I've implemented RSA encryption algorithm to encrypt the symmetric key used in data encryption, but the key size and the ciphertext size of RSA created a memory issue, so I searched other methods of public key cryptography for the solution. I found elliptic curve integrated encryption scheme (ECIES) and understand the theory behind it, however, I am a bit unclear that how this method be used as public/asymmetric encryption algorithm. The method computes the symmetric encryption with the key derived from the shared secret for both encryption and decryption (using the same key).
So how could it be taken as an asymmetric encryption algorithm?
Or Is there any method to implement it as asymmetric encryption?
Meta: this isn't really a programming or development question or problem. It probably belongs on crypto.SX; you might ask for migration.
To be exact, ECIES is a hybrid public-key encryption scheme, but so are most others. For example RSA is commonly used, just as you said, to encrypt a working (per-message) symmetric key, not to directly encrypt data.
Paraphrasing the wikipedia description:
(Usually in advance) Bob generates a (static) keypair and publishes the publickey authentically (for example using a certificate)
2-5. Alice generates an ephemeral keypair, derives the shared DEK, and encrypts the data, and sends it with her ephemeral publickey
(edit) and destroys the ephemeral privatekey
Bob uses his privatekey to derive the DEK and decrypts the data
ADDED, and expanded below, per comments: Yes the DEK is the same at both ends (notice I used 'the' meaning one and not several) and that's why this scheme works; and the part of ECIES that uses DEK for data encryption and decryption is symmetric, but all the other operations (which securely create the ephemeral shared DEK) are not.
It is vital no one besides Alice (or Bob) learns her ephemeral privatekey; if they do they can decrypt. But she doesn't need to explicitly keep it secret because she destroys it immediately after using it to send a message; that's what ephemeral means.
Let's see:
the recipient's publickey is public and anyone can encrypt
the recipient has the (static) privatekey and can decrypt
nobody else has Bob's (static) privatekey or Alice's ephemeral privatekey, and nobody else can decrypt
the recipient needs only one keypair; if there are multiple senders they can all use the same publickey but can't decrypt each other's traffic, and don't need to get the publickey secretly; for a thousand or a million senders this costs the same as or very little more than one sender
Consider the properties of a standard/traditional symmetric scheme instead:
the two parties must have a key (only one, not a pair) shared in advance; both must keep it secret and not share with anybody else
this typically requires the parties meet in advance, or use a physically secure means such as a courier to carry the key from one to the other or perhaps from a central authority to both
each key can only be used by one pair of parties; for multiple senders, Bob must have and manage that many different keys, and each sender (Alice, Abby, Anne, etc) must have a different key. Each sender must separately meet Bob, or they must each have a separate courier (or two), before they communicate with him. For a thousand or a million senders this becomes immensely costly
ECIES has none of these properties of a conventional or symmetric system, and all of the properties of a publickey or asymmetric system above, although it does also use some symmetric operations along with its asymmetric operations.
And that's why it sounds like (hybrid) public-key encryption to me!
#dave_thompson_085 has explained the concept well. However, I'd like to add an example to make it clear.
Eg:
Alice generates Public "qA" and private key "dA".
Alice sends over her public key to Bob.
Using this public key, Bob generates a random pair of symmetric keys (R and S).
Bob encrypts the message with key "S" and sends over this ciphertext along with key "R" over to Alice.
With this "R" key, Alice can multiply her private key "dA" and generate the symmetric key "S" to decrypt the ciphertext.
So the message is encrypted using a symmetric key, but over the network it is asymmetric as only the public key is exchanged over the network which is used to generate the symmetric key for the receiver and the private key is used to generate the same symmetric key on the sender's side.
Related
Is a stream cipher algorithm (Encryption) has to be always symmetric? Wikipedia has mentioned it but without a reason. This site also portrays some information about it, but not clearly why only symmetric keys are used to encrypt stream cipher but not asymmetric?
I remember that the teacher explained in class that the encryption and decryption speed of asymmetric ciphers is relatively slow, and stream encryption requires high speed, which may be one of the reasons.
You can check here, Salsa20 has 408MB/s and 4.3 cycles per byte, I do not think any asymmetric ciphers can reach this speed, you have to exchange key everytime you want to send any infomations, the same key cannot be encrypted twice in cryptography.
From what I can tell TLS works using both symmetric and assymmetric encryption.
The assymmetric schemes are used to exchange keys but when and what symmetric schemes are used?
The asymmetric schemes are used to exchange keys
and digital-signatures.
The symmetric schemes are used to data transfer with the agreed symnetric key during the key-exchange.
This is called Hybrid cryptosystem.
Yes you are right. Asymmetric algorithms are usually slower than the symmetric algorithms. However, symmetric algorithms require a shared secret key to encrypt and decrypt messages. Therefore, TLS allows the client and the server exchange a shared secret key using the asymmetric mechanism. Without an asymmetric algorithm, there is no way the shared secret can be exchanged between the two parties in a secured way. Once both the parties have the shared secret key, all subsequent communication between the client and the server are encrypted using the symmetric algorithm which is much faster than the asymmetric algorithm.
At a very high level, the steps in establishing a TLS connection looks like this:
Client -> Requests for secured session
Server -> Sends certificate & chain certificates
Client -> Verifies certificate
Client -> Generate random key for symmetric encryption
Client -> Encrypts the generated key with the server public key and sends the encrypted value to the server
Server -> Decrypt the client sent key with its own private key
Here onwards all subsequent communications between the server and the client will be encrypted using a symmetric algorithm.
Which specific algorithm will be used is determined by the cipher suites supported by the server and the client. During the connection setup, the cipher suite to be used is determined by the client preference.
A typical cipher suite name looks like this:
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256
Here
ECDHE - Key exchange algorithm
ECDSA - Digital Signature algorithm used for signing the key
AES_128_GCM - Block cipher and mode with 128 bit key
ECDHE stands for Elliptic Curve Diffie Hellman Ephemeral. The Elliptic variant (the first E) is used for performance, whereas the Ephemeral variant (the last E) is for forward secrecy. Forward secrecy means that if an attacker keeps recording all the communications over TLS and at a later point of time somehow gets hold of the private key, he/she cannot decrypt the past recorded communications.
ECDSA is used for authenticating (verifying the integrity of) the shared secret. ECDSA is weaker and slower than the other authentication algorithms like HMAC. Yet it is used for shared key authentication because it does not need the verifier know the secret key used to create the authentication tag. The server can very well use its private key to verify the integrity of the message.
AES_128_GCM - Once a common secret key is shared between both the parties (usually a browser and a web server), a symmetric block cipher algorithm is used to encrypt the message exchanges between the parties. In this particular case, the block cipher AES with 128 bit key and GCM authentication mode is used.
If you open a HTTPS website in a browser, you can see the cipher suite used using the browser utilities. For e,g, in Firefox you can see the details under the Security tab in the Page Info, as shown below:
Given a AES secret key, is it possible to fake a data that can be decrypt using that key? the decrypted data doesn't need to be meaningful, just want to know if can fake a encrypted data.
AES is a symmetrical cipher, i.e. the same key is used to both encrypt and decrypt data. As such, the key must be known to both ends of communication, and no one else. Authentication and key-exchange is done via public-key protocols, such as Diffie-Hellman key exchange.
Given these, if you are the third person to possess an AES key, I assume that you cannot send "fake data" to the recipient, as authentication will fail (no negotiation has taken place). If you have established such a connection, you can send whatever you want (you can encrypt gibberish and send it). If you mean to alter an encrypted packet, you can do it without decrypting it and re-encrypting it, but it's most likely to fail integrity tests (e.g. if hashes or CRC are present).
I would like to implement something-like-pay-TV encryption. In this system, the user has a smart card providing private key can decrypt the signal. However, I cannot find out its encryption-decryption step. Therefore, I invent some -_-!
In my system, there is a central server, a broadcast center and users. The central server generate a pair of RSA public-private key and send the public key to broadcast center. When a user want to connect to broadcast center, a request will be sent to central server. Then, the server will send the private key for user. User and broadcast center use this pair of key to encrypt-decrypt a data symmetric key (for example AES key).
Is it a good implementation if the RSA private key is used by multiple users?
RSA won't fit your needs. In RSA you would have to encrypt the data for every single user. RSA is an encryption standard with private/public keys. Each private key depends on his public key.
You can't modify RSA so that you need only one encryption. In PGP (uses RSA) for example when sending a PGP mail to five recipients, the mail is encrypted five times with different keys.
On pay TV they use conditional access http://en.wikipedia.org/wiki/Conditional_access.
By the way: do not implement your own encryption implementation. Use existing algorithms and implementations. They are proven secure.
Hi
I know a basic rules on https!
I know there is private & public key, and public key is for encryption and private key is for decryption!
Now I have questions:
* - IF I know the public key why I cannot decrypt data, Surely it's related to private key!!!
*- And does https protocol encrypt all data or only data that sent by client??
for emxample, If i go to gmail.com, html codes are encrypted or not?
now if answer is yes(and HTML codes are encrypted) how my browser can decrypt it and others can't??
If no, why we should use it for example for downloading backup of important data?
Okay, a couple of points of confusion here.
First, HTTPS isn't actually encrypted with a public/private key scheme -- technically, "asymmetric encryption." It's instead encrypted using a symmetric encryption -- one of several, actually -- with a session key that's established through an algorithm like Diffie-Hellman key exchange.
The result is that the encryption is carried out through a one-use key that's computed as part of the handshake setting up the SSL connection.
The Wikipedia article on Transport Layer Security (SSL was really a proprietary term from Netscape) is reasonably decent.
If you could get that key, you could indeed decrypt the data, but since the usual key now is 128 bits long, you have roughly 1 chance in 2128 of getting it right -- or, in another way of looking at it, you can expect to take about 2127 (170141183460469231731687303715884105728) tries before you'd find the key.
But second, asymmetric encryption does come in one way, however. When you're establishing an SSL connection, the host provides an X509 certificate to identify itself; that's so someone can't hijack DNS and make themselves appear to be paypal.com instead of Vlad's Cut Rate Hacking. The X509 certificate is signed using a public/private key pair: the signature is hashed using the private side of a trusted providers key -- say VeriSign. They provide the public side, which allows you to confirm that the certificate was indeed encrypted by VeriSign. That confirms the authenticity of the cert.
Public Key encryption systems are based on One Way Functions; functions that are far easier to compute in one direction than in the other. There are two common choices of one-way functions for public-key cryptography systems: Large integer factorization and Discrete Logarithms.
There are no mathematical proofs that large integer factorization doesn't have easy solutions: however, several decades of intense research hasn't found any polynomial-time algorithms. (Not that one would necessarily be fast, just that finding one has been a good long-term goal.) The RSA cryptosystem safety is based on the difficulty of factoring large primes.
There are mathematical proofs that solving discrete logarithms is very difficult. The El Gamal and Diffie-Hellman algorithms rely on discrete logarithms for their safety.
The public key mechanisms are only part of actual deployed solutions though. Public Key systems are usually used for digital signatures and for negotiating a session key that is used with a symmetric cipher. Symmetric ciphers are far faster, much safer to use on plain text with patterns, and are an integral portion of modern communications privacy and integrity.
Now, to directly address your questions :)
IF I know the public key why I cannot decrypt data, Surely it's related to private key!!!
They are related. And you could find one given the other. But the computational complexity of finding one is currently so much worse than generating new public / private key pairs, the key itself should have no value by the time you have cracked it. (Years for 'smaller' keys, probably millennium for 'larger' keys. Trouble is, the definition moves around. :)
And does https protocol encrypt all data or only data that sent by client?? for emxample, If i go to gmail.com, html codes are encrypted or not?
HTTPS itself encrypts everything in both directions. HOWEVER, some web sites will use unencrypted http for images, css, javascript, and https for the HTML that actually contains the user data. This is because serving unencrypted content is much faster than serving encrypted content. It is also very unsafe, because most of those types of contents can be replaced while in-flight, allowing intruders to modify the browser's DOM or inject other new code, that lets them get access to the private data. Most browsers complain about mixed SSL/TLS and unencrypted content, so hopefully not many sites do this.
how my browser can decrypt it and others can't?
During the SSL/TLS handshake at the start of the session, the server and browser negotiate a new session key that will be used for the session. All the traffic between browser and client are encrypted with the session key, and as a result of the way the SSL/TLS session is created, only the client and server know the key:
https://www.rfc-editor.org/rfc/rfc5246#page-64
8.1.1. RSA
When RSA is used for server authentication and key exchange, a 48-
byte pre_master_secret is generated by the client, encrypted under
the server's public key, and sent to the server. The server uses its
private key to decrypt the pre_master_secret. Both parties then
convert the pre_master_secret into the master_secret, as specified
above.
8.1.2. Diffie-Hellman
A conventional Diffie-Hellman computation is performed. The
negotiated key (Z) is used as the pre_master_secret, and is converted
into the master_secret, as specified above. Leading bytes of Z that
contain all zero bits are stripped before it is used as the
pre_master_secret.
Note: Diffie-Hellman parameters are specified by the server and may
be either ephemeral or contained within the server's certificate.
IF I know the public key why I cannot
decrypt data, Surely it's related to
private key!!!
Yes the are related, but to determine the private key from the public one would require solving a computational hard problem that is factorize a prime large number.
For telling it in simple words, you can do it, but the time it would require with the actual technologies is too long.