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10

Do the post-quantum ciphers also automag/tically address the 1st problem? Not really, however to explore that in any detail, we need to explore what the 1st problem is. If $P=NP$ is proven true, what does that practically mean? Well, it might have absolutely no practical ramifications, or it might mean that virtually all known cryptographical systems ...


6

Current symmetric cryptography and hashes are actually believed to be reasonably secure against quantum computing. Quantum computers solve some problems much faster than the best known classical algorithms, but the best known quantum attack against AES is effectively "try all the keys." In a quantum computer, the time taken to solve a general search problem ...


5

If you need security against quantum attacks, there aren't that many options. I would go for a lattice-based encryption like NTRU or something based on ring learning with errors. There are no "magic numbers" involved and the assumptions they are based on have been scrutinized by the academic community. NTRU has been around for a decade and has pretty good ...


5

First of all there does exist information theoretically secure message authentication codes suitable for use with a one time pad. An HMAC is not one of those information theoretically secure. As far as I recall the first article presenting such a construction is the 1981 article by Wegman and Carter: New hash functions and their use in authentication and ...


5

I believe that the conjugacy search problem is broken by probabilistic attacks (see chapter 7). I am not sure if this completely ends braid cryptography, however, since there are other difficult problems in braid groups that have not been studied extensively.


4

An old thread, but I thought it deserved an answer. Information-set decoding In short, the idea behind information-set decoding is to pick a sufficiently large set of error-free coordinates in a sent codeword such that the corresponding columns in the generator matrix form an invertible submatrix. Then, the information sequence can easily be obtained by ...


4

In order to answer this question, we need to understand the basis behind all of modern cryptography, which is computational hardness. Today, we believe that we know how to construct block ciphers that are secure, except for brute force search (or almost that secure). However, we don't really know this. We also think that factoring is hard, and so on. All of ...


3

The elliptic curve discrete logarithm—like integer factorization and the classic finite field discrete logarithm—is an instance of the abelian hidden subgroup problem. Any abelian (commutative) instance of the hidden subgroup problem can be efficiently solved in quantum computers with (variants of) the Shor algorithm; therefore all of the above problems ...


3

The Supersingular Elliptic Curve Isogeny Key Exchange that you refer to was first published in 2011 by DeFeo, Jao, and Plut. It builds on but is quite distinct from earlier work by Rostovetsev and Stolbunov in 2006. As a Post Quantum/Quantum Safe replacement for Elliptic Curve Diffie-Hellman (ECDH) it has several good properties: The number of bits that ...


3

In this notation, $f^k(x)$ means "apply $f$ $k$ times in succession". For example, $f^3(x)$ is defined to be $f(f(f(x)))$. Because of this definition $f^a(f^b(x)) = f^{a+b}(x)$ holds trivially (even though we known nothing else about $f$), as the the left side means "do $f$ $b$ times, and then do it $a$ times", while the right means "do $f$ $a+b$ times". ...


3

Supersingular isogenies are a rather recent attempt at post quantum security. You will have a hard time finding an efficient and secure implementation, and even if you write one yourself, the algorithms have not yet seen that much cryptanalysis. (Although that's a subjective judgement call.) If post quantum security wasn't a concern, you could choose from ...


3

Symmetric algorithms are secure post-quantum, only with less bits of security (usually about half). That means you only need to care about the authentication and key exchange parts of the cipher suite. Suites that don't use public key authentication or key exchange, i.e. preshared key suites, are post-quantum secure, but not useful in most usecases. There ...


2

Properly speaking, forward secrecy is a property of a protocol. The protocol is forward secret if compromise of the long term keys does not allow an attacker to decipher any past communications. (Occasionally a distinction is made between that and perfect forward secrecy, with the latter secure when the attacker also knows e.g. all other session keys.) You ...


2

If "it's a fact (not just theory) that quantum computing will break PKI in less then 10-20 years" then "we still use, advise PKI" because there is only a small amount of currently existing evidence for that fact. Specifically, there are known algorithms which can be used for PKI that are not known to be breakable by feasible quantum adversaries.


2

That Wikipedia article is full of errors and false claims. Most importantly, FSB has not been proven to be as hard as an NP-complete problem. This is because the syndrome decoding problem is NP-hard in the worst case, but FSB uses random instances of the problem. Indeed, these random instances may be much easier to break than arbitrary instances. There is no ...


2

One algorithm that is especially suited to one-use key pars is lamport signatures. Like many (all?) other signature functions, lamport signatures first hash the message to get it down to a size that is more reasonable to sign. For this use case, if you are willing to have $n^{2}$-bit signatures and $2n^{2}$-bit keys (public and private), you can sign a ...


2

Does using a slow-hash on the output of an asymmetric key-exchange offer any more protection in a quantum-computing era? No. $\:$ A quantum attacker would simply find seed even if you didn't use "a slow-hash on" it. Is the algorithm (greatly) diminished, or completely broken? The algorithm will still be completely broken by quantum attacks. ...


2

We recently discussed this question with some colleagues and this is what we came up with (no guarantees): Grovers algorithm only outputs a correct answer if it is feed with a input set such that the target function evaluates as 1 for a single input and as 0 otherwise. The algorithm then iterates a subroutine $\sqrt{N}$ times (where $N$ is the size of the ...


2

NTRU private polynomial $f$, as described in Section 9.2.1 of IEEE Std. 1363.1, is computed as $f = 1 + p \cdot F \mod q$, where $F$ is a ternary polynomial of degree $N-1$ with a specific number of coefficients equal to -1, 1, and 0, determined by parameter $d_F$ (i.e., $d_F$ coefficients equal to 1, $d_F$ coefficients equal to -1, and the rest are 0's). ...


2

Since the time you asked your question some new algorithms have shown great promise. The first set of algorithms are based on the Learning with Errors Problem in over polynomial rings. See http://www.cc.gatech.edu/~cpeikert/pubs/suite.pdf There is also an elliptic curve scheme based around supersingular elliptic curve isogenies. There's a Wikipedia ...


2

I am a little confused about why it is believed to be secure against quantum attacks, couldn't the hash function be attacked? Yes, the attacker could attack the hash function, for example, by trying to find a second preimage (and there are known Merkle Signature Schemes where we can show that forging a signature can be reduced to the second preimage ...


2

Yes, a stateless hashbased signature method called Sphincs was recently proposed. It works by having a moderately large Merkle tree (similar to what D.W. suggested), but instead of using Lamport or Winternitz one time signatures at the bottom, it uses a hash based few-time signature method; this allows an occasional collision at the very bottom of the tree. ...


1

The inventors of the Supersingular Isogeny Key Exchange, Defeo, Jao and Plut have posted some code on GITHUB at: https://github.com/defeo/ss-isogeny-software/ There is also a paper on implementation of this key exchange by some people from the University of Waterloo. Their paper is "Efficient Implementations of A Quantum-Resistant Key-Exchange Protocol on ...


1

Two approaches to Post Quantum Key Exchange that have acceptable bandwidth requirements are the NTRU/Ring-LWE lattice designs and the ECC Isogeny Key exchange you mention. Since the UK spy agency published an attack on a lattice based scheme they had designed, there has been an active discussion between Dan Bernstein and the Lattice Cryptographers over the ...


1

This [Carter-Wegman] MAC is not, in general, secure in the quantum setting This is true; however we need to ask "what is this setting, and is it a realistic one?" This setting is one where the adversary can ask queries that are composed of a superposition of quantum states, and the oracle returns the superposition of the answers. In other words, the ...


1

Yes; virtually all of them. Quantum computers give a quadratic speedup on a general search problems (so key lengths need to double), but I don't know of any symmetric schemes in actual use for which quantum computation gives a bigger speedup.


1

The secret key blob consist of 1718 bytes where the first 1500 indicates the corresponding public key. The last 200 ish bytes store the encoded secret key. The secret key is a trinary polynomial with coefficients -1,0,1. So we only need to store the position of non-zero coefficients. The last couple of hundreds of bytes in the encoded secret key suggest ...


1

You can take a look at Dan Berstein's Curve25519. It's a non-NIST, non-NSA curve and he has his own adaptation of DSA that goes with it. However, I suppose it's possible to parallelize an attack on this, so it may not be resistant to quantum computing attacks. As for symmetric encryption, it's important to note that AES was developed by the international ...



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