How to use the coppersmith method in sagemath?

Periodic_1_6
65 ●2 ●5 ●14

Z^2 + 665748*Z + 1494997090560 = 1501297920*W

to be fair, I am writing to you what it is. It is an exercise but it is understood well.

Comments

What is it ? What is your aim ?

FrédéricC ( 2021-12-17 09:54:58 +0100 )edit

Periodic_1_6 ( 2021-12-17 10:49:07 +0100 )edit

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Coppersmith's method for univariate polynomials is provided as .small_roots() method, or via PARI/GP as gp.zncoppersmith() function:

sage: R.<Z> = ZZ[]
sage: gp.zncoppersmith( Z^2+665748*Z+1494997090560, 1501297920, 2^14  )
[11520, 15852]

@Max Alekseyev thank you! what does 2^14 mean?

Periodic_1_6 ( 2021-12-17 15:14:16 +0100 )edit

Bound for the roots. I've provided links to documentation for both implementations.

Max Alekseyev ( 2021-12-17 15:48:46 +0100 )edit

Periodic_1_6 ( 2021-12-17 16:03:17 +0100 )edit

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: 2021-12-17 09:10:58 +0100

Seen: 1,103 times

Last updated: Dec 19 '21