Questions tagged [provable-security]

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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Multi-users RSA problem

Rivest and Kalisky's RSA problem considers various notions on security of the RSA One-Way Trapdoor Permutation. They do it only from the perspective of a single user. What's the state of the art in ...
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“Reduced to” vs “deduced from”

Assume it's proven: "Security of protocol $\Pi$ can be deduced from hardness of problem $P$". Is it correct to state: "Security of protocol $\Pi$ can be reduced to (hardness of) problem $P$" ? My ...
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Assumption of difficulty of attack in restricted short time

As well known, different assumptions of difficulty of some problems are used in provable security. E.g., if some crypto-scheme is breakable only in case the attacker finds preimages for hash function, ...
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Are there only two ways to prove a cryptographic protocol is secure?

If I want to prove my protocol is secure, can I just use a game based approach and/or a simulator approach? Or are there other common approaches?
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What is the underlying hard problem in the reduction of game-based proofs?

I am confused by how game-based proofs fit in the provable security paradigm. I understand reductions in the style of proving secrecy of RSA reducing it to integer factorization. However, when proving ...
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Balanced Feistel networks: Are there any lower bounds on the computational complexity of breaking a $k$-round Feistel cipher?

This paper by Patarin presents an attack (section 9) on balanced Feistel networks with $k$ rounds, where the input is a bit-string is of length $2n$. (Since it is balanced, this means each PRF takes ...
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MAC security game

In the applied cryptography book by Boneh and Shoup, Chapter 6 on MACs, it is stated that one can modify SUF-CMA game by removing verify oracle access to the adversary. Therefore, the two versions are ...
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The security of blind RSA signatures with modular exponentiation as padding

It is known that (blind) RSA signature implementations should apply some sort of padding to messages before signing or blinding them. Does blind RSA signature with modular exponentiation as a padding ...
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Using RSA encryption to encrypt large files

The following post discusses the use of RSA for file encryption: https://medium.com/@ismailakkila/black-hat-python-encrypt-and-decrypt-with-rsa-cryptography-bd6df84d65bc The file encrypted is a JPEG ...
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Time cost of security reduction

The following theorem is the description of one-more unforgeability in the paper lattice based blind signatures. I want to ask if the time $t^{'}$ is an exponential time since the $q_{H}$ and $q_{...
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Abstract Cryptography: why local simulators?

In the paper that introduced Abstract Crypto [MauRen11], the Theorem 2 page 15 states that, basically, if there exists some local simulators that can be pluged on a resource $S$ such that this new ...
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LOR implies unpredictability?

It should be true that classical LOR(Left or Right)-indistinguishability of some mode of operation implies unpredictability. However I've got stuck with the proof of this fact. LOR-...
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Related-key impossible differential search on SIMECK via MILP?

What should be the objective function , constraints and bounds for the model for Related-key impossible differential search on simeck cipher using mixed integer linear programming (MILP)?
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Proof by reduction definition in “Serious Cryptography”: Cipher reduced to hardness problem or other way around?

In Serious Cryptography by Jean-Philippe Aumasson on p. 46, paragraph "Provable Security", it says: Provable security is about proving that breaking your crypto scheme is at least as hard as ...
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Proofs that NM-CPA implies IND-Cpa and $\text{IND-CCA} \leftrightarrow \text{NM-CCA}$

I am looking for a proof for the following two claims from "Serious Cryptography" by Aumasson. NM-CPA implies IND-CPA. [...] IND-CCA and NM-CCA are equivalent notions that imply the presence of the ...
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Provably secure way of expanding permutations

Gimli is a 384-bit permutation which makes use of an internal 96-bit permutation which works on columns. Every 4 rounds starting from the 1st a "small swap" is performed and every 4 rounds starting ...
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Regarding security of blind signature schemes

I'm new to blind signatures, trying to understand security notions of it: blindness and one-more unforgeability. I found out that in the security game for blindness property, the adversary $\mathcal{...
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Understanding a security proof

I am reading the paper "RingCT 3.0 for Blockchain Confidential Transaction: Shorter Size and Stronger Security" (https://eprint.iacr.org/2019/508.pdf), an improvement to Ring Confidential Transactions....
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Why does the random oracle receive much more criticism than the ideal cipher?

The random oracle model seems to be criticized a lot as lacking practical relevance, making wrong predictions, being programmable, etc. However, I have never heard such criticism about the ideal ...
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Is the EdDSA signature scheme provable security?

The EdDSA signature scheme is a deterministic scheme. So could it be proven provable security in Random oracle model?
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Game-based proofs and semantic security

After reading this question, I understood that "game-based" and "simulation-based" have to do with the way that security properties are postulated. In particular, IND-CPA is a canonical example of ...
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Are there any hash functions that are commutative yet secure for ordered lists?

I'm looking for a hashing function that can combine random numbers together in any order yet still find the same value. But it needs to be secure against hackers. The idea is if I'm hashing together: ...
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Simulation-based proof in a particular scenario

Suppose we have a two-party protocol in the semi-honest model, which is based on an additive homomorphic cryptosystem like Paillier.(P2 will generate the public and private key and publish the public ...
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Simulation-based proof in the semi-honest model when a party is corrupted

Full paper Would you mind telling me based on the attached file, why in case 3(corrupted client B), the authors did not use the real input which is $S_B$ and instead they have generated $S'_B$? In ...
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Is 128-bit security still considered strong in 2020, within the context of both ECC Asym & Sym ciphers

Given that much of our ECC crypto primitives provide “only” 128-bit security when defined over a 256-bit curve due to pollard-rho, is it then still safe in 2020 to consider 128-bit security safe for ...
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Need help in proving of disproving security of generic partially-blind-signature construction

I have a project where I need to use a linear partially blind signature scheme. I looked at Abe-Okamoto, but I can't easily make it linear. So I looked at Okamoto-Schnorr blind signatures (here and ...
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How to intuitively realize the Diverse Group System in the Hash Proof System(HPS)?

In the paper Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption by Cramer & Shoup, projective hash family derived from group system can be easily ...
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Help understanding syntax used in security proof

I am looking through this paper and am trying to understand the proofs better. One of the theorems the authors are proving (Theorem 5.1) contains syntax of Adv followed by "cdh" in the superscript and ...
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Security properties of ElGamal encryption variants

I'll use Taher ElGamal's A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms (July 1985 in IEEE Transactions on Information Theory, formerly in proceedings of Crypto 1984) as ...
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Is non-adaptive CPA strictly weaker than standard CPA security?

Today during a cryptography lecture an interesting question came up: Whether non-adaptive CPA security is equivalent to adaptive (FtG / LOR) CPA security. Now for a short description of what this ...
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decrypting a one-time-pad that outputs 0,1 in preknown probabilities

assuming a two users want to use a one time pad ciphersystem, and they are using a program that was developed by a third party that was supposed to create random undependable bits, but for some reason ...
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What are standard cryptographic assumptions?

I am struggling to understand what is meant by "standard cryptographic assumption". The Wikipedia artice on the Goldwasser–Micali system (GM) reads "GM has the distinction of being the first ...
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Does an information-theoretically secure hash function exist?

Does an information theoretically secure hash function exist? (By exist I mean is discovered/invented and implemented, not whether it could exist.)
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Computationally indistinguishably vs Perfect Indistinguishably [duplicate]

I know that perfect security means absolutely no information about the plaintext is leaked to the adversary while computational secrecy is okay with a tiny amount of leak. But, what is the difference ...
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Again on discrete gaussians over lattices [duplicate]

Define $$\rho_{s,c}(x) = exp(-\pi \cdot \frac{\|x - c\|^2}{s^2})$$ and $$\rho_{s,c}(L) = \sum_{x \in L} \rho_{s,c}(x)$$ Then Discrete Gaussian over $L$ with center $c$ and standard deviation $s$ is ...
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The security level of double encryption

Let PKE $\Pi' = (Gen', Enc', Dec')$ and it is secure in the sense of $S'$. Let PKE $\Pi'' = (Gen'', Enc'', Dec'')$ and it is secure in the sense of $S''$. $S'$ and $S''$ may be separation which ...
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Statistical closeness implies computational indistinguishability

This is so trivial that authors usually don't bother to give an explicit proof. But for me there is some vagueness. We say that two ensembles $X_n$ and $Y_n$ are statistically close, if $$ \Delta(n) ...
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Security of MAC-Then-Encrypt without MAC key authentication

We have the following settings in our system: TLS 1.2 using legacy cipher suite - OFB mode (using 64 bit block cipher) and trunkated CBC-MAC (32 bit). The goal is to achieve authenticated encryption ...
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1/(2^n)! is negligible function?

By definition $\frac {1} {n}$, $\frac{1}{2^n}$ and $\frac{1}{n!}$ are negligible functions. I have got the function $$f(n) = \frac{1}{(2^n)!}$$ where $n$ is security parameter. I don't understand, ...
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How does the challenger choose the message randomly in the one-wayness security game of PKE?

I have read some papers that give the definition of one-wayness of PKE schemes. Let $\Pi = (G,E,D)$ be a PKE scheme, and the security game of OW-CPA is defined as follow: $$\mathrm{Adv}_{\Pi,\...
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How does the security parameter within a digital locker help prove that it unlocked correctly?

I refer to Canetti et all, "Reusable Fuzzy Extractors for Low-Entropy Distributions", available here. Paraphrasing the relevant part from §3:- The locking algorithm $lock(key,val)$ outputs ...
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On the security definitions [duplicate]

What are the differences between: perfect security information-theoretic security semantic security indistinguishability Are there any other definitions which are closely related? Do these security ...
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Are there any more ways to validate a security proof except peer review?

Are there any ways better than peer review to validate a security proof? Are there any ways to make your security proof easier to validate; using a simulator based proof instead of a game based proof? ...
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Do simulator based proofs still rely on the random oracle model?

I have seen many game based proofs using the random oracle model (ROM), do simulator based proofs require it? Is it possible to do a simulator based proof for every game based proof? For context: ...
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Shamir Secret Sharing: Using $a_0 \ldots a_k$ to store secret? [duplicate]

Let's assume I have a truly random secret $s$ that is 256 bits long, and I want to use SSS with e.g. $(k=4,n=8)$. The normal approach is to set $a_0=s$ and choose $a_1 \ldots a_{k-1}$ randomly, ...
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In an encryption scheme, why can we say that the Encryption and Decryption are PPAs?

In cryptography, a reasonable computational complexity definition for an encryption scheme, is 3 algorithms, (Generate, Encrypt, Decrypt) where encrypt and decrypt can be probabilistic polynomial ...
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Are there any classical proven secure cryptographic algorithms other than OTP? [duplicate]

Boiled down to the core as I understand it: A cryptographic algorithm has provable security if it's unbreakable, even if an adversary has unlimited computational power / time. If my understanding ...
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Are interactive proofs more secure their non-interactive counterpart?

Given an interactive zk proof, if we use fiat-shamir to make it nizk proof, does the proof become less secure? Are there any new attack vectors that get introduced? Is there any reason to use the ...
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1answer
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Are oracles needed in security proofs to prove that one problem is equivalent to the other?

I have seen a few security proofs where they show that solving one problem is equivalent to solving the other, via use of an oracle. For example, when proving that problem A is equivalent to problem ...
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Why ``adversary'' and ``challenger'' and what are typical roles of those?

I'm confused with words adversary and challenger, that are used in proof of security of some cryptosystems. For example, adversary and challenger appear in the formal definitions of IND-CPA, IND-CCA, ...

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