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How to use the coppersmith method in sagemath?

asked 2021-12-17 09:10:58 +0200

Periodic_1_6 gravatar image

updated 2021-12-19 20:11:16 +0200

slelievre gravatar image

How to use the coppersmith method in sagemath?

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.

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What is it ? What is your aim ?

FrédéricC gravatar imageFrédéricC ( 2021-12-17 09:54:58 +0200 )edit

@FrédéricC (1) https://en.wikipedia.org/wiki/Coppers... (2) I need it for a factorization algorithm

Periodic_1_6 gravatar imagePeriodic_1_6 ( 2021-12-17 10:49:07 +0200 )edit

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answered 2021-12-17 14:57:17 +0200

Max Alekseyev gravatar image

updated 2021-12-17 14:58:15 +0200

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

Periodic_1_6 gravatar imagePeriodic_1_6 ( 2021-12-17 15:14:16 +0200 )edit
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Bound for the roots. I've provided links to documentation for both implementations.

Max Alekseyev gravatar imageMax Alekseyev ( 2021-12-17 15:48:46 +0200 )edit

@Max Alekseyev thank you

Periodic_1_6 gravatar imagePeriodic_1_6 ( 2021-12-17 16:03:17 +0200 )edit

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Asked: 2021-12-17 09:10:58 +0200

Seen: 131 times

Last updated: Dec 19 '21