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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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 ...
15
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1answer
500 views

What exactly is the base for the KECCAK (SHA3) claim that a security strength of 256 bits 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 → ...
14
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4answers
1k views

What security do Cryptographic Sponges offer against generic quantum attacks?

In the face of non-quantum attacker, Keccak[r=1088,c=512] with 512 bits of output provides: Collision resistance up to $2^{256}$ operations Preimage resistance up to $2^{256}$ operations Second ...
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4answers
2k views

What is the post-quantum cryptography alternative to Diffie-Hellman?

Post-quantum cryptography concentrates on cryptographic algorithms that remain secure in the face of large scale quantum computers. In general, the main focus seems to be on public-key encryption ...
12
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3answers
511 views

What exactly is the impact of the hidden subgroup problem on cryptography?

I understand my group theory (allegedly), so I can make partial sense of The Hidden Subgroup problem: Given a group $G$, a subgroup $H \leq G$, and a set $X$, we say a function $f : G \Rightarrow ...
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3answers
521 views

Is key size the only barrier to the adoption of the McEliece cryptosystem, or is it considered broken/potentially vulnerable?

A recent paper showed that the McEliece cryptosystem is not, unlike RSA and other cryptosystems, weakened as drastically by quantum computing because strong Fourier sampling cannot solve the hidden ...
8
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1answer
298 views

Did NIST verify “post-quantum” claims in the SHA3 proposal papers?

I have been reading Bernstein’s “Quantum attacks against Blue Midnight Wish, ECHO, Fugue, Grøstl, Hamsi, JH, Keccak, Shabal, SHAvite-3, SIMD, and Skein” paper from 2010… This document disproves ...
8
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1answer
133 views

Is the Couvreur et al. polynomial time attack on McEliece practical?

There's a new e-print out on arXiv titled "A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems" by Alain Couvreur, Irene Márquez-Corbella and Ruud Pellikaan: ...
7
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1answer
1k views

Is AES-256 a post-quantum secure cipher or not?

We know Grover's algorithm speedup brute-force attacks two time faster in block ciphers (e.g brute-forcing 128 bit keys take $2^{64}$ operations not $2^{128}$). That explains why we are using 256 bit ...
7
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2answers
1k views

How will Cryptography be changed by Quantum Computing?

I realise this isn't a 'yes or no' question, and I apologise for asking something that could be seen as a discussion thread, but I had to ask. I'm currently doing an EPQ in CS (specifically how QC ...
7
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1answer
147 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 ...
7
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1answer
2k 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 ...
6
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3answers
809 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 ...
6
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1answer
2k views

How long does it take a quantum computer to brute force AES?

I understand that using Grover's algorithm it only requires $2^{64}$ lookups for a 128 bit AES encryption, leading people to say we need to increase to 256 bit keys. But how long would it actually ...
5
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1answer
133 views

Using encryption schemes for identification

I've been researching how to implement a post-quantum SSL-like connection authentication, especially correct identification&authentization of the server/client. Because good post-quantum digital ...
4
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1answer
195 views

Long-term data protection, storage of old encrypted traffic and quantum cryptocalipse

Tony Arcieri makes an interesting point in his Imperfect Forward Secrecy article which basically boils down to: large entities such as NSA are storing encrypted internet traffic, also what's to stop ...
4
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2answers
94 views

post-quantum threshold secret sharing

I am looking for a references for post-quantum threshold secret sharing schemes. I am especially interested in knowing whether any one based on one-way compressor functions or cryptographic hashes ...
4
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1answer
210 views

For a one-time pad, which MAC method is information-theoretically secure?

In the the main post about MAC methods it mentions a few methods: Authenticate And Encrypt: The sender computes a MAC of the plaintext, encrypts the plaintext, and then appends the MAC to the ...
4
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2answers
278 views

Is there any research about cryptography on nondeterministic Turing machines?

I know it's a highly theoretical topic, but I was wondering if there was any research out there about what cryptography would be like assuming that we had access to nondeterministic Turing machines. ...
4
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1answer
154 views

Which MAC scheme is quantum resistant?

will HMAC survive Grover algorithm ? if not then which MAC scheme provide post-quantum security ?
4
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1answer
396 views

Implementations of Ntru TLS

Has anyone come across any implementations of Ntru TLS? I'm working a project for uni that does quantum secure encryption. It relies on a mix of Ntru & AES, but I can't find an implementation of ...
4
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1answer
96 views

McEliece and cryptanalysis

What is the computational time to break McEliece on a quantum computer? I've seen that polynomial time algorithms exist, but for special conditions. What about the general case?
4
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1answer
214 views

Does Grover's algorithm effect block size or only key size?

We know that Grover's algorithm can speed up cracking symmetric keys. Basically the key space is halved. This means we have to use at least a 256 bit key (to get 128 bit security). I heard somewhere ...
4
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1answer
105 views

Deterministic Rand function for Winternitz One Time Signatures

Suppose you are implementing a Generalized Merkle Signature Scheme, using the Winternitz One-Time Signature Scheme for the node signatures. Furthermore, suppose the implementation is to be stateless ...
4
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2answers
194 views

Fractal Merkle Traversal

I am studying Fractal Merkle Tree Traversal algorithm in this book. In the [pag. 54] I don't understand this paragraph: We may determine the number of pebbles returned at these times by ...
3
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3answers
167 views

Can one use a Cryptographic Accumulator to efficiently store Lamport public keys without the need of a Merkle Tree?

One of the problems of one-time Lamport signatures is that public keys are disposed after use, so you must generate many keys and store them in a Merkle tree. The root is the "real" public key and ...
3
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1answer
107 views

Is SRP post-quantum secure?

Is SRP-6a post-quantum secure? If it is not post-quantum secure, do any post-quantum secure alternatives similar to SRP-6a exist?
3
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2answers
137 views

Merkle Tree High Tree

I'm reading Merkle tree signatures and I like know if the security of the that scheme depends, also, of the high of the tree or only depends that hash function is resistant to collision?
3
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1answer
215 views

Public-key cryptosystems without poly-time quantum attacks

It's well-known that Shor's algorithm can solve integer factorization, discrete logarithm and discrete log over elliptic curves in cubic time. This implies that cryptosystems like RSA, ElGamal, and ...
3
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2answers
188 views

Stateless hash based public key cryptography?

Merkle-Winternitz signatures based on fractal hash trees are an attractive alternative to other post-quantum cryptographic schemes, in particular since they are conceptually simple, the security ...
3
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2answers
259 views

Are hash trees an alternative, quantum-resistant signature scheme which can replace RSA?

Can hash trees provide quantum resistant signatures to replace RSA for signing securely? What is the key size and how many times can we use same key?
3
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1answer
114 views

What is the quantum-resistant signature scheme with the smallest signature + pubkey?

After playing cat and mouse with an number of quantum-resistant signature schemes and coming up with nothing with small enough signatures, I'm turning to Crypto.SE. I need a quantum-resistant ...
3
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1answer
224 views

Quantum resistance of Lamport signatures

The Lamport-Diffie signature scheme is said to be quantum-resistant. Why is that? What would a quantum attempt to attack this signature scheme look like, and how does it fail?
3
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3answers
151 views

Asymmetric algorithm for one time signing of small cleartext

I want to generate a key pair such that the private key can be used once to sign a small message (1024 bytes) at some indeterminate point in the future and the public key can be used to verify that ...
3
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1answer
117 views

Why is Lamport-Diffie secure?

Why is Lamport-Diffie secure? I note that there is a demonstration based on onewayness (in the book postquantum cryptography). But a one way function is not sufficient to ensure that it can not infer ...
3
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2answers
114 views

Basic attacks on McEliece; finding S and P

Take a McEliece cryptosystem with public generator matrix $G' = S G P$ where $G$ is a generator of a secret code with known fast decoding (not necessarily a Goppa code over $\mathbb{F}_2$), $S$ is ...
3
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0answers
90 views

FHE over the integers - Is that paper's scheme known to be insecure against quantum adversaries?

I was reading the paper Fully Homomorphic Encryption over the Integers, and started wondering if there is a known quantum attack on their main scheme, because There is an efficient quantum attack ...
2
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1answer
67 views

Are post-quantum cryptographic ciphers *also* secure if the P=NP conjecture holds true?

First of all, I only understand the P versus NP debate on a rather shallow level as I am not a computer scientist. So perhaps the answer to the question is straightforward but if not, I would be ...
2
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1answer
451 views

Diffie-Hellman is Post-quantum secured?

If Alice and bob have a secure channel for key-exchange and mallory don't man-in-the-middle attack them but in the future eavesdrop connection and see the key exchanged, can mallory break it like RSA ...
2
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1answer
379 views

using Post-quantum asymmetric ciphers instead of RSA

We can't trust RSA to encrypt our Emails so what is best post-quantum cryptography system as alternative for RSA which provide good security and don't be breakable? because McEliece cryptosystem looks ...
2
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1answer
104 views

Generalized Merkle Signatures, SHA-3 and Sakura

Sakura specifies a tree hash mode for e.g. Keccak (SHA-3). Are there any reasons to use the Sakura tree hash mode in a Generalized Merkle Signature Scheme? It seems to me Sakura primarily solves a ...
2
votes
1answer
349 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 ...
2
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0answers
43 views

space complexity of quantum collision search

Is there a known way to reduce the space complexity of quantum collision search beyond what is offered by the built-in time-space tradeoff, while keeping the time complexity significantly below what ...
2
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0answers
41 views

McEliece information set decoding attack vulnerability

Wikipedia states that McEliece is open to "information set decoding attack". What is an "information set decoding attack" and how serious is the vulnerability? (is it just a matter of choosing proper ...
2
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0answers
79 views

PKC McEliece + $S$ + $P$ [closed]

I am trying implement the McEliece crytosystem in SAGE. My question is How I will be able to choose the appropriate matrix $S$ and $P$?. I ask this because when I trying obtain the vector $\hat{m}=mS$ ...
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5answers
981 views

Using one-way hash functions as the encryption method

Suppose two parties want to communicate securely with each other (Bob and Alice) using a simple messaging system in English. There are approximately 180,000 currently used words in the English ...
1
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1answer
107 views

Is there any restriction in using lossless compression algorithms for huge key sizes?

I'm studying McEliece and Multivariate Public Key cryptographic systems. The main problem here is the huge key size. Is there any restriction in using lossless compression algorithms to fix this ...
1
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1answer
152 views

Merkle Signature Generation

In the section 2 (page 42) of the book "Post Quantum Cryptography", it says: Then he generates the one-time signature $\sigma_{\text{OTS}}$ of the digest using the $s$-th one-time signature key ...
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2answers
82 views

McEliece key size

There's a lot of references about McEliece key size being the barrier for proper usage of the algorithm, exactly (or roughly) how large are the keys?