
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221 views

When knowledge soundness implies soundness

In the work of Bellare–Goldreich that defines knowledge soundness BG92, the discussion of Section 4.5 specifically decouples knowledge soundness from soundness. That is, proving knowledge soundness ...
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102 views

The number of cipher texts possible for each plaintext

This is from Dan Boneh's book Theorem 2.1. Let X = (E, D) be a Shannon cipher defined over (K, M, C). The following are equivalent: (i) X is perfectly secure. (ii) For every $c \in C$, there exists $...
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Correctness and security of a scheme

Is correctness of a scheme considered part of the security of that scheme or is it separate? I've seen both approaches in different papers.
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37 views

What is a quantifier in game-based definitions?

I'd like to know what are quantifiers in game-based security definitions (in cryptography) Some relevant examples and sources are also much appreciated. Edit: for example, in a formal definition, we ...
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63 views

Why do we need multiple adversaries in a game-based definition?

Consider we have a protocol, where multiple algorithms of it are run by an adversary. When we want to define a game for that protocol (or its security properties), I have seen that an adversary is ...
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56 views

Can we determine a security parameter in the hybrid argument where the number of hybrids is polynomially bounded but not known?

Let $\lambda$ be a statistical security parameter. Consider a security proof that is based on hybrid argument, where there are polynomially many (say, $n = p(\lambda)$) hybrids, $H_1, ..., H_n$. Any ...
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80 views

Formal proof that the following definitions of perfect secrecy are equivalent

I've seen the following two definitions of perfect secrecy for an encryption scheme (Gen, Enc, Dec). ...
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143 views

Proving security of $\Pi' = E_k(E_k(m))$ knowing $\Pi = E_k(m)$ is secure

I recently started studying cryptography but I am not sure I quite understand the concept of proof by reduction. Question I am trying to solve is as follow: Suppose $\Pi$ is a symmetric encryption ...

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