Timeline for Is any safe prime sufficient for a secure DH key exchange?
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| Dec 14, 2023 at 10:28 | comment | added | fgrieu♦ | @James Arlington: the safe primes you consider are not really "vulnerable", because they are so large. They are only less invulnerable than random ones of the same size. You can ask a question about generating large random safe primes. If we used brute force search for $b=100,000$ bit, that would require testing about $(b\,\ln2)^2\approx5,000,000,000$ candidates, which would be hard. But here are ways to cut on that enormously, including generating something convincingly noting-up-my-sleeves, e.g. by restricting to $p$ with a remainder modulo small primes compatible with being a safe prime. | |
| Dec 12, 2023 at 19:35 | comment | added | user113099 | Are there known large 100,000+ bit safe primes that are not vulnerable to SNFS? | |
| Dec 12, 2023 at 10:15 | history | edited | Daniel S | CC BY-SA 4.0 |
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| Dec 12, 2023 at 10:12 | comment | added | fgrieu♦ | About why SNFS is the algorithm of choice for all of the primes linked to: if you have a rule of thumb for limits of $a$, $r$, $e$, $b$ such that SNFS is the algorithm of choice for modulus $a\,r^e±b$ (or same for that $a\,r^e±b\,s^f$ form I just learn about from wikipedia), please add this or a link! | |
| Dec 12, 2023 at 9:50 | history | edited | Daniel S | CC BY-SA 4.0 |
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| Dec 12, 2023 at 9:44 | history | answered | Daniel S | CC BY-SA 4.0 |