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The twist attack is best explained in Fouque et al's paper. While the (quadratic) twist of the curve $E : y^2 = x^3 + ax + b \in \mathbb{F}_p$ is indeed of the form $E^t : y^2 = x^3 + d^2ax + d^3b \in \mathbb{F}_{p}$ for nonsquare $d$, you can also think of the twist as the set of points $(x, y)$ in $E^2 : y^2 = x^3 + ax + b \in \mathbb{F}_{p^2}$ where $x$ ...


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Short Answer: Yes Long Answer: From what I understand about quantum computing, they are only more efficient as long as the bit-depth of the problem falls within the bit-processing capabilities of the quantum processor. Example: a 64-bit quantum processor could solve 64-bit traditional encryption keys in a near-zero real time. 128-bit keys would still take a ...


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Typical scenario is to run the raw shared secret through a key derivation function to generate keys for any symmetric primitives they will use.


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DH: OpenSSL commandline has three options for creating certs, but all of them either selfsign the cert or require a selfsigned CSR, and DH can't do either of those. OpenSSL library called from a program you write can construct an X509 object (cert) containing a DH publickey, subject and other attributes as you specify, signed by an RSA key corresponding to a ...


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Mostly. The two problems are actually more closely equivalent in a gap model than in a non-gap model. Square-DH clearly reduces to CDH either way, but CDH reduces to two calls to Square-DH (you have 3, but you can use $(u-v)^2$ to make it 2). This is fine if the Square-DH adversary is always right, but maybe the adversary only solves the Square-DH problem ...



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