Programming .NET Security : Asymmetric Encryption Explained (part 1) - Creating Asymmetric Keys

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Asymmetric encryption, often called "public key" encryption, allows Alice to send Bob an encrypted message without a shared secret key; there is a secret key, but only Bob knows what it is, and he does not share it with anyone, including Alice. Figure 1 provides an overview of this asymmetric encryption, which works as follows:

Figure 1. Asymmetric encryption does not require Alice and Bob to agree on a secret key

  1. Bob creates a pair of keys, one of which he keeps secret and one of which he sends to Alice.

  2. Alice composes a confidential message and encrypts it using the key that Bob has sent to her.

  3. Alice sends the encrypted data to Bob.

  4. Bob uses his secret key to decrypt the data and reads the confidential message.

The key that Bob sends to Alice is the public key, and the key he keeps to himself is the "private" key; jointly, they form Bob's "key pair."

The most striking aspect of asymmetric encryption is that Alice is not involved in selecting the key: Bob creates a pair of keys without any input or agreement from Alice and simply sends her the public key. Bob retains the private key and keeps it secret. Alice uses an asymmetric algorithm to encrypt a message with Bob's public key and sends him the encrypted data, which he decrypts using the private key.

Asymmetric algorithms include a "key generation" protocol that Bob uses to create his key pair, as shown by Figure 2. Following the protocol results in the creation of a pair of keys that have a mathematical relationship—the exact detail of the protocol and the relationship between the keys is different for each algorithm.

Figure 2. Bob uses a key generation protocol to create a new key pair

When we talk about an asymmetric encryption algorithm, we are actually referring to two related functions that perform specific tasks: an encryption function that encrypts a message using a public key, and a decryption function that uses a secret key to decrypt a message encrypted with the corresponding public key.

The encryption function can only encrypt data. Alice cannot decrypt ciphertext that she has created using the encryption function. This means that Bob can send his public key to several people, and each of them can create ciphertext that only Bob's secret key can decrypt, as shown in Figure 3.

Figure 3. Alice and Anthony are able to use the same public key to create ciphertext that can only be decrypted using Bob's secret key

The one-way nature of the encryption function means that messages created by one sender cannot be read by another (i.e., Alice cannot decrypt the ciphertext that Anthony has created, even though they both have Bob's public key). Bob can give out the public key to anyone who wants to send him a message, and he can even print his public key on his business card and hand it out to anyone who might want to send him a message. He can add the public key to an Internet directory of keys, allowing people Bob has never met to create messages that only he can read.

If Bob suspects that Eve has guessed his private key, he simply creates a new key pair and sends out the new public key to anyone who might send him a message. This is a lot easier than arranging to meet in a secure location to agree on a new symmetric secret key with every person that might want to communicate with him.

Bob's pair of keys allows Alice to send him encrypted messages, but Bob cannot use them to send a message back to Alice because of the one-way nature of the encryption and decryption functions. If Bob needs to send Alice a confidential message, Alice must create her own pair of keys and send the public key to Bob, who can then use the encryption function to create ciphertext that only Alice can decrypt with her private key.

The main limitation of public key encryption is that it is very slow relative to symmetric encryption and is not practical for encrypting large amounts of data. In fact, the most common use of public key encryption is to solve the key agreement problem for symmetric encryption algorithms.

In the following sections, we demonstrate how an asymmetric encryption algorithm works. We use the RSA algorithm for our illustration because it is the only one implemented in the .NET Framework. Ronald Rivest, Adi Shamir, and Leonard Adleman created the RSA algorithm in 1977, and the name is the first letter of each of the inventors' last names. The RSA algorithm is the basis for numerous security systems, and remains the most widely used and understood asymmetric algorithm.

1. Creating Asymmetric Keys

Most asymmetric algorithms use keys that are very large numbers, and the RSA algorithm is no exception. In this section, we demonstrate the RSA key generation protocol and provide you with some general information about the structure and usage of asymmetric keys.

We step through the RSA key generation protocol, using small test values. The protocol is as follows:

  1. Choose two large random prime numbers, p and q, of equal length and multiply them together to create n, the RSA key modulus.

    Select p as 23 and q as 31, so that the modulus, n, is:

    n = p x q = 23 x 31 = 713

  2. Randomly choose e, the public exponent, so that e and (p - 1)(q - 1) are relatively prime.

    Numbers are "relatively" prime when they share no common factors except 1. For these test values select a value for e that has no common factors with 660. Select e as 19.

  3. Compute the private exponent, d, where d = e-1mod((p - 1)(q - 1)).

    For our example, we calculate d as follows:

    d = 19-1mod(22 x 30) = 139

  4. The public key consists of e and n. The private key is d. Discard p and q, but do not reveal their values.

You can see how simple it is to create an RSA key pair. Bob sends the value of e (19) and n (713) to Alice and keeps the value of d (139) secret. Most asymmetric encryption algorithms use a similar approach to key generation.

Sidebar 1. Random Prime Numbers

Selecting prime numbers at random is a requirement of many different key generation protocols. It is very time-consuming to check that a random number is truly a prime number, especially when dealing with numbers that have hundreds of digits.

The compromise between the need for prime numbers and the need to generate them in a reasonable time is to create numbers that are "probably" prime, which means that there is a small possibility that a number seems to be a prime number, but is actually not. Probable prime numbers are subject to a level of confidence, so that a level of 16 means that the probability that a number is a true prime number exceeds:

Some asymmetric encryption algorithms are significantly less secure if numbers that are supposed to be prime numbers turn out not to be, and so care must be taken when generating numbers with a low level of confidence. There is a balance between the confidence in a prime number and the amount of computation that is required to attain that confidence level.

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