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Questions tagged [post-quantum-cryptography]

Cryptography that will remain secure should large-scale quantum computing become feasible. Based on hard problems with no known polynomial-time quantum algorithm (e.g., Shor's algorithm).

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18 views

Post-quantum aggregate / multi signatures

Are there any practical post-quantum aggregate / multi signatures? Currently, the aggregate / multi signature schemes seem to be limited to pre-quantum elliptic curve assumptions only, e.g., [BDN18], [...
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Why round off vector sampling from continuous Gaussian distribution not directly sample from discrete Gaussian distribution

For any vector $\mathbf{c}$, real $s > 0$, and lattice $\Lambda$, define the probability distribution $D_{\Lambda, s,\mathbf{c}}$ over $\Lambda$ by $$D_{\Lambda, s,\mathbf{c}}(\mathbf{x})=\frac{...
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45 views

Is CECPQ2 forward secure?

Is the CECPQ2 key exchange, as deployed by Google[1] and Cloudflare[2] in TLS 1.3 forward secure against quantum computers? I know that it is using HRSS+SKY as the post-quantum part of the key ...
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94 views

Post-Quantum security of Pseudo-Random Functions

I am wondering what is the exact post-quantum security of a PRF. I know that for most symmetric mechanisms, it is assumed it is sufficient to double the key size, but I am looking for a more precise ...
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Explanation of the tables found in Kyber round1 code?

The precomp.c file in Kyber NIST round 1 submission has three tables, could you please let me know how to generate these three tables? If I want to understand how ...
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143 views

Are there post-quantum cryptosystems with a gap between classical and quantum security?

Is there a gap between classical attacks and quantum attacks against some post-quantum security assumptions? (I'm particularly interested in asymmetric cryptography.) I understand that there is no ...
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Lattice Based Cryptography domain

Some cryptosystems operate on the domain of the form $\mathbb{Z}_q[x]/\langle x^n-1\rangle$ and others operate on $\mathbb{Z}_q[x]/\langle x^n+1\rangle$. What's the security impact of the two forms?
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Why is the vector sampled from Gaussian or Subgaussian distribution in lattice-based cryptography? [duplicate]

I have known that the vector is sampled from Gaussian distribution in lattice-based cryptography because the distribution of the vector $\mod{\mathcal{P}(\mathbf{B})}$ approximates to uniform ...
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A proposal for randomization of Niederreiter cryptosystem

The Niederreiter cryptosystem is a public key cryptosystem using Goppa code. Unfortunately it it is insecure unless it is a binary code. So I thought I could insert random linear codes into randomly ...
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67 views

Canonical embedding vs. plaintext slots in Ring-LWE

I'm working on the canonical embedding mentioned in [LPR10] and [LPR13]. What confuses me is that the difference and the relationship between the canonical embedding and the concept of ''plaintext ...
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Precise Definition of 1-out-of-2 Oblivious Transfer

What's the precise definition for 1-out-of-2 OT? and what's the best way to show that it can't be achieved under unconditionally secure setting? I am reading about it and just couldn't get my head ...
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Public points in SIDH

I was going through a presentation titled "SIKE in Hardware" by professor Reza Azarderakhsh. On the page $10$ of the presentation he introduces a variable $w$. Could you please explain what the ...
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1answer
67 views

How secure is a hash based signature scheme after signing assuming quantum computers?

Consider a hash based signature scheme that requires taking the $k$-bit hash of an arbitrary length message to be signed (e.g. Lamport one-time signature scheme). My understanding is, assuming that ...
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Check validity of generated parameters for SIDH

In section 4.1 of the paper Towards Quantum-Resistant Cryptosystems From Supersingular Elliptic Curve Isogenies by Feo, Jao and Plût it is described how you generate valid parameters for the SIDH ...
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1answer
61 views

Post-quantum alternative to ElGamal? (public key verifiability)

Are there any alternatives to ElGamal that would be resistant/annoying to quantum machines? I would like to preserve public key derivability/verifiability -- ability to ensure existence of ...
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What's the difference beteween SIDH and SIKE?

I'm a semi newbie in crypto (I've had that uni course of discrete math that includes basic cryptography principles) and wanted to go a bit further in isogeny graphs. I have downloaded the C ...
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1answer
39 views

Calculation of failure probability in basic Ring-LWE-DH key agreement

This is the basic unauthenticated Ring-LWE-based Diffie-Hellman key exchange, based on Peikert's Ring-LWE KEM: (from BCNS15) Alice and Bob have shared public polynomial $a$ randomly drawn from $R_q = ...
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Is McEliece secure with non-binary Goppa codes?

A binary Goppa code with codewords of length $n$ bits that can fix $t$ errors with a polynomial over $GF(2^m)$ can encode $k = n - mt$ bits long data. That is one needs to add $mt$ check bits to fix $...
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Complete Attack on RLWE Key Exchange with reused keys, without signal leakage

I am studying a research paper "Complete Attack on RLWE Key Exchange with reused keys, without signal leakage" . On page number 21 to 28, there is toy example explaining the scheme. I am unable to ...
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SIDH: key agreement - why does it work?

In SIDH both parties agree on the key in following way: Alice calculates a kernel $R = mPB + nQB$ Thanks to Velu formulas (and further improvements), she can now compute isogeny $\phi_a$ She uses $\...
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127 views

Could a quantum computer recover files from ransomware if the attacker doubly encrypted them with RSA-4096?

How would a quantum computer decrypt a file (or find the keys to such a file) if it were encrypted with standard RSA 4096 encryption, but encrypted two times with different keys? The keys are known by ...
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SIDH cryptosystem question

I'm trying to understand the SIDH cryptosystem and got confused at this point: Alice fixes base $\{P_A,Q_A\}$ so that it generates $E_0[l_A^{e_A}]$. Then she chooses secret parameters $m_A,n_A$ and ...
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Gentry-Halevi’s Fully-Homomorphic Encryption and hermite factor

In section 7.2, page 18 in Chen-Nguyen paper regarding BKZ 2.0, they point out different Hermite factors related to Gentry-Halevi FHE. More precisely, it is said that the critical Hermite factor for ...
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RSA vs. Super Computer vs. Quantum Computer [closed]

I know that RSA is known to be secure in the current landscape of computing, and I know that RSA is known to be broken in the world of quantum computing and cryptography. I have two questions, can ...
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IETF Recommendations for preparation for PQC- clarify in what way they are referring to bits

Which bits are being referred to when it is said by the IETF, "Continue to avoid baking-in algorithms, either explicitly or implicitly (e.g. via maximum field sizes)" ? Does that mean leave enough ...
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Is NIST testing all the round 2 submissions to quantum-resistant crypto?

Is NIST confirming the self-published quantum-resistant crypto round 2 data and do they make that available to the public when they do?
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1answer
140 views

How resistant are stream ciphers like Salsa20 or ChaCha in a post-quantum world?

What kind of quantum computer would be required, if it is possible to break such ciphers?
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83 views

NTRUSign (considered broken) as a one or few time PQ signature scheme

As many know, original NTRUSign is considered broken as signatures leak information about the private key. It takes a number of signatures to accomplish a break though, with the original break paper ...
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95 views

How does the Signature Scheme in Picnic Works

I am trying to understand how signature scheme proposed to NIST, Picnic, works. The propossal uses ZKboo and ZKboo++ as their basis. I can see how the ZKPoK works, where the witness x is some key ...
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103 views

Does the block size of a symmetric cipher impact the security of the cipher itself? [duplicate]

Will a 128 bit block have some security implication in post-quantum cryptography?
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1answer
62 views

Can I connect the hardness of a linear short integer solution problem to that of SIS problem?

As we know, SIS problem is defined as: for a function $f_A(s)$=$As$, where $A$ is a fixed, randomly-chosen matrix in $\mathbb{Z}_q^{r \times n}$, it is hard to find elements $s \in \mathbb{Z}_q^{n}$ ...
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How does post quantum key exchange in OpenSSH 8 work?

OpenSSH 8 supports a post quantum KEX, namely sntrup4591761x25519-sha512@tinyssh.org It says in its description that it is basically NTRU + ECC X25519. However, I have tried but cannot understand how ...
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Minimal secure index of quasi-cyclic codes for code-based cryptography

It is well-known that keys (generator matrices) of code-based cryptography are very large for its practical usage. To reduce them scientists propose to use families of quasi-cyclic codes. I remind ...
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Regarding the isogeny path problem

Given two elliptic curves, it is hard to calculate an isogeny of large degree between them. Does this only apply to supersingular isogenies or to ordinary ones as well? Additionally, is the mapping ...
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140 views

Why doesn't “Classic McEliece” need scrambling?

The original McEliece scheme uses two random matrices S and P to scramble the generator matrix and uses $\mathsf S·\mathsf G·\mathsf P$ as the public key. The Niederreiter variant also does about the ...
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70 views

Dilithium signature scheme - Public key derivation

Good day! I am very new to Cryptography but I want to make sure I understand the concept of the scheme correctly before using it to our system. So I was looking at post quantum signature schemes, and ...
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Why is it safe to generate the secret key and masking vectors using rejection sampling in CRYSTALS-Dilithium?

In CRYSTALS-Dilithium module lattice-based digital signatures, the secret key vectors $s_1, s_2$ with coefficients in $[-\eta, \eta]$ and the signature masking vector $y$ with coefficients in $(-\...
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154 views

Quantum Resistant Algorithms and types: PKE vs PKEs vs KEM vs KEMs vs DSS

I am trying to wrap my head around the second round Quantum Resistant Algorithm candidates currently under the NIST PQC Effort. Can someone verify if the following is a correct summary of the 17-...
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386 views

What is a simple 8-bit cryptographic hash function that I can use in a quantum simulation of Grover's algorithm?

I'm taking a quantum computing course in which, for our final project, we must create a proof-of-concept implementation of Grover Search for finding hash collisions up to a difficulty (similar to ...
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126 views

Can I replace DH by a post-quantum key exchange in IBAKE for post-quantum identity-based authenticated key exchange?

IETF RFC 6539 IBAKE - Identity Based Authenticated Key Exchange describes a Hybrid key exchange using both Identity based cryptography and a standard ephemeral elliptic curve Diffie-Hellman key ...
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Differences between “NewHope” and “NewHope-simple”

The well-known paper described a key exchange (KE) scheme named "NewHope" on USENIX 2016. The authors then proposed "NewHope-Simple" - a PKE/KEM scheme. They also submitted "NewHope for NIST" - ...
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80 views

Cost of upgrading to PQCrypto

We already have recommendations on what PQCrypto to use: PDF (page 11) Symmetric encryption Thoroughly analyzed, 256-bit keys: AES-256 Salsa20 with a 256-bit key Symmetric ...
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1answer
124 views

NIST security categories (post quantum)

Here (https://www.safecrypto.eu/pqclounge/round-2-candidates/) are collected all the proposals which passed the first round of NIST Post-Quantum Cryptography Standardisation process. What does the ...
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78 views

Niederreiter cryptosystem

I can't understand how Niederreiter cryptosystem works. If $c=mH^{'T}$ than why we cannot compute $m$ directly by multiplying $c$ with the $(H^{'T})^{-1}$? Can you give me an example of a "fast ...
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CSIDH: Why do we need ideals in the form of $\langle \ell, \pi \pm 1 \rangle$ in order to apply Vélu's formulas when computing the action?

I am trying to understand the action of the CSIDH protocol. Let $E_0:y^2=x^3+ax^2+bx$ be a Montgomery elliptic curve over $\mathbb{F}_p$ for some prime $p$. If we take $\mathcal{O}$ as $End_{\mathbb{...
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Associative Multivariate Permutation

Popular multivariate schemes are constructed by having a several easy-to-invert functions/maps as parivate key, and their composition as the public key. When signing, the hash, or a padded form of ...
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64 views

Question about degree of regularity

I have been reading some papers on cryptography based on multivariate systems and I have a question. How does one relate the difficulty of calculating Gröbner basis (GB) of a multivariate system with ...
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177 views

Differences between NewHope-CPA-KEM and NewHope-CCA-KEM

According to the web page for NewHope, an R-LWE post-quantum key encapsulation mechanism (KEM) candidate for standardization, it comes in types that are IND-CPA or IND-CCA secure. I know what CPA and ...
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92 views

How reassuring is 64-qubit security?

After we've concluded that 64-bit is an insecurity for classical computers, I think many would like to know, how secure in a perspective view, is 64 quantum bits security. As we know, the Grover's ...