Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.
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According to Recommended Elliptic Curve Domain Parameters, Koblitz curve secp256k1 defined by $T = (p, a, b, G, n, h)$ $p$ defines the finite field $\mathbb{F}_p$, $p=2^{256} − 2^{32} − 2^{9} − 2^8 − 2^7 − 2^6 − 2^4 − 1$ or in hex FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F The curve $E: y^2 = x^3 + ax + b$ over $\mathbb{F}...


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You are confusing the prime $p$ over which the curve is defined (the coordinate of the points are all defined mod $p$) with the prime $q$ which is the curve cardinality and is also prime. We have $qG = G + \ldots + G = \infty$ the neutral element (like $0$ with the addition with numbers). Taking your example, you have: $T_1 = (p+5)G$ and $T_2 = 5G$. Of ...


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First, the size: the best attacks for breaking elliptic curve cryptography are algorithms that break the discrete log (given a point $P = kG$, find the integer $k$; which in ECC translates to: given the public key, find the private key). These attacks have complexity of $O(2^{n/2})$, where $n$ is the size of the field. So, in a 256-bit field (i.e. with a 256-...


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Curve25519 was chosen to have the Montgomery shape $y^2 = x^3 + A x^2 + x$ to support the fast single-coordinate Montgomery ladder for Diffie–Hellman: given $x(P)$ and $a$, it is cheap to compute $x([a]P)$, so there is no need to pass the $y$ coordinate and implementors are not tempted to use secret-dependent conditionals to compute scalar multiplication ...


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A signature under a public key $P$ is a pair $(R,s)$ such that $[s]G = R + [e]P$, where $G$ is the standard base point, and $e$ is the challenge. If $e = H(P, m)$ doesn't involve $R$, then I can just pick $s$ arbitrarily and compute $R = [s]G - [e]P$ to forge any signature I want. The motivation for the Schnorr signature scheme is the Schnorr ...


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