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Laël Cellier on Sun, 16 Mar 2025 12:22:23 +0100
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How to find a congruence to the type of that simple equation without factoring the modulus?
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- To: pari-users <pari-users@pari.math.u-bordeaux.fr>, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Subject: How to find a congruence to the type of that simple equation without factoring the modulus?
- From: Laël Cellier <lael.cellier@laposte.net>
- Date: Sun, 16 Mar 2025 12:22:17 +0100
- Delivery-date: Sun, 16 Mar 2025 12:22:23 +0100
- Disposition-notification-to: Laël Cellier <lael.cellier@laposte.net>
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Bonjour,simple question. I ve B and a semiprime A which are very large
unrelated fixed integers impossible to factor.How to find y and z such as
y²≡z²×B mod A? Which pari functions to use? Nfroots? Cordialement,
You best bet is zncoppersmith, but this will only work if there is a solution
(y,z) with relatively small y and z which will almost never be the case.
You need fundamentaly new ideas.
Cheers,
Bill.
Hi, sorry for the delay.
And if I’m free to chose B² mod A (thereby being indirectly free to chose B), and thus only A can’t be chosen, would it be something easy to make y and z findable through zncoppersmith as a result, and if yes, how ?
Sincerely,