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RSA issue





akshar
If Ram discovers that his private key is same as Sita's public key, should he has a reason to get owrried?
Should he change his pair of keys
would that mean that Ram's public key=Sita's private key?
Animal
akshar wrote:
If Ram discovers that his private key is same as Sita's public key, should he has a reason to get owrried?
Should he change his pair of keys
would that mean that Ram's public key=Sita's private key?

There would be no way of Ram knowing if Sita's public key was the same unless he had access to both. If so, Sita's public key would be compromised and there would be no point in using it for encryption.

It depends what you mean by "the same" though. If it has the same ID number, for example 0x123AB45C, this may happen by sheer chance. The only way to tell if they were potentially the same would be to check the key fingerprint. These should never be the same since they are determined by the user ID (eg. Ram or Sita) and the email addresses the keys were assigned to. If the fingerprint is the same, there is most definitely a problem, but this is extremely unlikely.

Do you know how to check key fingerprints? If not, what software are you using? PGP or GnuPG? (or other?)
akshar
As per my knowledge Public key is available to any one intersted


Now say you make available your public key on a directory

I too posses a pair of public and private key

I discover that my private key is just exact as your public key.

So....
Animal
Ah... sorry, I mis-read that. I assumed that you meant the private keys were the same.

In this case, it's actually impossible for a private key to be the same as a public key. This is because of the way the keys are configured and used. You could not use a public key to encrypt or sign an outgoing email so it's therefore not possible for Ram's private key to be the same as Sita's public key because this would mean that Ram was signing/encrypting outgoing mail using a public key.

I hope this makes a little more sense than my last message! Embarassed
akshar
I suspect you have failed to get my question again. Or may be i am not getting your answer. I suspect that you are comparing the situation in a very practicle world, where as i am trying to look at it theoretically.

In the scenario i am describing no mails or no information is being sent by Ram or Sita. Let us assume they are under graduate students who get a pair of private and public key each from the college administrator.

Both ram and sita are frinds. Ram just browses through the directory of public keys and just for fun tries to compare his private key with Sita's public key listed over their. He is surprised to find both of them alike.

Theoretically if you know how RSA works as private key or RAM will consist or tow decimals say (n1, d1) and sitas public key say is (n2 ,e2) here (n1,d1)=(n2,d2)

where say is M is plaintext
M = M^(e1d1) mod n

is the RSA algorithm. I admit that I am a total newbie. MAy be you are looking the the problem from a perspective that I will gain only after some more hardwork.

I will be very thankful if you ca nguide me more.
Animal
akshar wrote:
In the scenario i am describing no mails or no information is being sent by Ram or Sita. Let us assume they are under graduate students who get a pair of private and public key each from the college administrator.

When you say the college administrator gives both Ram and Sita a private and public key, do you mean he gives them his own private and public key, or that he generates individual keys for bothe Ram and Sita individually?

akshar wrote:
Both ram and sita are frinds. Ram just browses through the directory of public keys and just for fun tries to compare his private key with Sita's public key listed over their. He is surprised to find both of them alike.

Theoretically if you know how RSA works as private key or RAM will consist or tow decimals say (n1, d1) and sitas public key say is (n2 ,e2) here (n1,d1)=(n2,d2)

where say is M is plaintext
M = M^(e1d1) mod n

is the RSA algorithm. I admit that I am a total newbie. MAy be you are looking the the problem from a perspective that I will gain only after some more hardwork.

I will be very thankful if you ca nguide me more.

You're correct. I'm looking at this problem in terms of public key infrastructure email cryptography rather than in terms of the actual mathematics of RSA. However, I'm 99.99999% sure that if the keys were separately generated for Ram and for Sita, the keys would not be compromised at all.
akshar
Yeah the keys were individually generated for both and were given to them separately through an secure manner. Administator is not givng his keys but the keys he has generated for Ram and Sita.

Quote:

However, I'm 99.99999% sure that if the keys were separately generated for Ram and for Sita, the keys would not be compromised at all.


What exactly do you mean my compromising? Compromising means revealing something you are not supposed to reveal. And such a thing is not happening here.

You have missed my point again friend.
Animal
akshar wrote:
What exactly do you mean my compromising? Compromising means revealing something you are not supposed to reveal. And such a thing is not happening here.

You have missed my point again friend.

No... I know what you mean. Perhaps my use of the word "compromised" was inaccurate. By that, I mean that even with small similarities in the actual mathematics of the keys, Ram has no reason to be worried that Sita's public key is similar to his private key. If the keys are actually identical then Ram should consider changing his keys, but as discussed above, I don't think this is possible due to the way RSA key pairs are generated.
akshar
Now I am satisfied with your answer and this is exactly what i had thought.
Our university is such a ... this question had appeared in my exam papers.

Actually if you got to see if both Sita and Ram get thewri keys from the same CA it is impossible that the keys could be same.

But one question still remains if Rams private is exactly same as Sita's public key would opposite be true as well? i.e.

Rams public key will be same as Sita's private key?

The answer to this question I feel is YES.
Animal
akshar wrote:
But one question still remains if Rams private is exactly same as Sita's public key would opposite be true as well? i.e.

Rams public key will be same as Sita's private key?

The answer to this question I feel is YES.

I really really doubt it. As I discussed in a previous post, public keys and private keys are different in terms of their content. I don't think it's actually possible for one public key to be the same as another private key, but by the mathematics involved in generating each type of key, I would imagine that if the two keys (Sita's public key / Ram's private key) were similar, the opposing private/public keys would be very different.

I think the keys are generated in a similar way to the RSA signature system - any changes in characters used would result in a very different signature being produced. I'll use this example to demonstrate: Using an RSA key with WinPT, GnuPG and using the SHA256 signing algorithm, I signed the following message: "Test message one - RSA proof of concept"

Quote:
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

Test message one - RSA proof of concept
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.5 (MingW32) - WinPT 1.1.0

iQEVAwUBRWYGZ8zZNY9LRfb1AQjbLggAs/zKJpL0akop2ZtuCtnfAVF6G74M0eoR
91t6QoVo0Rlp7TRzD6E9IhPKqcJh/l5ODcKtOl36/zX7MFV0XXQrWlQnykmKN5nM
luTlovWjR2798Aa/T+pbB8aRyEVtV38EJHmm6POGgSRtCasZ7+n8qpYJXx70hvCH
xmPx7FJoomf17fF+6hdj2QFk/tRr/cVWFzq9OHhT/OXOrkcMBfkX8kpN3mMNgMp4
fSB12wePwq/CJD1WCiy+/q/FeZ8aMfL2dpJe8JuyXx7Tq2c5fx43WApMwPKlg9JJ
lSSaBNvqvPiZmtynbj/B8qGhwYMHyn/0UcE1p9VDyr+1MbIhTIYzgw==
=pHyA
-----END PGP SIGNATURE-----


I then slightly changed the message (changed the word "concept" to "concert") then re-signed it using the same RSA key:

Quote:
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

Test message one - RSA proof of concert
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.5 (MingW32) - WinPT 1.1.0

iQEVAwUBRWYHMszZNY9LRfb1AQierwf/ZWi9LctMEhaFpUqqcpomZPQnOj+Kk5be
gq74eIlDYKJUe0I/dWOdJefZiJT9tHCN4r0tWHB+9rzk4s91d+zj2VSsmsJxnQqm
hH3EKKIBOSzEkDEHxqqvRwxESOVGlEXwYcHMS0inVYJsXQOG6VsTceZdxjgST4AG
54w77fertOC/OxTBwFnpVaL81y7c4bYGHRDhfoKBPpchgDmInpCArvZs+TnmDZvx
7jBSi1ckZ8xXsMzjJpiKLzSwFiag/BiojX51hnRzTMPUFBLRWIjAyDX05UNMIOf7
QaZO4lAY1jzr5WBw4s998Iy4So7BRyyIw3SFRngjO4vqGZICFVlBhA==
=iul5
-----END PGP SIGNATURE-----


As you can see, the signatures are significantly different. Just look at the last ten characters - in the first message these were zgw== =pHyA and in the second, they were BhA== =iul5.

By changing the name on the key, it's extremely unlikely (if not impossible) for the keys to be generated exactly the same because of implemented methods similar to those that I've demonstrated above.

However, you might find the Wikipedia Article on RSA extremely useful for your studies Wink
akshar
What you have explained above is avalanche effect. A small shange in the word resulted into totally different value of keys.


But theoretically there is no difference between a public key and private in RSA by no difference I mean to say that values will certainly be different but given two keys there is no way one can tell that this key is public and other is private. It is upto the party which generates the keys to decide which one to make public and which one to make private.

So i feel that for any given public key there will be only one and only one associated private key and vice versa.

Please correct the above statement if it is wrong.
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