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In the usual definition of security of Elliptic Curves, curve25519 security is in fact 126 bits. If look at safecurves's rho page you can see the rho complexity for curve25519 is $2^{125.8}$ in accordance to what you say. Curve25519 author basically doesn't accept that definition of security. In the Curve25519 paper he states in section 1: Every known ...


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Assuming this is the paper you're talking about, your modification completely eliminates resilience to collisions in the underlying hash function $H$. The EdDSA scheme (and in the Schnorr scheme on which it is based) is highly resilient against collisions in $H$. Specifically, in the generic group model, the Schnorr scheme has been proven to be secure even ...



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