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A Wired Equivalent Privacy (WEP) key is a security code that one must enter in order to access a secure WiFi network. The characters in the key are used from the numbers 0 to 9 and letters from \(\mathrm{A}\) to \(\mathrm{F}\), which gives 16 possibilities for each character of the key. Note that repeats are allowed, that is, the same letter or number can be used more than once in a key. A WEP key for a WiFi network with 64 -bit security is 10 characters long. a. How many different 64 -bit WEP keys can be made by using the given numbers and letters? b. A specific 64 -bit network has a WEP key in which the 2 nd, 5 th, 8 th, and 9 th characters are numbers and the other 6 characters are letters. How many different WEP keys are possible for this network? c. A hacker has determined that the WiFi network mentioned in part b will lock him out if he makes 20,000 unsuccessful attempts to break into the network. What is the probability that the hacker will be locked out of the network?

Step by step solution

01

Determine total combinations for a 64-bit WEP key

A WEP key for a WiFi network with 64-bit security is 10 characters long. The characters in the key consist of the numbers 0 to 9 and letters from A to F, which gives 16 possible characters for each character of the key. Each character in the key is chosen from these 16 possibilities, and each character is independent of the others. So the total number of possible keys is the product of the number of possibilities for each character. Therefore, the total number of keys is \(16^{10}\).

02

Calculate specific WEP key combinations

A specific 64-bit network has a WEP key in which the 2nd, 5th, 8th, and 9th characters are numbers and the other 6 characters are letters. This means that for the 2nd, 5th, 8th, and 9th characters we have 10 choices (0-9), and for the remaining 6 characters we have 6 choices (A-F). Applying the multiplication principle again, the number of different WEP keys for this network is \(10^4 * 6^6\).

03

Calculate the probability that a hacker will be locked out

A hacker is locked out after 20,000 unsuccessful attempts. This means we can divide the number of unsuccessful attempts by the total number of possible keys calculated in Step 2 to find the probability of being locked out. The probability that the hacker will be locked out of the network is \(20000 / (10^4 * 6^6)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Probability

Probability is the measure of the likelihood of an event occurring. It's expressed as a fraction or percentage denoting how often one outcome will happen compared to the possible outcomes. In simple terms, if there are 10 possible events and only 1 is favorable, the probability of that event is 1/10 or 10%. In the context of network security, probability can describe how likely a hacker is to guess a correct WEP key by brute force. The more possible keys, the lower the probability of guessing correctly. The formula used is:

• The number of successful outcomes
• Divided by the total number of possible outcomes

By calculating probabilities, network administrators can understand how secure a network is against random guessing attempts.

Network Security

Network security is essential in protecting data and resources from unauthorized access and attacks. A secure network uses various protocols and encryption methods to keep information safe. WEP, or Wired Equivalent Privacy, is a network security protocol for wireless networks. It was one of the initial attempts to secure wireless networks. However, over time, vulnerabilities were found, and more advanced protocols like WPA or WPA2 are used nowadays for better security.
In ensuring network security, each access point employs security keys such as the WEP key, which uses a combination of letters and numbers to restrict access. Regular updating and on-time patching of security practices are vital to safeguarding network integrity.

Permutations

Permutations refer to different arrangements or orderings of a set of elements. For example, if you have the letters A, B, and C, different permutations would include ABC, ACB, BAC, etc. In the context of a WEP key, the characters can be arranged in many different ways. Each arrangement represents a unique key. Since each position in the key is independent, the number of total permutations is determined by raising the number of choices for each character to the power of the length of the key.
Problems involving permutations are fundamental in understanding combinatorics concepts crucial for creating and evaluating secure access codes.

Cryptography

Cryptography is the science of encrypting and decrypting information to protect data. It transforms readable data into an unreadable format, making it accessible only to authorized individuals. WEP keys use cryptography to guard wireless communications. Encryption methods like WEP masks data with a code, requiring someone attempting to access the network to input the correct key.
However, cryptography is ever-evolving. As vulnerabilities in systems like WEP are discovered, new encryption methods are developed. Keeping up-to-date with cryptographic advancements is crucial for maintaining effective security measures against potential breaches.