Timeline for How safe is a prime with $P=2 \cdot Q \cdot R \cdot S \cdot t+1$ for discrete logarithm? How to enhance/compare?
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| Jul 20, 2019 at 21:01 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 5, 2019 at 21:33 | vote | accept | J. Doe | ||
| May 5, 2019 at 19:37 | answer | added | J. Doe | timeline score: 2 | |
| May 4, 2019 at 23:04 | comment | added | theREALyumdub | It was more of a guess than an answer, if I knew the answer to what you were asking I probably would have posted below! But you may want to see the Silver-Pohlig-Hellman algorithm if that helps at all, over here on this site: crypto.stackexchange.com/questions/10380/…. My guess is Q, R, and S need to be about the same size as U, but I'm not sure you haven't introduced something fatal also. | |
| May 4, 2019 at 19:31 | comment | added | J. Doe | Thanks for response. The use case need three of it with about equal size. What would be large enough $Q,R,S$? Assuming a prime $U$ would be large enough for a single disc. problem: $g^a \mod U$. How large $Q,R,S$ need to be to get same security? $Q,R,S$ need to be as large as $U$? As large as $U^2$? As large as $U^3$? As large as $\sqrt[2]U$? As large as $\sqrt[3]U$?As large as $\sqrt[4]U$? | |
| May 4, 2019 at 15:35 | comment | added | theREALyumdub | I should point out that Pohlig-Hellman causes you some trouble. I think that if you choose $ Q, R, S $ large enough, you may get out of cryptographic problems, but you don't gain any security over storing info as separate discrete logarithms (unless your use case really requires that). | |
| May 4, 2019 at 14:22 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 4, 2019 at 14:12 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 4, 2019 at 12:17 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 3, 2019 at 23:29 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 3, 2019 at 20:22 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 3, 2019 at 18:00 | history | tweeted | twitter.com/StackCrypto/status/1124373260253241355 | ||
| May 3, 2019 at 15:52 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 3, 2019 at 15:45 | history | edited | AleksanderCH | CC BY-SA 4.0 |
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| May 3, 2019 at 15:40 | history | edited | J. Doe | CC BY-SA 4.0 |
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| May 3, 2019 at 15:23 | history | asked | J. Doe | CC BY-SA 4.0 |