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 $\mathbb{F}... 3 You are confusing the prime$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 ... 3 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-... 3 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 ... 1 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 ...