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Old 2022-01-06, 15:18   #5
Alberico Lepore
 
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May 2017
ITALY

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Quote:
Originally Posted by Alberico Lepore View Post
mi รจ venuta un IDEA

PROOF of factorizazion in polynomial time [8 digit]

reference

PART I
https://www.academia.edu/48848013/Le...rization_nr_88
&
https://www.academia.edu/66788027/Fattorizzazione_wg


Supponiamo di voler fattorizzare N=9967*6781=67586227

A=sqrt(N) B=2*sqrt(N/2)

log_5(2*sqrt(N/2))=log_5(11631)=6

67586227*25^6=16500543701171875

A=sqrt(N) B=2*sqrt(N/2)*25^6

C=A D=(B+8)*25^6


Scegliamo
A=8821 B=11631*25^6
C=8821 B=11639*25^6


solve
N=16500543701171875
,
M=(8821)*11631*25^6
,
H=(8821)*11639*25^6
,
(M-3)/8-(a*n+(M-N)/8)-[4-(a-7)*(a-5)/8]=a*(a+11631*25^6-12)/8
,
(H-3)/8-(a*m+(H-N)/8)-[4-(a-7)*(a-5)/8]=a*(a+11639*25^6-12)/8

->m=n-244140625


solve
N=16500543701171875
,
M=(8821)*11631*25^6
,
H=(8821)*11639*25^6
,
(M-3)/8-(a*n+(M-N)/8)-[4-(a-7)*(a-5)/8]=a*(a+11631*25^6-12)/8
,
(a*n+(M-N)/8)*(a*(n-244140625)+(H-N)/8)=X
,
a*n=t
,
a,X

->

11631^2*25^12*X=t^2+2136891113281250*t+1141575907505095005035400390625

Use Coppersmith method

PROOF

t=6781*(9967*25^6-11631*25^6)/8

-t=344347656250000<11631^2*25^12
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