Chapter 1. Introduction to Public-Key Cryptography

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Public-key cryptography and related standards underlie the security features of many products such as signed and encrypted email, single sign-on, and Transport Layer Security/Secure Sockets Layer (SSL/TLS) communications. This chapter covers the basic concepts of public-key cryptography.
Internet traffic, which passes information through intermediate computers, can be intercepted by a third party:
Information remains intact, but its privacy is compromised. For example, someone could gather credit card numbers, record a sensitive conversation, or intercept classified information.
Information in transit is changed or replaced and then sent to the recipient. For example, someone could alter an order for goods or change a person's resume.
Information passes to a person who poses as the intended recipient. Impersonation can take two forms:
  • Spoofing. A person can pretend to be someone else. For example, a person can pretend to have the email address or a computer can falsely identify itself as a site called
  • Misrepresentation. A person or organization can misrepresent itself. For example, a site called can purport to be an on-line furniture store when it really receives credit-card payments but never sends any goods.
Public-key cryptography provides protection against Internet-based attacks through:
Encryption and decryption
Encryption and decryption allow two communicating parties to disguise information they send to each other. The sender encrypts, or scrambles, information before sending it. The receiver decrypts, or unscrambles, the information after receiving it. While in transit, the encrypted information is unintelligible to an intruder.
Tamper detection
Tamper detection allows the recipient of information to verify that it has not been modified in transit. Any attempts to modify or substitute data are detected.
Authentication allows the recipient of information to determine its origin by confirming the sender's identity.
Nonrepudiation prevents the sender of information from claiming at a later date that the information was never sent.

1.1. Encryption and Decryption

Encryption is the process of transforming information so it is unintelligible to anyone but the intended recipient. Decryption is the process of decoding encrypted information. A cryptographic algorithm, also called a cipher, is a mathematical function used for encryption or decryption. Usually, two related functions are used, one for encryption and the other for decryption.
With most modern cryptography, the ability to keep encrypted information secret is based not on the cryptographic algorithm, which is widely known, but on a number called a key that must be used with the algorithm to produce an encrypted result or to decrypt previously encrypted information. Decryption with the correct key is simple. Decryption without the correct key is very difficult, if not impossible.

1.1.1. Symmetric-Key Encryption

With symmetric-key encryption, the encryption key can be calculated from the decryption key and vice versa. With most symmetric algorithms, the same key is used for both encryption and decryption, as shown in Figure 1.1, “Symmetric-Key Encryption”.
Symmetric-Key Encryption

Figure 1.1. Symmetric-Key Encryption

Implementations of symmetric-key encryption can be highly efficient, so that users do not experience any significant time delay as a result of the encryption and decryption.
Symmetric-key encryption is effective only if the symmetric key is kept secret by the two parties involved. If anyone else discovers the key, it affects both confidentiality and authentication. A person with an unauthorized symmetric key not only can decrypt messages sent with that key, but can encrypt new messages and send them as if they came from one of the legitimate parties using the key.
Symmetric-key encryption plays an important role in SSL/TLS communication, which is widely used for authentication, tamper detection, and encryption over TCP/IP networks. SSL/TLS also uses techniques of public-key encryption, which is described in the next section.

1.1.2. Public-Key Encryption

Public-key encryption (also called asymmetric encryption) involves a pair of keys, a public key and a private key, associated with an entity. Each public key is published, and the corresponding private key is kept secret. (For more information about the way public keys are published, see Section 1.3, “Certificates and Authentication”.) Data encrypted with a public key can be decrypted only with the corresponding private key. Figure 1.2, “Public-Key Encryption” shows a simplified view of the way public-key encryption works.
Public-Key Encryption

Figure 1.2. Public-Key Encryption

The scheme shown in Figure 1.2, “Public-Key Encryption” allows public keys to be freely distributed, while only authorized people are able to read data encrypted using this key. In general, to send encrypted data, the data is encrypted with that person's public key, and the person receiving the encrypted data decrypts it with the corresponding private key.
Compared with symmetric-key encryption, public-key encryption requires more processing and may not be feasible for encrypting and decrypting large amounts of data. However, it is possible to use public-key encryption to send a symmetric key, which can then be used to encrypt additional data. This is the approach used by the SSL/TLS protocols.
The reverse of the scheme shown in Figure 1.2, “Public-Key Encryption” also works: data encrypted with a private key can be decrypted only with the corresponding public key. This is not a recommended practice to encrypt sensitive data, however, because it means that anyone with the public key, which is by definition published, could decrypt the data. Nevertheless, private-key encryption is useful because it means the private key can be used to sign data with a digital signature, an important requirement for electronic commerce and other commercial applications of cryptography. Client software such as Mozilla Firefox can then use the public key to confirm that the message was signed with the appropriate private key and that it has not been tampered with since being signed. Section 1.2, “Digital Signatures” illustrates how this confirmation process works.

1.1.3. Key Length and Encryption Strength

Breaking an encryption algorithm is finding the key to the access the encrypted data in plain text. For symmetric algorithms, breaking the algorithm usually means trying to determine the key used to encrypt the text. For a public key algorithm, breaking the algorithm usually means acquiring the shared secret information between two recipients.
One method of breaking a symmetric algorithm is to simply try every key within the full algorithm until the right key is found. For public key algorithms, since half of the key pair is publicly known, the other half (private key) can be derived using published, though complex, mathematical calculations. Manually finding the key to break an algorithm is called a brute force attack.
Breaking an algorithm introduces the risk of intercepting, or even impersonating and fraudulently verifying, private information.
The key strength of an algorithm is determined by finding the fastest method to break the algorithm and comparing it to a brute force attack.
For symmetric keys, encryption strength is often described in terms of the size or length of the keys used to perform the encryption: longer keys generally provide stronger encryption. Key length is measured in bits.
An encryption key is considered full strength if the best known attack to break the key is no faster than a brute force attempt to test every key possibility.
Different types of algorithms — particularly public key algorithms — may require different key lengths to achieve the same level of encryption strength as a symmetric-key cipher. The RSA cipher can use only a subset of all possible values for a key of a given length, due to the nature of the mathematical problem on which it is based. Other ciphers, such as those used for symmetric-key encryption, can use all possible values for a key of a given length. More possible matching options means more security.
Because it is relatively trivial to break an RSA key, an RSA public-key encryption cipher must have a very long key — at least 2048 bits — to be considered cryptographically strong. On the other hand, symmetric-key ciphers are reckoned to be equivalently strong using a much shorter key length, as little as 80 bits for most algorithms. Similarly, public-key ciphers based on the elliptic curve cryptography (ECC), such as the Elliptic Curve Digital Signature Algorithm (ECDSA) ciphers, also require less bits than RSA ciphers.
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