Secret Key Cryptography

This chapter is from the book

Basic XOR

The XOR operation denoted by + is a bit-wise function that maps an element of {0, 1}x{0,1} onto the set {0, 1} as follows:

```0 +0 =0
0 +1 =1
1 +0 =1
1 +1 =0```

If we take the second operand to be a key value, the XOR operation can be thought of as being simply a bit-level substitution based upon the bit values of the key. With such assumption, XOR sends a 0 or 1 to itself when the corresponding key bit is 0 and inverts a 0 into a 1 and a 1 into a 0 when the corresponding key bit is 1. XOR exhibits the following properties.

```a +0 =a
a +a =0,and thus
a +b +b =a```

The last property implies that using a fixed key value, the XOR operation can be applied to encipher a plaintext, which can then be recovered by simply applying the XOR operation to the ciphertext and the same key value. This property has led to the proliferation of many variants of weak encryption methods that solely rely on the simple XOR operation and thus are easily breakable.

Assume that a fixed-length key, K, is used for the XOR of some plaintext blocks. Knowing a block of plaintext, P, and its XOR transformation directly leads to K, by way of XORing the plaintext with the corresponding ciphertext.

```C =P +K
P +C =P +P +K
=K```

Similarly, by knowing two ciphertext blocks alone one can XOR them together to yield the XOR of the corresponding plaintext blocks as follows:

```C1 +C2 =P1 +K +P2 +K
=P1 +P2```

Examining the bit patterns of P1 + P2 can easily result in recovering one of the plaintexts. The latter can then be XORed with its ciphertext to yield the keystream.

By transforming one bit at a time the XOR operation lends itself well to a class of encryption algorithms known as stream ciphers. In contrast, block ciphers divide a plaintext into identical size blocks, generally of length greater or equal to 64 bits, then apply the same encryption transformation to encrypt each block at a time. Stream ciphers are geared for use in situations where memory buffering is limited or when characters are individually transformed as they show up at an endpoint of a transmission medium. Because they generally transform plaintext bits independently from one another, error propagation remains limited in the event of transmission anomaly.

Despite the simplicity of the XOR operation and the weakness of encryption algorithms that use it with fixed keys, there is a way of making the sole use of such basic operations result in a perfect encryption scheme. If the keystream digits are randomly generated and each keystream is used only once, the resulting ciphertext referred to as a one-time pad yields a perfect cipher. Such a cipher is provably secure against attacks in which a code breaker has knowledge of a set of ciphertexts. Figure 1.4 is a graphic illustration of the simple XOR-based one-time pad cipher.

FIGURE 1.4 A simple one-time pad based on the XOR operation

The security of the one-time pad is due to the uncertainty in attempting to guess the keystream is equal to that of directly guessing the plaintext. Note that the length of the keystream for the one-time pad is equal to that of the plaintext being encrypted. Such a property makes it difficult to maintain and distribute very long keystreams which has led to the development of stream ciphers whereby the keystream is pseudorandomly generated from a fixed secret key that is manageable.

The bit-level one-time pad applies equally well at the character level. In fact, historically a one-time pad was applied to characters when it was first invented by Major Joseph Mauborgne and Gilbert Vernam. Each keypad character is applied to only one plaintext character. The receiving entity uses the same keypad to decrypt the cipher and then destroys the key.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children

This site is not directed to children under the age of 13.

Marketing

Pearson may send or direct marketing communications to users, provided that

• Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
• Such marketing is consistent with applicable law and Pearson's legal obligations.
• Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
• Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

• As required by law.
• With the consent of the individual (or their parent, if the individual is a minor)
• In response to a subpoena, court order or legal process, to the extent permitted or required by law
• To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
• In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
• To investigate or address actual or suspected fraud or other illegal activities
• To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
• To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
• To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.