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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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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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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75 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 ...
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82 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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308 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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138 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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322 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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361 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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87 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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392 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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64 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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252 views

Can there be a need for 1024-bit (symmetric) encryption?

I think we are all aware of the CAESAR-competition. Now the aim of this competition is to select a (portfolio of) winner(s) which provide authenticated encryption. I'll now assume that the results ...
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189 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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68 views

Keyless Signature Infrastructures as a secure Post-Quantum Scheme

I came across a company that relies on hashing, similar to block chain technology. They explicitly stated in their white paper that hash based cryptographic schemes are inherently post-quantum ...
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65 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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139 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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329 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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76 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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130 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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81 views

Parameter choice Supersingular Isogeny DH

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies” by DeFeo, Jao and Plut (PDF), the public parameters are defined as: Supersingular curve $E$, and bases $P, Q$ ...
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232 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 ...
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130 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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In NTRU, if $N$ is not prime, prove that one can recover the private key by solving a lattice problem in dimension lower than $2N$

In the NTRU cryptosystem, it is suggested to take $N$ prime. I want to understand why. In Jeffrey Hoffstein, Jill Pipher and H. Silverman An Introduction to Mathematical Cryptography, they suggest (...
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39 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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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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147 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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64 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 ...
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136 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 ...
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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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797 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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65 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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52 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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262 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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51 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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117 views

What aspect of elliptic curve encryption paradigms makes them especially susceptible to quantum based attack algorithms?

This was a statement made during a talk at today's DFN-CERT conference but unfortunately it wasn't explained further. Can anyone shed light on why elliptic curves are susceptible to quantum based ...
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338 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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598 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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Message expansion in NTRU: why is it $\log_p(q)$-to-$1$?

Suppose that we are working with the original version of NTRU with parameters $(N,p,q,k,d_f,d_g,d_\phi)$. In this case we are working with the original NTRU with the digital envelope and the ...
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70 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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58 views

Security of MSS

I have started reading about the Merkle Signature Scheme. I am a little confused about why it is believed to be secure against quantum attacks, couldn't the hash function be attacked? What would make ...
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448 views

Supersingular Isogeny Key Exchange Software [closed]

Are there any optimised implementations of the Supersingular Isogeny Key Exchange by Defeo, Jao, and Plut. It seems like this would be a great drop-in replacement for Diffie-Hellman in both OpenSSL ...
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1answer
221 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 ...
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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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43 views

Choosing between RLWE-KEX methods.

Recently, I've been researching and implementing a bit of post-quantum cryptography, and I came across two RLWE-KEX algorithm for key exchange. The first one, which I implement in my software, is ...
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37 views

DSSP reduction to DSSI

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies" by DeFeo, Jao and Plut, a reduction from the Decisional Supersingular Product (DSSP) problem to Decisional ...
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274 views

Post-quantum authenticated encryption

It is well-known that the Grover's algorithm reduces cryptographic strength of symmetric ciphers to a square-root - e.g. AES-256 becomes only 2128 strong. However, these statements are always made ...
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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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163 views

PQ Key Exchange based on Elliptic Curve Isogenies

I was reading the Wikipedia article on Post Quantum Cryptography and was interested in opinions as to whether the Supersingular Elliptic Curve Isogeny Diffie-Hellman listed there would be a good Post ...
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120 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 ...