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I have searched for HOURS on how this works and I just can't get how this can be. The only given definitions are that public keyed encrypted message can only be decrypted by private key. To me, that's just nonsense and I will explain.
A website needs to be downloaded by your browser which also means that Javascript scripts and all the other stuff are accessible to anyone that catches your website if he wishes too. This also means that now, this person knows how you calculate your stuff with your public key making it possible WITHOUT the private key to decrypt it.
I'm just trying to figure out how this works and to me it does not make sens that you CANNOT decrypt an ecrypted text from a public key when you have access to all the calculations made from the side it encrypted.
I mean, when you send a password for example, first, on YOUR end, the browser's end, it encrypts the data to be recieved by the server. By encrypting the data from the browser's end, anyone that took a look on your source code can know how you encrypted it which now can be used to decrypt it. I am creating a new encryption system for our website where the server randomly creates a session key that can only be used by the user with the corresponding session. So only the 2 computers can talk to each other with the same key so if you use the same key on another computer, it just won't work as each key is stored for each session which the key dies after a set amount of time. With what I read, this seams to be called a symetric key system. I want to try and program my own assymetric key system but in all cases when I read, I can only figure out that no matter what happens as an encryption on the client's side, if a malicious person intercepts just before sending the information, he has access to how the encryption worked and therefor, does not need the private key on the server side as he just needs to reverse the process knowing how it was done on the client's side.
I'm starting to think myself as stupid thinking that way.
I'll add a little more information as I think we don't quite catch what I mean. When sending a password, say my name "David" and let's name our user WebUser. We will name our maleficient user BadGuy. So BadGuy hapopens to integrate himself in between WebUser and his browser. BadGuy also recieves ALL javascripts of the webpage permitting him to see how the calculations work before it is sent. WebUser enters his password "David" which is submitted to the javascript encryption system. Right off the bat, BadGuy does not need to decrypot anything as he already caught the password. BUT when the website responds, BadGuy has all the calculations and can use the receieved encrypted data and decrypt it using the decryption calculations he can see in the recieved web pages code.
So the only thing I can understand is that Assymetric keys are used for encryption which technically is decryptable using public known numbers. But in cas of RSA, these 2 numbers are so large that it would take years to figure out the known decryptor. As I can also undersnat is that it is pretty much easier to create the 2 numbers from the private number. But in any case, the encryption process usually ends up with a shared temporary intimate key between the two parties for for faster commuinication and that noone can ever prevent a BagGuy between User and Browser but with todays technocolgies, the real threat is more MiTM attacks where one will sniff the network. In all cases, there is no definate way to communicate 100% of the data in a undecryptable way as at least 50% of it is decryptable i/e data coming from one side or data going to the other side.
Assymetric encryption has two keys, a public and a private key, as you correctly described, so don't feel stupid. Both keys can be used for encryption and decryption, however, if data encrypted by the public key can only be decrypted by the private key and data encrypted by the private key can only be decrypted by the public key.
As a result, in order to be successfully involved in a communication using assymetric encryption you will need to have both a public and a private key.
You share your public key with others, that is, whatever data you receive, it will be encrypted with the public key. You will subsequently be able to decrypt it using your private key, which is your secret. When you send data to the other side of the communication, you encrypt it using your private key and the other side, which has your public key will be able to decrypt it.
Consider the example of versioning. You are involved in a project with some team members. When you pull the commits of others, it is encrypted with your public key, so once it is downloaded at your end, you will be able to decrypt it via your private key. As you work and do your commits, you will push the changes into the repository, encrypted using your private key. The other side of the communication already has your public key and will be able to decrypt it. It is important that you do not share your private key with anyone, so your team-mates will not be able to impersonate you, committing malicious code in your name. You can share your public key with anyone, but it is recommended to share it only with trusted people, like your team-mates, so no one else will be able to decrypt anything encrypted by your private key.
Essentially your public key is a ridiculously large number, which is the result by multiplying two primes (private key). The two primes could be found out by prime factorization, but since the public key is a very very large number, doing the prime factorization would take such a looong time that no one will sit and wait for the time (centuries) while the factorization is being executed and the results are found out.
A session id is a value which identifies a session. If there is a single such value, then it is not an assymetric encryption, as there is no public and private key involved and once someone steals the session ID, as you correctly pointed out, the malicious third person/system can impersonate the actual user and do nasty things. So the problem you have identified actually exists, but this is not a new problem and solutions were implemented. The solution you are looking for is HTTPS. Once your site gets a proper certificate, you will be able to use assymetric encryption safe and sound. Under the hood the server will have the public key of the user's session, while the user will use the private key to encrypt/decrypt and if a middle man intercepts the public key of the session (which is not a session id), the malicious third person will not be able to impersonate the actual user. Read more here:
https://en.wikipedia.org/wiki/Transport_Layer_Security
extending the previous answer
I'm just wandering how an attacker positionned between the user and his browser cannot intercept the connection details when they are clear texte to beggin with and to end with.
The magic here is called DH key exchange.
The symmetric encryption key is derived using Diffie–Hellman key exchange, where the common encryption key is exchanged.
Any "listening" party (your BadGuy) woudn't be able to derive the session key even by sniffing out the whole communications. The server will use its certificate and private key to make sure the client communicates with the legitimate target. This prevents an active "man in the middle" to pose as a false server.
it does not make sens that you CANNOT decrypt an ecrypted text from a public key when you have access to all the calculations made from the side it encrypted.
Asymmetric cryptography is based on so called "trapdoor" funtions. It means it is easy to calculate the function one way (e.g. encrypt data), but very difficult (not feasible) to od it opposite way without some secret value (private key). Indeed sometimes it is difficult to understand it and there are a lot of constraints under the asymmetric encryption is really secure. That's why you would always use some trusted library than do it yourself.
By encrypting the data from the browser's end, anyone that took a look on your source code can know how you encrypted it which now can be used to decrypt it.
Not without the random secret key, which is derived between the client and server during the key exchange (see the first paragraph).
I am creating a new encryption system for our website where the server randomly creates a session key that can only be used by the user with the corresponding session.
It's one of the rules in the field of cryptography - do not design your own crypto!
That's usually a bad idea. Please note the currently used secure channels (SSL, TLS, .. based on RSA, ECC) are designed, reviewed and used by a lot of smart people who know what they are doing, how to mitigate different attack vectors. And IMHO it is still not perfect, but it's the best we have.
I am sorry but my mind suddenly goes blank for this question....
EDIT (Scenario)
If I want information to bypass simple filters like f-ck, is it OK to encrypt the information with public key, and sign by private key?
The public key may have already exchanged by both sides, and it is even hard to get the public key.
EDIT 2
The information itself may not that much credential.
The point of encryption and signature is for bypassing and integrity.
RSA is two algorithms: one for asymmetric encryption and one for signatures. It so happens that both algorithms can use the same private key structure (this is a source of confusion: many documentations, including the RSA standard, try to explain the signature as "an encryption with the private key", which is, at best, inaccurate).
Using the same key for both usages is possible, but not really recommended, because interactions between both kind of usages have not been fully explored; also, keys for encryption and keys for signatures usually have different life cycles with distinct protection mechanisms (for instance, you normally want to keep a backup of the private key for encryption, to prevent data loss: losing the private key means losing all data which has been encrypted with that key; while you do not want a backup of the signature key).
Your scenario is a bit unclear. Asymmetric encryption uses the public key, while generating the signature uses the private key. If A wants to send a message to B with encryption (for confidentiality) and a signature (for integrity), then A will encrypt the data with a public key for which B knows the private key; and A will sign the data with a private key for which B knows the public key. This calls for two pairs of key: one pair is used for encryption and decryption (A encrypts, B decrypts, B knows the private key), and the other pair is used for signatures (A signs, B verifies, A knows the private key). If both A and B know the private key, then they have a shared secret, and it is much simpler (and faster) to use symmetric encryption (AES) and integrity checks (HMAC).
Standard disclaimer: you look like you are designing your own cryptographic protocol. Do not do this. This road leads to the same security failures that countless other smart people have stumbled upon. Use a tried-and-proven protocol such as SSL/TLS or OpenPGP.
Yes:
encryption: you encrypt with public
key, decrypt with private (obviously)
signing: you encrypt the content digest (hash) with private key, verify with public
See http://en.wikipedia.org/wiki/RSA#Signing_messages
Imagine that a server is serving public keys of the users to their partners to make encrypted communication possible. However, the server does NOT have access to the private keys..
Anyway - imagine the server is hacked and it sends not the requested public keys:
Alice requests Bob's public key
Server sends Eve's public key
Bob requests Alice's public key
Server sends Eve's public key
Alice sends a message to Bob
Server unpacks message, reads it and repacks it -> sends to Bob...
Bob sends a message to Alice
Server unpacks message, reads it and repacks it -> sends to Alice...
My question is - how to prevent such abuse? How can Alice be sure that she's using Bob's public key and vice versa?
Under the scheme you just proposed, you can't. The key here (no pun intended) is if the method used to verify the validity of the keys is compromised, you lose.
SSL tries to avoid this by creating a signature chain - some (very carefully guarded, and verified by other methods) key signs another key, signs another key, signs Alice's key. By verifying each step in the chain you can (in principle) know that the chain is valid - but if the private key along any step in the chain is compromised, you lose.
PGP (aka GPG) tries to solve the problem in a different, but similar way - keys can be signed by any number of other keys, forming a graph (called the web of trust). You select some keys that you have confirmed valid by, for example, verifying them in person, and mark them as trusted. Then any keys reachable by less than N steps (and/or from M distinct paths from different trusted roots) are also considered valid.
If you're really paranoid, you can, of course, physically hand the key to the other person. Of course, they have to be sure it's not someone disguised as you...
That said, the only truly foolproof way of verifying the validity of a key is generating it yourself... unless your hardware/OS/compiler/brain is compromised too :)
The crucial part missing here is authentication. Alice needs a way to know that she is really using Bobs public key. One way would be to exchange the keys personally but that is not always possible.
That is what the Web of Trust is for. Other parties can sign the public key of a user if they are sure that this key belongs to him. If enough (3) of your other contacts (which you trust) signed the public key of Bob, you can be relatively sure that it is his key.
This is the primary problem with public key encryption. You don't have any way to verify that the public key you receive is actually the public key for your intended recipient. The way HTTPS/SSL gets around this is through the use of trusted certificate authorities. The certificate authority signs the public key of the party in question with their private key, guaranteeing that the public key hasn't been changed since it was provided to the certificate authority. Even then, it is only guaranteed that the key provided to you when you request it is the same key that was originally provided to the certificate authority. However, if the server providing those certificates is compromised, you're still in trouble. Even having the server sign the keys as suggested above isn't fool proof if the sever itself is compromised. Ultimately, the security if your key distribution server must be maintained for this system to work.
The FAQ for PGP (Pretty Good Privacy) explains this issue.
I would also recommend reading Bruce Schneier's excellent book "Applied Cryptography" for "friendly and digestible" discussions of these topics.
If I want to sign and encrypt a message using an X509 certificate, is there any reason not to use the same certificate for encryption and signing?
Update: Looking back, I think that this must be the most hair-brained question I ever asked on SO. I'm sorry.
The sender uses his own private key to sign a message. The message is encrypted with the recipient public key. A certificate contains a public key. Presumably, the sender public key (corresponding to the sender private key used for signing the message) is also represented in a certificate.
The recipient uses his own private key (corresponding to the public key in his certificate) to decrypt the incoming message. The recipient uses the sender public key (from the sender certificate) to verify the signature.
That being said, you may envision a generic scenario where everybody can send and receive email. Therefore, everyone has a key pair (with public part in a certificate) which is used to encrypt and decrypt emails (Bob's public key is used to encrypt emails sent to Bob, and Bob uses the corresponding private key to decrypt them, i.e. to read the emails). Also, everyone has a key pair for signatures (Bob uses his private key to sign the messages that he sends, Alice uses Bob's public key to verify the signatures purportedly computed by Bob).
The question is then: will Bob have two key pairs (one for encryption/decryption, and one for signature/verification), or only one key pair which is used for both jobs ?
It so happens that the RSA public encryption algorithm and the RSA signature algorithm can use the same kind of key, called (quite logically) "RSA keys". So this is doable, and actually it happens quite often.
However, generally speaking, signature keys and encryption keys have distinct life cycles and management procedures. In a business context, the direction keeps in a safe a copy of all private keys used for encryption, because losing an encryption key means losing data. And employees can become "unavailable" (employee is fired, employee retires, employee is hit by a bus...). Conversely, when a signature key is lost, previously emitted signatures are still valid and verifiable, so one simply has to create a new key pair to be able to produce other signatures. Besides, digital signatures may get a strong legal status only if there is no copy of the key in a safe somewhere. So the general advice is to keep encryption and signature keys separate. Using the same key for both is an approximation which may have unwanted side-effects (such as data loss or lack of legal value). Depending on the context, this may or may not be a problem.
An X509 certificate contains a public key. To encrypt, you use the recipient's public key presumably obtained from their certificate. To sign, you use your private key, presumably from a secure store. The recipient verifies the signature using your public key, presumably from your certificate. Those are the basics.
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What is the difference between encrypting some data vs signing some data (using RSA)?
Does it simply reverse the role of the public-private keys?
For example, I want to use my private key to generate messages so only I can possibly be the sender. I want my public key to be used to read the messages and I do not care who reads them. I want to be able to encrypt certain information and use it as a product-key for my software. I only care that I am the only one who can generate these. I would like to include my public key in my software to decrypt/read the signature of the key. I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.
Is signing useful in this scenario?
When encrypting, you use their public key to write a message and they use their private key to read it.
When signing, you use your private key to write message's signature, and they use your public key to check if it's really yours.
I want to use my private key to generate messages so only I can possibly be the sender.
I want my public key to be used to read the messages and I do not care who reads them
This is signing, it is done with your private key.
I want to be able to encrypt certain information and use it as a product key for my software.
I only care that I am the only one who can generate these.
If you only need to know it to yourself, you don't need to mess with keys to do this. You may just generate random data and keep it in a database.
But if you want people to know that the keys are really yours, you need to generate random data, keep in it a database AND sign it with your key.
I would like to include my public key in my software to decrypt/read the signature of the key.
You'll probably need to purchase a certificate for your public key from a commercial provider like Verisign or Thawte, so that people may check that no one had forged your software and replaced your public key with theirs.
In RSA crypto, when you generate a key pair, it's completely arbitrary which one you choose to be the public key, and which is the private key. If you encrypt with one, you can decrypt with the other - it works in both directions.
So, it's fairly simple to see how you can encrypt a message with the receiver's public key, so that the receiver can decrypt it with their private key.
A signature is proof that the signer has the private key that matches some public key. To do this, it would be enough to encrypt the message with that sender's private key, and include the encrypted version alongside the plaintext version. To verify the sender, decrypt the encrypted version, and check that it is the same as the plaintext.
Of course, this means that your message is not secret. Anyone can decrypt it, because the public key is well known. But when they do so, they have proved that the creator of the ciphertext has the corresponding private key.
However, this means doubling the size of your transmission - plaintext and ciphertext together (assuming you want people who aren't interested in verifying the signature, to read the message). So instead, typically a signature is created by creating a hash of the plaintext. It's important that fake hashes can't be created, so cryptographic hash algorithms such as SHA-2 are used.
So:
To generate a signature, make a hash from the plaintext, encrypt it with your private key, include it alongside the plaintext.
To verify a signature, make a hash from the plaintext, decrypt the signature with the sender's public key, check that both hashes are the same.
There are two distinct but closely related problems in establishing a secure communication
Encrypt data so that only authorized persons can decrypt and read it.
Verify the identity/authentication of sender.
Both of these problems can be elegantly solved using public key cryptography.
I. Encryption and decryption of data
Alice wants to send a message to Bob which no one should be able to read.
Alice encrypts the message with Bob's public key and sends it over.
Bob receives the message and decrypts it using his private Key.
Note that if A wants to send a message to B, A needs to use the Public
key of B (which is publicly available to anyone) and neither public
nor private key of A comes into picture here.
So if you want to send a message to me you should know and use my public key which I provide to you and only I will be able to decrypt the message since I am the only one who has access to the corresponding private key.
II. Verify the identity of sender (Authentication)
Alice wants to send a message to Bob again. The problem of encrypting the data is solved using the above method.
But what if I am sitting between Alice and Bob, introducing myself as 'Alice' to Bob and sending my own message to Bob instead of forwarding the one sent by Alice. Even though I can not decrypt and read the original message sent by Alice(that requires access to Bob's private key) I am hijacking the entire conversation between them.
Is there a way Bob can confirm that the messages he is receiving are actually sent by Alice?
Alice signs the message with her private key and sends it over. (In practice, what is signed is a hash of the message, e.g. SHA-256 or SHA-512.)
Bob receives it and verifies it using Alice's public key. Since Alice's public key successfully verified the message, Bob can conclude that the message has been signed by Alice.
Yeah think of signing data as giving it your own wax stamp that nobody else has. It is done to achieve integrity and non-repudiation. Encryption is so no-one else can see the data. This is done to achieve confidentiality. See wikipedia http://en.wikipedia.org/wiki/Information_security#Key_concepts
A signature is a hash of your message signed using your private key.
Signing is producing a "hash" with your private key that can be verified with your public key. The text is sent in the clear.
Encrypting uses the receiver's public key to encrypt the data; decoding is done with their private key.
So, the use of keys is not reversed (otherwise your private key wouldn't be private anymore!).
You are describing exactly how and why signing is used in public key cryptography. Note that it's very dangerous to sign (or encrypt) aritrary messages supplied by others - this allows attacks on the algorithms that could compromise your keys.
Signing indicates you really are the source or vouch for of the object signed. Everyone can read the object, though.
Encrypting means only those with the corresponding private key can read it, but without signing there is no guarantee you are behind the encrypted object.
Functionally, you use public/private key encryption to make certain only the receiver can read your message. The message is encrypted using the public key of the receiver and decrypted using the private key of the receiver.
Signing you can use to let the receiver know you created the message and it has not changed during transfer. Message signing is done using your own private key. The receiver can use your public key to check the message has not been tampered.
As for the algorithm used: that involves a one-way function see for example wikipedia. One of the first of such algorithms use large prime-numbers but more one-way functions have been invented since.
Search for 'Bob', 'Alice' and 'Mallory' to find introduction articles on the internet.
What is the difference between encrypting some data vs signing some data (using RSA)?
Encryption preserves confidentiality of the message ("some data"), while signing provides non-repudiation: i.e. only the entity that signed it could have signed it. There are functional differences as well; read on.
Does it simply reverse the role of the public-private keys?
Absolutely not. The use of the same private keys for signing and decryption (or, likewise, the same public keys for verification and encryption) is frowned upon, as you should not mix purposes. This is not so much a mathematical issue (RSA should still be secure), but a problem with key management, where e.g. the signing key should have a shorter live and contain more protection before it is used.
For the same message, you should use the senders private key for signing and the receivers trusted public key for encryption. Commonly sign-then-encrypt is used otherwise an adversary could replace the signature with his own. Likewise you should use the private key of the receiver for decryption and the trusted public key of the sender for verification.
Furthermore, you should understand that signature generation doesn't use "encryption with the private key". Although all RSA operations are based upon modular exponentiation, the padding scheme is entirely different for signature generation. Furthermore, the public key has entirely different properties than the RSA private key in all practical uses of RSA.
For example, I want to use my private key to generate messages so only I can possibly be the sender.
That's non-repudiation property, which can be achieved by signing.
I want my public key to be used to read the messages and I do not care who reads them.
The public key should be considered known by all. If you want everybody to read the messages, then you simply do not encrypt them.
Signing will generally not influence the content of the message. The message is is considered separate from signatures. Officially such signatures are known as "signatures with appendix" where the appendix is the message. It's a bit weird name as the message is considered more important than the signature over it, but yeah. Only few signatures offer (partial) message recovery; they are not used much anymore and are generally considered deprecated.
Note that signature protocols such as CMS may deploy a container format that includes both the message and the signature. In that case you'd need first get the - still unencrypted - message out of the container, much like unzipping a file from a plain .zip archive. So the message may be hidden from view and cannot be directly used in that case.
I want to be able to encrypt certain information and use it as a product-key for my software. I only care that I am the only one who can generate these.
Encryption is used to achieve confidentiality. In the past RSA signature generation was often thought of as "encryption with the private key". However, the operations are quite different as explained above, and the later standards desperately try and separate encryption and signature generation.
I would like to include my public key in my software to decrypt/read the signature of the key. I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.
Yes, this is called establishing trust in the public key. However, protecting your program code is very different from protecting messages. You can perform code signing but then you'd need something to check the signature outside of your code. There are operating systems that offer this.
There is Microsoft Authenticode for instance. Application stores like the iStore and Android app store may or may not use code signing, but they offer some reassurance that your application isn't cloned or at least not cloned within the store. Cryptography is not always the solution after all.
Keeping your code from being cloned / altered at all is much harder, and you'd be solidly in DRM territory if you go that way.
Is signing useful in this scenario?
Yes, absolutely. It can certainly help making sure that the messages were only signed by you, if there is trust in the public key. If it can be helpful for authenticating your application code / integrated public key depends entirely on the environment that you expect to run the code in.
In your scenario, you do not encrypt in the meaning of asymmetric encryption; I'd rather call it "encode".
So you encode your data into some binary representation, then you sign with your private key. If you cannot verify the signature via your public key, you know that the signed data is not generated with your private key. ("verification" meaning that the unsigned data is not meaningful)
Answering this question in the content that the questioners intent was to use the solution for software licensing, the requirements are:
No 3rd party can produce a license key from decompiling the app
The content of the software key does not need to be secure
Software key is not human readable
A Digital Signature will solve this issue as the raw data that makes the key can be signed with a private key which makes it not human readable but could be decoded if reverse engineered. But the private key is safe which means no one will be able to make licenses for your software (which is the point).
Remember you can not prevent a skilled person from removing the software locks on your product. So if they have to hack each version that is released. But you really don't want them to be able to generate new keys for your product that can be shared for all versions.
Python
The PyNaCl documentation has an example of 'Digital Signature' which will suite the purpose. http://pynacl.readthedocs.org/en/latest/signing/
and of cause NaCl project to C examples
What is the difference between encrypting some data vs signing some data (using RSA)?
RSA merely the only public-key cryptosystem that naively supports both public-key encryption and digital signatures.
This usually confuses beginners since various sources/lecturers that say
RSA decryption is the RSA signature.
No, it is not!
The confusing comes from the textbook RSA
the textbook RSA encryption;
message m and calculates c = m^e mod n for encryption and m = c^d mod n for the decryption.
the textbook RSA signatures;
message m and calculates sg = m^d mod n for verification and m == sg^e mod n for the signature verification.
Both are not secure and they are not used in the real-life!
Does it simply reverse the role of the public-private keys?
No, it is not!
Encryption
For RSA encryption one must be using either RSASSA-PKCS1-v1_5 padding or Optimal Asymmetric Encryption Padding (OAEP). These paddings have overhead to the message. For example, PKCS1-v1_5 defined as
It has an EM structure as this
EM = 0x00 || 0x02 || PS || 0x00 || M.
so what are they;
PS is at least eight FFs block
M is the message
the first 0x00 guarantees that EM is less than the modulus.
The rest details like the size of FF block etc. can be found in rfc 8017 section 7.2.1
So it has a special message structure to be secure which is proven to be secure very lately (2018). The padding has at least 11-byte overhead.
Signature
The correct term for signature is signing and verification. For secure signing, RSA needs RSA-PSS (Probabilistic signature scheme). The structure is a bit complex, a picture will tell most of it
Once you hash the message and properly padded, then you can use your private key to sign your padded message!
For the verification, use the public key on the signed message and verify using the padding rules.
Prefer OAEP since RSASSA-PKCS1-v1_5 hard to implement correctly and those incorrect implementations caused many attacks over the year despite that is is proven to be secure.
Let finish all with the Cornell University page;
RSA Signing is Not RSA Decryption