math gcd problem need help - Page 5

crack11 · 2017-09-23, 10:59

dear sir if you don t mind can you pm your skype id than i give you more exmpel..

Dr Sardonicus · 2017-09-23, 13:26

Curiously, the OP's original question was posted to a Wolfram Stackexchange chat room the day before it was posted to this august Forum.

The user zhk had identified the trouble as an overflow problem.

I also found an old thread in this Forum with exactly the same kind of calculation as in this one. Major difference: When asked, the OP in that thread described precisely what he was trying to do and why: It's possible to calculate an unknown RSA modulus?

crack11 · 2017-09-23, 13:43

yes DR sir my calculating string same like this:http://www.mersenneforum.org/showthread.php?t=13524

R. Gerbicz · 2017-09-23, 14:36

Quote:

Originally Posted by axn

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.

Yes, exactly that!

Code:

m1^e==c1 mod N  [1]
m2^e==c2 mod N  [2]

from here: N | gcd(Z1,Z2)=gcd(m1^e-c1,m2^e-c2), because N|Z1,Z2, but it is NOT TRUE, that gcd(Z1,Z2)=N. But since for random numbers gcd is "small", the gcd(Z1,Z2) will be a small multiple of N, hence you (not me) can "easily" factor that, and using [1] or [2] we can easily choose the true value of N (in almost every cases) as a divisor of gcd(Z1,Z2). The first hard step is to get gcd(Z1,Z2).

And why would anybody solve this problem where the original message is KNOWN

, these are m1 and m2. Or there are other c values, where m is unknown.

Dr Sardonicus · 2017-09-23, 15:00

We've repeatedly told the OP "The numbers are too big"

Repeatedly ignored.

chris2be8 · 2017-09-23, 16:25

Could it be done by calculating everything mod some suitable prime larger than N, eg 2^521-1 (assuming N is RSA512)? Or mod several smaller primes and applying the Chinese Remainder Theorem to recover N?

Chris

crack11 · 2017-09-25, 13:15

Dear all.

my string same like this N modul recover..

science_man_88 · 2017-09-25, 13:20

Quote:

Originally Posted by crack11

Dear all.

my string same like this N modul recover..

there are very basic results you could get if you tried. but since you don't seem to know about PARI/GP etc. odds are you don't know what my comment means.

crack11 · 2020-08-13, 04:15

no body try to solve this issu overflow?

paulunderwood · 2020-08-13, 06:50

Quote:

Originally Posted by crack11

no body try to solve this issu overflow?

Arbitrary precision arithmetic is a solved problem.

crack11 · 2020-08-13, 10:45

dear sir,

your send link not solve the probleam

its all ready solve like old exp-65537 5 digt

but new exp-12 digit

can it possibel with exp calculating start?

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2017-09-23, 10:59	#45
crack11 Sep 2017 2³×3 Posts	dear sir if you don t mind can you pm your skype id than i give you more exmpel..

2017-09-23, 13:26	#46
Dr Sardonicus Feb 2017 Nowhere 2²·1,039 Posts	Curiously, the OP's original question was posted to a Wolfram Stackexchange chat room the day before it was posted to this august Forum. The user zhk had identified the trouble as an overflow problem. I also found an old thread in this Forum with exactly the same kind of calculation as in this one. Major difference: When asked, the OP in that thread described precisely what he was trying to do and why: It's possible to calculate an unknown RSA modulus?

2017-09-23, 13:43	#47
crack11 Sep 2017 2³·3 Posts	yes DR sir my calculating string same like this:http://www.mersenneforum.org/showthread.php?t=13524

2017-09-23, 15:00	#49
Dr Sardonicus Feb 2017 Nowhere 103C₁₆ Posts	We've repeatedly told the OP "The numbers are too big" Repeatedly ignored.

2017-09-23, 16:25	#50
chris2be8 Sep 2009 1,973 Posts	Could it be done by calculating everything mod some suitable prime larger than N, eg 2^521-1 (assuming N is RSA512)? Or mod several smaller primes and applying the Chinese Remainder Theorem to recover N? Chris

2017-09-25, 13:15	#51
crack11 Sep 2017 18₁₆ Posts	Dear all. my string same like this N modul recover..

2020-08-13, 04:15	#53
crack11 Sep 2017 24₁₀ Posts	no body try to solve this issu overflow?

2020-08-13, 10:45	#55
crack11 Sep 2017 18₁₆ Posts	dear sir, your send link not solve the probleam its all ready solve like old exp-65537 5 digt but new exp-12 digit can it possibel with exp calculating start?