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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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 ...
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73 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?
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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 ...
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85 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 ...
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98 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 ...
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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 ...
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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 ...
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132 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 ...
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115 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 ...
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32 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 ...
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2answers
64 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?
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1answer
175 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 ...
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189 views

How can I simulate and measure brute force hacking using RSA?

I want to implement brute force hacking using RSA. How can I simulate and measure time duration? What software (or software-based simulator) would be needed?
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117 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: ...
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Question Error Correcting Codes

Let $C$ be a code over the finite field $GF(2)$ with generator matrix $G$ and parity matrix $H$. Let $e+C=C'$ be a coset of code $C$. Let $S$ be a non-singular matrix and $H'=H\times S$. Finally, let ...
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122 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 ...
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63 views

Can you provide an example in relation to Hidden Field Equations Multivariate?

I'm reading about Hidden Field Equations Multivariate scheme. My lecture states that the central map is a univariate polynomial $$P(X)=\sum_{i=0}^{r-1}\sum_{j=0}^{r-1}p_{ij}x^{q^i+q^j} \in K[X]$$ ...
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272 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 ...
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111 views

Why use two affine transformations in Multivariate Cryptography?

I'm reading Multivariate Cryptography and would like to know why we use two affine transformations to scramble the central map? Why not use only one?
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78 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 ...
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1answer
141 views

What is a Trapdoor in Merkle Signature?

Merkle signature (pag. 40) use than public key (verification key) the root of the Merkle Tree and than private key (to sign) the set of pre-images of the $g(Y_i)$ where $Y_i$ is the verification key ...
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1answer
107 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?
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1answer
184 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 ...
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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 ...
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1answer
101 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 ...
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84 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 ...
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745 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 ...
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69 views

LogSpace Merkle Traversal

I am studying LogSpace Merkle Tree Traversal algorithm in "Post Quantum Cryptography". I don't understand the Table 1 on page 58. My question is: Why within of the $2^h$ rounds for $NEED_h$ exist ...
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260 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. ...
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187 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 ...
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455 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 → ...
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1answer
1k 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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Merkle path authentication

In point 4 of the Algorithm 4.2 (Classic Merkle Tree Traversal) of *"Post_Quantum_Cryptography.pdf"* shows *"Stack_h.update(2)"* each stack receives two updates. I am trying understand to understand ...
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147 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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99 views

Merkle signature + PRNG?

In the section 3 (page 44) of the book "Post Quantum Cryptography", it says: Then each one-time signature key must be generated twice, once for the MSS public key generation and once during the ...
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1answer
275 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 ...
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202 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?
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658 views

University for Crypto grad study [closed]

(I thought twice before asking this question and quite reluctant to type as well, but I think this would be helpful). I am an undergrad student and choose theoretical computer science as my major. ...
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1answer
78 views

Sematically Secure McEliece

I am read the Lemma 2 (pp13) in the paper "Kazukuni Kobara and Hideki Imai: Semantically Secure McEliece Public-Key Cryptosystems –Conversions for McEliece PKC– (PKC 2001)". Related to the question ...
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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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125 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 ...
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151 views

Which MAC scheme is quantum resistant?

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

Implementations of Ntru TLS

I posted this in a reply to What is the post-quantum cryptography alternative to Diffie-Hellman? but since it's actually another question, it was deleted. Has anyone come across any implementations ...
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246 views

What are some different cryptography methods?

Some of the most effective cryptography methods and algorithms are based of factoring large prime numbers (e.g. RSA). I'm curious whether there are some other cryptography methods. Somethings that is ...
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233 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?
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1answer
204 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 ...
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391 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 ...
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329 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 ...
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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 ...