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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SAT-Based Public Key Cryptosystem

I am researching post quantum cryptography and I've stumbled upon this article which presents a PKC with an np-complete (SAT) trapdoor. I was wondering if someone could help me understand the way the ...
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2answers
578 views

How dead is braid based cryptography

Braid groups has drawn the attention of cryptographers for a few years, as a promising platform for post-quantum cryptographic protocols. The security of the proposed schemes mostly relied on ...
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1answer
44 views

How does the key size in supersingular isogeny schemes relate to their security level?

I'm looking at the De Feo, Jao, and Plût 2014 paper: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. My understanding of section 3.2 Key Exchange, is that Alice'...
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1answer
37 views

Find an example of a lattice such that LLL algorithm can't find the shortest vector of the lattice, satisfying

I want to find an example of a basis of a lattice of dimension $n$ such that LLL algorithm can't find the shortest vector of the lattice, and such that the shortest vector of this lattice, say $b=...
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1answer
64 views

proof of correctness Ring-LWE cryptosystem

I've been studying Ring-LWE based crytposystems such as the one in this paper, but I can't seem to find/come up with a proof of correctness for this particular scheme. The encryption goes as follows: ...
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37 views

Quantum complexity of LWE

As per my understanding LWE is quantum secure because there is no known quantum algorithm to solve LWE in polynomial time. Due to the reductions given by Regev et al. If there is any algorithm that ...
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1answer
120 views

Quantum vs. regular computing time to break ECC?

How long exactly would it take for a regular computer to crack an elliptic curve public/private key via bruteforce, vs. a quantum computer using Shor's algorithm with a couple thousand qubits? Can ...
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368 views

Can Shor's algorithm compromise RSA when both the public and private key are secret?

If RSA is to create a public private key pair and encryption is performed on plain test P to create cipher text C, given P and C could Shor's algorithm be used to find either of the public and private ...
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Now that quantum computers have been out for a while, has RSA been cracked?

D-wave systems has released a commercially viable quantum computer. This means in theory, that all asymmetric encryption algorithms — such as RSA — are now useless due to the speed at which quantum ...
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1answer
53 views

Why are the bit lengths of keys and digests equal in Lamport signatures?

In Lamport's one time signature scheme: One way function to convert a pseudo random number private key to a public key takes $\{0,1\}^n$ and returns $\{0,1\}^n$. Cryptographic hash function to ...
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47 views

On a proposition in NTRU original paper: $\gamma_1 |f|_2 |g|_2 \leq |f \circledast g|_\infty \leq \gamma_2 |f|_2 |g|_2$

In the original paper of NTRU cryptosystem, we have the following proposition (that is said to be suggested by Don Coppersmith): For any $\epsilon > 0$, there are constants $\gamma_1,\gamma_2 &...
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3answers
56 views

Why the exponent is a power of 2 in Ring-LWE?

I was reading some papers on Ring-LWE. I found almost all of them talk to choose the polynomial modulo $x^n+1$ where $n$ is a power of $2$. I did not understand why this condition is necessary?
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1answer
250 views

Is the “New Hope” Lattice Key Exchange vulnerable to a lattice analog of the Bernstein BADA55 Attack?

In the paper, "Post Quantum Key Exhange - A New Hope," the authors present a lattice-based key exchange based on the work of Chris Peikert. In this "New Hope" key exchange the authors try to gain ...
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2answers
280 views

Which elliptic curves are quantum resistant? [closed]

If I want to learn about quantum resistant crytography what are the best resources? Which type of elliptic curves should I be studying?
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2answers
206 views

Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
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1answer
42 views

McEliece variants that support signatures

Besides the Niederreiter cryptosystem, are there any other variants that support digital signatures? Can any of them sign arbitrary signatures unlike the Niederreiter cryptosystem? What are the key ...
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1answer
193 views

How many qubits are required to break RSA 2048 or 4096 with a universal quantum computer?

So in the news this week, IBM have created a universal quantum computer with 5 fully functional qubits. Logic and Moore's law dictates they will be able to scale this up to a lot more qubits within a ...
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1answer
49 views

BB84 quantum protocol

In BB84 protocol, when Alice and Bob make key distribution, what is the private thing? They select randomly bases and then make a measurement according to these bases. Used bases are private? I mean ...
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1answer
68 views

Understanding the Hidden Subgroup Problem specific to Integer Factorization

I've been reading about the Hidden Subgroup Problem (HSP), specifically trying to understand how it is related to the integer factorization problem. I've read What exactly is the impact of the hidden ...
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80 views

Secure entropy extractor for thermal noise collected from camera input?

I have read this paper (pdf) which talks about measuring the entropy of thermal noise collected from camera input. They estimate the minimum entropy at about 4 bits per pixel. Probably estimating 1 ...
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0answers
16 views

How to generate a bilinear group of prime order p [duplicate]

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
4
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1answer
170 views

How to generate a bilinear group of prime order p for key generation

I am trying to implement an IEEE Paper In Cryptography. I read many reference regarding an RSA key generation. But i am confused with above statement. Please someone explain me What it says with ...
3
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1answer
84 views

Why is 128-bit considered “medium term” security?

Why is 128-bit encryption considered good enough for medium term security only? How is expected to be eventually broken? Quantum computing or brute force attack?
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1answer
50 views

Practical lattice based signatures and key exchange with strong security reduction

I am looking for practical lattice-based signatures and key exchange with strong security reductions. Specifically: Provable security under the relevant standard assumptions. Fast in software while ...
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34 views

Is an instruction similar to PCLMULQDQ valuable in post quantum key exchange?

This paper describes a Quantum Key Exchange based on the Ring Learning With Errors problem. When used with ECC, there is only a slight performance impact. Assuming this is the popularized approach ...
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1answer
1k views

Proof for the SHA3 claim that 256 bit security is “post-quantum sufficient”?

On page 14 of "Keccak and the SHA-3 Standardization" (February 6, 2013) it says: Instantiation of a sponge function the permutation KECCAK-f 7 permutations: b → {25,50,100,200,400,800,...
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Best Attack Against HFE cryptosystem

I am looking for the best know attack against HFE cryptosystem. Reading this paper DEGREE OF REGULARITY FOR HFE I found the next claim However, Faugere and Joux demonstrated that we can solve and ...
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40 views

Would LWE problem be still secure if error were like this $e=2e_1$?

In the Learning with error problem, if the error term $e$ from equation $b=<a,s>/q+e$ were of this kind $e=2e_1$, where $e_1$ is chosen according to the probability distribution for the LWE ...
6
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1answer
85 views

Are CSPRNGs quantum-resistant?

It's fairly well known that Shor's algorithm kills RSA, DSA, ECDSA, DH, ... and that symmetric ciphers (AES and 3DES) and hashes (SHA-2, SHA-3) are safe as long as you double your key size / output ...
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3answers
139 views

List of post quantum cryptography protocols [closed]

What are the post quantum cryptography protocols that have been proposed until now? I know about McEliece cryptosystem, and LWE scheme. What are the others? Can you provide me a list or a website ...
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63 views

A topic for my master thesis on post quantum cryptography [closed]

I am a master´s student. I am interested to work on post quantum cryptography. None of my professors are offering any topic this year related to post quantum cryptography. However I have the freedom ...
4
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1answer
53 views

How is McEliece chosen plaintext secure?

Suppose a challenger creates a McEliece encryption system where there is a public key consisting of a matrix $G$ representing some linear code, and a number $t$ for the number of errors. Then the ...
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186 views

Supersingular Isogeny Key Exchange broken?

Found this report detailing a quantum algorithm for computing isogenies between supersingular elliptic curves. http://cacr.uwaterloo.ca/techreports/2014/cacr2014-24.pdf with the quote "...
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Why Sflash signature scheme is constructed in this way?

Sflash is a Multivariate signature scheme that was accepted by NESSIE in 2003, and completely broken in 2007 by a differential attack. Despite I know the total break of Sflash signature scheme and the ...
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1answer
4k views

Assuming a 1024qb quantum computer, how long to brute force 1024bit RSA, 256bit AES and 512bit SHA512

Assuming in the future there was a functioning 1024 qubit quantum supercomputer and it could run Shor's algorithm or Grover's algorithm to crack encryption very quickly. I'm interested in how the ...
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1answer
40 views

Attack being kind of completely puzzled?

I am reading this paper "The security of Hidden Field Equations (HFE)" and at the end of the page 4 the author wrote: Thus, after all, this belief about every attack being kind of ”completely ...
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1answer
33 views

The security of Hidden Field Equations - sentence

I am reading this paper "The security of Hidden Field Equations (HFE)" and at the end of the page 3 the author wrote: The random oracle paradigm would be to ignore that the function formulae ...
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2k views

McEliece Cryptosystem Implementations

Are there any current implementations (language irrelevant) of the McEliece Cryptosystem? I have been hunting around all day, and yet, have only found a few mathematical equations pertaining to the ...
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1answer
75 views

Stern identification scheme to signature scheme

I'm trying to understand the comment in the page 103 of the book Postquantum Cryptography. about convert the identification Stern procedure for signing. Can you write an example of signature of this ...
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1answer
43 views

Winternitz Signature in standard model

I am studying the Winternitz signature and I describe its algorithms in the next W-OTS Key Generation. Select the parameter $w\geq 2$ that is the bit size of the partitions of the message to be ...
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1answer
235 views

Secure, patent-free alternative to NTRU

I'm working on a P2P communications and chat framework, and am looking for a quantum-secure asymmetric key exchange algorithm which I can use to perform a key exchange of an AES-256 bit key. This is ...
0
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1answer
69 views

Fast Forward Hash Signatures

As a follow up to the Q/A session: Small Quantum Signatures - Reality check needed I have implemented the discussed idea for a new short-quantum-safe signature system using fast-forwarding hash. It ...
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2answers
868 views

Winternitz One-Time Signature

I am reading the page 38 in this "Post Quantum Cryptography" book (Equations 8 and 9). My question is, why to compute the verification key $Y$, $f$ is applied $2^w-1$ times? Are there any security ...
3
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1answer
57 views

Truncating ciphertexts on ring-LWE schemes

On the section 5.4 of the paper Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme, the authors explain how to discard some bits of the ciphertexts to get smaller ciphertexts and ...
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2answers
244 views

Can Grover's Algorithm be combined with a meet-in-the-middle attack?

We all know and love the meet-in-the-middle attack which basically makes double encryption pointless using a time-memory-tradeoff. Now there was recently the recommendation by the NSA to use double ...
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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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2answers
136 views

Small Quantum Signatures - Reality check needed

I've been thinking a bit lately about how to get quantum resistant signatures fast and (relatively) small. One idea I've been keen on exploring is finding a crypto PRNG that allows fast-forwarding, e....
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Number of qubits and breaking hashes [duplicate]

Noting D-Wave's press release on a 1000 qubits quantum computer had me wondering... Does the number of qubits nonlinearly change the speed/rate at breaking a SHA256 hash? If someone makes a say 10,...
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1answer
279 views

Quantum on hash

Perhaps this has been answered before. Grover's algorithm should result in a 256 bit hash being complexity 128 bits to crack. I was wondering, what if you had a 512 bit hash , and xor'd the lower 256 ...
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58 views

Quantum circuit to implement McEliece cryptosystem

I've come up with the proposal of implementing McEliece cryptosystem with the help of quantum gates and quantum programming, creating a circuit to do the encryption based on the McEliece original ...