Generating Rsa Key And Signing

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To sign an assembly with a strong name, you must have a public/private key pair. This public and private cryptographic key pair is used during compilation to create a strong-named assembly. You can create a key pair using the Strong Name tool (Sn.exe). Key pair files usually have an.snk extension. May 27, 2010 Linux Generate RSA SSH Keys. You need to use the ssh-keygen command as follows to generate RSA keys (open terminal and type the following command). This will invoke OpenSSL, instruct it to generate an RSA private key using the DES3 cipher, and send it as an output to a file in the same directory where you ran the command. Hit Enter  to generate your private key. You will be informed that your private key is being generated, then prompted for a pass phrase. According to PKCS1.5, when signing the format of the data that goes into the RSA operation looks something like this: (The metadata specifies which hash function has been used.) This format is what openssl dgst -verify is looking for when you try to verify the signature. However this is not what you create in your steps.

Signing a document with pen and ink (the obvious equivalentof a digital signature) is quite different than opening padlocked box with a key (the perhaps less obvious equivalent ofdecryption). Nevertheless, both involve using a secret: how towrite your own distinctive signature, and the shape of adistinctive key.

There arealgorithms for digital signatures, and algorithms for encryptionschemes. Sometimes it turns out that the key idea underlying an algorithm can be used for both purposes. For example,the key idea behind the El Gamal encryption algorithm can also be used to build a digital signature algorithm.The same is true for the well-known RSA algorithm.

Unfortunately, there's a tendency to oversimplify by assertingthat digital signature algorithms are the same as the corresponding encryption scheme algorithms. They aren't.Nonetheless, you will sometimes find claims that (for example)RSA signing is the same as RSA decryption. That kind of claimis partially true, but also partially false.

The RSA Function

Let's look carefully at RSA to see what the relationship betweensignatures and encryption/decryption really is. But let's leave some of the mathematical details abstract, so that we don't have to get intoany number theory.

In 1977, Rivest, Shamir, and Adelman discovered that the following functioncould be used for building cryptographic algorithms. I'll call it the RSA function:

R(x,k,n) = x^k (mod n)

Arguments x, k, and n are all integers, potentially very largeintegers. But n won't be important in the rest of ourdiscussion, so from now on, we'll leave it out and simplywrite R(x,k).

Along with the RSA function, Rivest, Shamir, and Adelman discovered a way of choosing two keys, K and k, such that

R(R(x,K),k) = x, and
R(R(x,k),K) = x.

That is, applying R with K 'undoes' applying R with k, and viceversa.

RSA Encryption

We could use R to attempt to build an encryption scheme usingpublic encryption key K and private decryption key k:

Generating Rsa Key And Signing 2017

Enc(m; K) = R(m,K)
Dec(c; k) = R(c,k)

To encrypt a plaintext m, just apply the RSA function with thepublic key; to decrypt, apply it with the private key.

That's where many textbook descriptions of RSA encryption stop. But it's not the whole story.

In practice, using the 'textbook' version of RSA encryptionis actually insecure. There are many attacks on it. Here's justone:

Suppose Alice sends two messages, m1 and m2, encrypted with her public key K_A.

c1 = Enc(m1; K) = R(m1,K) = m1^K (mod n)
c2 = Enc(m2; K) = R(m2,K) = m2^K (mod n)

What happens if m1 and m2 happen to be the same plaintext m?

c1 = m^K mod n = c2

Therefore a Dolev-Yao adversary observing the network will be able to learn something about the plaintexts m1 and m2--- namely, that they are the same---by observing ciphertexts c1 and c2! A secure encryption scheme shouldn't allow the adversary to learn that.

For more attacks, see [D. Boneh, A. Joux, and P. Nguyen. Why Textbook ElGamal and RSA Encryption are Insecure.In Proc. AsiaCrypt, 2000.] and [J. Katz and Y. Lindell.Introduction to Modern Cryptography, section 10.4. Chapman & Hall/CRC, 2008.].

To make 'textbook' RSA encryption secure, we preprocess the plaintext mbefore applying the RSA function. We correspondingly do some postprocessingduring decryption after applying the RSA function:

Enc(m; K) = R(pre(m),K)
Dec(c; k) = post(R(c,k))

There are several pre- and post-processing schemes. They are usually calledpadding schemes, though that's a slight misnomer: they do more than just padding. One of the best is OAEP: optimal asymmetric encryption padding,invented by Bellare and Rogaway in 1994. Amongst other things, OAEP pre-processingprevents the attack we observed above by XORing a cryptographic hash of an unpredictable nonce to the plaintext.

In more (though not quite full) detail, OAEP pre-processing works as follows:

Generating Rsa Key And Signing Form

OAEP-pre(m):
r = random nonce
X = (m 00..0) XOR H(r) // pad m with zeros
Y = r XOR H(X)
output X Y

Notation denotes bit concatenation, and H is a cryptographic hash function.OAEP post-processing undoes the pre-processing:

OAEP-post(m'):
split m' into X Y
r = Y XOR H(X)
(m 00..0) = X XOR G(R)
output m

Putting this all together, we get the RSA-OAEP encryption scheme:

To reiterate, I have sealed with.snk file before but want to know how to seal it with a certificate provided by CA and the looking for the instructions for it. So, what is the file provided by CA that I should use to seal a MP and how do I use that file to seal it. I want to sign the mp with a certificate. So, if I approach a CA like verisign they give us a file with the public and private keys (I am not sure what the name of the file will be but if I do the certificate myself it will be like.cer). Generate snk file from public key.

Generating Rsa Key And Signing Form

Enc(m; K) = R(OAEP-pre(m),K)
Dec(c; k) = OAEP-post(R(c,k))

RSA-OAEP is provably secure for some very strong, well-accepted definitionsof security of encryption schemes. 'Textbook' RSA, of course, is notsecure in that sense.

RSA Digital Signatures

We could use R to attempt to build a digital signature scheme usingpublic verification key K and private signing key k:

Sign(m; k) = R(m,k)
Ver(m; s; K) = R(s,K) m

To sign a message m, just apply the RSA function with theprivate key to produce a signature s; to verify, apply the RSA functionwith the public key to the signature, and check that the result equals the expected message.

The main problem with the simple scheme just suggested is that messagesmight be too long---roughly speaking, the RSA function can't accomodate messages thatare longer than the key. With encryption schemes, we solve that problemwith block cipher modes. With digital signatures schemes, we insteadsolve that problem with cryptographic hashes:

Generating

Generating Rsa Key And Signing 2017

Sign(m; k) = R(H(m),k)
Ver(m; s; K) = R(s,K) H(m)

That's the textbook description of RSA signatures. And it's more-or-lessthe whole story. You can think of the hash function H as being the equivalentof both the pre- and post-processing used for RSA encryption.

(There is a more complex pre- and post-processing scheme for signatures calledPSS (probabilistic signature scheme) that is provably secure. It's not as widelyimplemented, nor do I know of any attacks on the simpler hashing scheme above.)

RSA Encryption vs. RSA Digital Signatures

Repeated from above, here is our RSA encryption scheme and our RSA digitalsignature scheme in their 'textbook' form:

Enc(m; K) = R(m,K)
Dec(c; k) = R(c,k)
Sign(m; k) = R(m,k)
Ver(m; s; K) = R(s,K) m

And here are the same algorithms in their practical form, as used inreal implementations:

Enc(m; K) = R(OAEP-pre(m),K)
Dec(c; k) = OAEP-post(R(c,k))
Sign(m; k) = R(H(m),k)
Ver(m; s; K) = R(s,K) H(m)

Generating Rsa Key And Signing

Given what we know now, let's consider the claim that RSA signing is thesame as RSA decryption: is the Sign function the same as the Decfunction? In the real, practical world, clearly not. Sign involves ahash function H, whereas Dec involves a post-processing functionOAEP-post. With Sign, H is applied directly to the message, then theRSA function is applied later. With Dec, the RSA function is appliedfirst, and OAEP-post is applied later. Likewise, RSA signatureverification is clearly different from RSA encryption.

But there is one way in which RSA signing is similar to RSA decryption:both involve a call to the RSA function with private key k asan argument. Likewise, RSA signature verification and RSA encryptionboth involve calling the RSA function with public key K as an argument.You can see that in the 'textbook' formulations of the algorithms.

Conclusion

In the abstract world of textbooks, RSA signing and RSA decryption do turn outto be the same thing. In the real world of implementations, they are not.So don't ever use a real-world implementation of RSA decryption to computeRSA signatures. In the best case, your implementation will break in a waythat you notice. In the worst case, you will introduce a vulnerabilitythat an attacker could exploit.

Furthermore, don't make the mistake of generalizing from RSA to concludethat any encryption scheme can be adapted as a digital signature algorithm.That kind of adaptation works for RSA and El Gamal, but not in general.