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Interactive Proofs: Why $delta lt frac 13$ for Soundness & Completeness?

From a text on Interactive Proofs

$x in {0,1}^n$ is input
$V$ is verifier
$P$ is prover
$r$ is $V$‘s internal randomness

$P$ provides a value $y$ which is claimed to be equal to $f(x)$

  1. (Completeness) For every $x in {0,1}^n$

$Pr[out(V, x, r, P) = 1] ge 1 – delta_c$

  1. (Soundness) For every $x in {0,1}^n$ and every deterministic prover strategy $P’$, if $P’$ sends a value $y ne f(x)$ at the start of the protocol, then

$Pr[out(V,x,r;P’) = 1] le delta_s$

An interactive proof system is valid if $delta_c, delta_s le frac 13$

What is the significance of $frac 13$ here? Why has $frac 13$ been chosen as the what the 2 $delta$s have to be lesser than? I mean why not $frac 14$ or $frac 12$ or something else?

EC has lower CPU consumption than RSA under what condition?

When I searched Google, the top result said On average, processing for ECC is about four times less CPU-intensive than for RSA. Yeah, but under what condition? The page says "A 256-bit EC certificate (the minimum length supported) is roughly equivalent to a 3k RSA cert. " Then, does the above 1/4 consumption mean a::Listen

When I searched Google, the top result said

On average, processing for ECC is about four times less CPU-intensive than for RSA.

Yeah, but under what condition? The page says "A 256-bit EC certificate (the minimum length supported) is roughly equivalent to a 3k RSA cert. " Then, does the above 1/4 consumption mean a situation like 256-bit EC vs 3K RSA, which is "roughly equivalent" security? Also, don’t modern CPU’s have some sort of hardware acceleration for RSA? Does the above assume when the encryption is done purely on software, without using such hardware acceleration?

Interactive Proofs: Why $delta lt frac 13$ for Soundness & Completeness?

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