math gcd problem need help - Page 2

crack11 · 2017-09-19, 03:45

SIR ,

any algo use to solve this issu..

crack11 · 2017-09-19, 11:48

Dear all exparts.

Please help me to calculate GCD ...

science_man_88 · 2017-09-19, 12:32

Quote:

Originally Posted by crack11

Dear all exparts.

Please help me to calculate GCD ...

find some other software if you think it's so easy and plug it in there's many computer algebra systems.

Dr Sardonicus · 2017-09-19, 14:11

xilman · 2017-09-19, 17:36

Quote:

Originally Posted by crack11

Dear all im new in this Greatest forum i have problem in mathe matica i need calculat

...

As you have subsequently clarified, this problem arises from a desire to solve a particular 512-bit RSA system. By far the easiest way known to approach this one is to factor the public modulus. A 512-bit integer factorization is not yet trivial but it is straightforward with current technology.

Post the public modulus and why you want it factored (that is, what does the key protect?) and a number of people here could solve your problem. I certainly could. Remember: just because they can doesn't mean they will. In other words, what's in it for me? Why should I divert resources from the things which presently interest me?

Of course, I've already diverted resources, my time, in posting the above but I regard that as a relatively small but speculative investment which may yield a worthwhile return.

jwaltos · 2017-09-19, 21:46

Quote:

Originally Posted by Dr Sardonicus

Ditto.
No goblins or sock puppets either.
Leprechauns, unicorns, good fairies and wizards unite.

axn · 2017-09-20, 03:04

Quote:

Originally Posted by xilman

Post the public modulus and why you want it factored (that is, what does the key protect?) and a number of people here could solve your problem. I certainly could. Remember: just because they can doesn't mean they will. In other words, what's in it for me? Why should I divert resources from the things which presently interest me?

It looks to me, from the numbers posted above, that they know the plaintext/ciphertext pairs, but doesn't know the N, and the gcd is supposed to give the N?

Weird.

crack11 · 2017-09-20, 13:28

Z1:= (7580104959982914109394378405621081680045277328933902877018950173722431866047182165909685701898461476201769271496346873969218041590426190558248064238412-(5542744080416549313204339685348101804092633280776996094712323671936025724303663565120968650288374354487920966943136994524637343823470109069100536001825061^65537));
Z2:= (7580104959982914109394378405621081680045277328933902557064898247755957479231576299665165903124564064889635003580310606233252493957322555511313835652894-(2210052959863233666352631743605544948489669349588589762935731382353706272687862251429121203091727087209430630578779213774169437578222468020592099358198793^65537));
Z3:= (7580104959982914380707737866198974081289603526426728444663905520185161944615556517456155284414829089801734045676331442459189567878379004868410811939884-(7769917532858189300573807160645252136211403803199106971490637897656073492246460627329132405022210291064618462659663590068082649667914372368725493336150572^65537));
ToUpperCase[IntegerString[(GCD[Z1,Z2,Z3]),16]]

ruselt512:BDDA237EB5F92257D6D114DA2F28FB442A1EE793813902905374CCF24F2DE4AA3560931BB8718B3EA665AEDBC7FE20AB30293BF85765E72695A7A085513B547B
this string give rsa 512

xilman · 2017-09-20, 17:32

Quote:

Originally Posted by crack11

ruselt512:BDDA237EB5F92257D6D114DA2F28FB442A1EE793813902905374CCF24F2DE4AA3560931BB8718B3EA665AEDBC7FE20AB30293BF85765E72695A7A085513B547B
this string give rsa 512

Thank you. We are able to make progress.

Now, why is this particular public modulus of interest? I ask because it isn't included in my, admittedly small, collection of interesting moduli nor can I find it on the web with a quick and simple search.

Dr Sardonicus · 2017-09-20, 21:13

I've got some other questions:

1) Why does this procedure involve taking the gcd of three integers?

2) Why are the integers of the form a - b^p, for a prime p? (I can think of some possible reasons, but I'm not at all sure.)

I was able to verify that your hex string does represent a 512-bit integer that does divide the three integers in your second example. In decimal, this integer is

9943361511736887180525193238781951852048704466124378491895895799799940176852818360584496466538746226491733937270575629104317392858375709260953122655392891

I checked that it is composite, and it has no small factors.

crack11 · 2017-09-21, 02:54

Dear xilman sir.

this is a cryptoworks smartcards rsa string but new string and old same just plaintext change ciphertext same and exp change new is very big and mathematica show problem to start kindly help me to solve this issu please solve this string any other app like matlab or mapel maybe you solve this :
(7580104959982914123117804044806461820154572036369549529405552162648856956231245030405896783337631871321017085933334306430501343909365379890910193903441-(7601611438277968963930435339966375537762723788929138241505092335032216337024111944145650540579951639515460945444623092013993572866002842083492323809287290^17592186175489));
Z2:= (7580104959982914123117804044806461820154572036369549301773204651044654156328611994019678602790933052049997074737942147009504600337458372628655015658163-(5472021051232020294637156058031796107019454396525172260491306567922450488302345750910648307191204110931670031994886144725045972546892458995859985546716414^17592186175489));
Z3:= (7580104959982914050609440727680305970398447676033232174897745114621599628756001756455762578505630805317234747401759098214730033873908508468766892578356-(2716401471494295676405217606243925186946305783849093640906079739928627393562677984831598246598185728284424287135181309232467496805930321500988187816347957^17592186175489));
ToUpperCase[IntegerString[(GCD[Z1,Z2,Z3]),16]] this is new exp string

2017-09-20, 13:28	#19
crack11 Sep 2017 2³×3 Posts	Z1:= (7580104959982914109394378405621081680045277328933902877018950173722431866047182165909685701898461476201769271496346873969218041590426190558248064238412-(5542744080416549313204339685348101804092633280776996094712323671936025724303663565120968650288374354487920966943136994524637343823470109069100536001825061^65537)); Z2:= (7580104959982914109394378405621081680045277328933902557064898247755957479231576299665165903124564064889635003580310606233252493957322555511313835652894-(2210052959863233666352631743605544948489669349588589762935731382353706272687862251429121203091727087209430630578779213774169437578222468020592099358198793^65537)); Z3:= (7580104959982914380707737866198974081289603526426728444663905520185161944615556517456155284414829089801734045676331442459189567878379004868410811939884-(7769917532858189300573807160645252136211403803199106971490637897656073492246460627329132405022210291064618462659663590068082649667914372368725493336150572^65537)); ToUpperCase[IntegerString[(GCD[Z1,Z2,Z3]),16]] ruselt512:BDDA237EB5F92257D6D114DA2F28FB442A1EE793813902905374CCF24F2DE4AA3560931BB8718B3EA665AEDBC7FE20AB30293BF85765E72695A7A085513B547B this string give rsa 512 Last fiddled with by crack11 on 2017-09-20 at 13:30

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2017-09-19, 03:45	#12
crack11 Sep 2017 2³×3 Posts	SIR , any algo use to solve this issu..

2017-09-19, 11:48	#13
crack11 Sep 2017 2³·3 Posts	Dear all exparts. Please help me to calculate GCD ...

2017-09-19, 14:11	#15
Dr Sardonicus Feb 2017 Nowhere 2²×1,039 Posts

2017-09-20, 21:13	#21
Dr Sardonicus Feb 2017 Nowhere 4156₁₀ Posts	I've got some other questions: 1) Why does this procedure involve taking the gcd of three integers? 2) Why are the integers of the form a - b^p, for a prime p? (I can think of some possible reasons, but I'm not at all sure.) I was able to verify that your hex string does represent a 512-bit integer that does divide the three integers in your second example. In decimal, this integer is 9943361511736887180525193238781951852048704466124378491895895799799940176852818360584496466538746226491733937270575629104317392858375709260953122655392891 I checked that it is composite, and it has no small factors.

2017-09-21, 02:54	#22
crack11 Sep 2017 11000₂ Posts	Dear xilman sir. this is a cryptoworks smartcards rsa string but new string and old same just plaintext change ciphertext same and exp change new is very big and mathematica show problem to start kindly help me to solve this issu please solve this string any other app like matlab or mapel maybe you solve this : (7580104959982914123117804044806461820154572036369549529405552162648856956231245030405896783337631871321017085933334306430501343909365379890910193903441-(7601611438277968963930435339966375537762723788929138241505092335032216337024111944145650540579951639515460945444623092013993572866002842083492323809287290^17592186175489)); Z2:= (7580104959982914123117804044806461820154572036369549301773204651044654156328611994019678602790933052049997074737942147009504600337458372628655015658163-(5472021051232020294637156058031796107019454396525172260491306567922450488302345750910648307191204110931670031994886144725045972546892458995859985546716414^17592186175489)); Z3:= (7580104959982914050609440727680305970398447676033232174897745114621599628756001756455762578505630805317234747401759098214730033873908508468766892578356-(2716401471494295676405217606243925186946305783849093640906079739928627393562677984831598246598185728284424287135181309232467496805930321500988187816347957^17592186175489)); ToUpperCase[IntegerString[(GCD[Z1,Z2,Z3]),16]] this is new exp string