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13

Some claim that Curve25519 has 112 bit security, others that it has 128 bit security; which is it? Well, actually, neither - it's actually somewhere in the middle. For a curve without known weaknesses (and Curve25519 doesn't have known weaknesses), then if the curve order has a large prime factor around $2^{2k}$, then the best known attacks against it ...


6

SHA-1 is still thought to be secure whenever collision resistance isn't required. The hash is both used for signing certificates and ECDHE public keys. There's however a difference with regard to collision attacks. It is possible for an attacker to attack the collision resistance with certificates by getting their own certificate signed by a CA. In ECDHE ...


5

Any key generation algorithm for any cryptosystem is going to be weak if the attacker can predict what seed was used to generate the key. They can just generate the same key. However, assuming the the random number generator is not that bad, different algorithms start to look different. If you are just using the output of the random number generator as a ...


4

No, Curve25519 signature is not vulnerable to bad RNG during signature generation; that's because Curve25519 signature needs no random number during signature generation. By contrast, in ECDSA, a fresh random number is needed for each signature, and if it gets known, that allows to recover the private key from the signature and public key; same if the same ...


3

1. The equation $-x^2+y^2=1-(121665/121666)x^2y^2$ defining the curve $E$ is quadratic in $x$, hence for any given $y\in\mathbb F_q$, there are at most two points on $E$ which have $y$ as their second coordinate. In this case, the two possible $x$-coordinates for a point on $E$ with $y$-coordinate $4/5\in\mathbb F_q$ are the solutions to the equation $$ ...


2

Edwards curves can be implemented using a unified formula for addition and doubling; i.e., one can implement addition such that $$\mathrm{dbl}(P)=\mathrm{add}(P,P).$$ Performance wise it is however more efficient to consider both functions separately, since the doubling can be implemented more efficiently than the addition. Depending on the representation ...


2

[...] the only one that is listed (secp256k1) are marked as unsafe. Some of the others are there too. NIST P-224 is the same curve as secp224r1, and similarly for P-256 and P-384. Those are marked unsafe as well. Assuming we trust djb, are the elliptic curves that are currently supported by this reasonably new version of OpenSSL (and therefore ...


2

Sorry I will have to answer my own question. I received a mail from Luca De Feo a moment ago. "Nope, I discussed this at length with Jean-Fran├žois Biasse, and we couldn't find a way to apply this kind of attack to SSIKE." I'll leave this question around for reference for the next person who wonders.


1

Also, the algorithm given in the mentioned paper has a complexity os $\tilde{O}(p^{\frac{1}{4}})$. The best known attack (As mentioned by de Feo, Jao and Plut) on the SSIKE is based on the claw finding problem (see below) and has a complexity of $\theta(p^{\frac{1}{6}})$. Very interesting paper btw ;): Claw finding algorithm using quantum walk


1

TL;DR: use (D)TLS. This is exactly the kind of problem it was meant to solve. If possible, use cert pinning too (if you get to deploy the code on both ends of the channel, this should be possible). The general rule is: don't design your own crypto protocol unless both of the following apply. You have done a detailed review of what exists already and ...



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