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/*
* Public Key Work Factor Functions
* (C) 1999-2007,2012 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/workfactor.h>
#include <algorithm>
#include <cmath>
namespace Botan {
size_t dl_work_factor(size_t bits)
{
/*
Based on GNFS work factors. Constant is 1.43 times the asymptotic
value; I'm not sure but I believe that came from a paper on 'real
world' runtimes, but I don't remember where now.
Sample return values:
|512| -> 64
|1024| -> 86
|1536| -> 102
|2048| -> 116
|3072| -> 138
|4096| -> 155
|8192| -> 206
For DL algos, we use an exponent of twice the size of the result;
the assumption is that an arbitrary discrete log on a group of size
bits would take about 2^n effort, and thus using an exponent of
size 2^(2*n) implies that all available attacks are about as easy
(as e.g Pollard's kangaroo algorithm can compute the DL in sqrt(x)
operations) while minimizing the exponent size for performance
reasons.
*/
const size_t MIN_WORKFACTOR = 64;
// approximates natural logarithm of p
const double log_p = bits / 1.4426;
const double strength =
2.76 * std::pow(log_p, 1.0/3.0) * std::pow(std::log(log_p), 2.0/3.0);
return std::max(static_cast<size_t>(strength), MIN_WORKFACTOR);
}
}
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