You work in the security department of a bank’s website. To access their accounts, customers of the bank must create an 8-digit password. It is your job to determine the password requirements for these accounts. Security guidelines state that for the website to be secure, the probability that an 8-digit password is guessed on one try must be less than 1/60^8, assuming all passwords are equally likely.
Your job is to use the probability techniques you have learned in this chapter to decide what requirements a customer must meet when choosing a password, including what sets of characters are allowed, so that the website is secure according to the security guidelines.
2. Answering the Question
a. What password requirements would you set? What characters would be allowed?

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to ensure that the probability of guessing an 8-digit password in one try is less than 1/(60^8). This involves calculating the total number of possible passwords and ensuring it is large enough to meet the security guideline.
2. Step 2: Define the total number of possible passwords. If the password consists of 8 characters, and each character can be chosen from a set of 'n' possible characters, the total number of possible passwords is given by n^8. Use the formula: $n^8$.
3. Step 3: Set the inequality for security. To meet the security guideline, the total number of possible passwords must satisfy the inequality: $n^8>\; 60^8$. Solve this inequality to determine the minimum value of 'n', the size of the character set.
4. Step 4: Determine the character set. Based on the value of 'n' obtained in Step 3, decide what characters should be included in the password. For example, if 'n' is 62, you might include uppercase letters (26), lowercase letters (26), and digits (10). If 'n' is larger, you may need to include special characters.
5. Step 5: Formulate the password requirements. Based on the character set determined in Step 4, specify the password requirements. For example, you might require that passwords include at least one uppercase letter, one lowercase letter, one digit, and one special character, and be exactly 8 characters long.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it helps determine how likely it is for a randomly generated password to be guessed correctly. Understanding probability is crucial for assessing the security of password combinations and ensuring that the chance of unauthorized access remains low.

Combinatorics

Combinatorics is a branch of mathematics dealing with combinations and permutations of objects. In the context of password creation, it helps calculate the total number of possible passwords based on the allowed characters and their arrangement. This calculation is essential for determining whether the number of potential passwords meets the security guidelines set by the bank.

Character Sets

Character sets refer to the groups of characters that can be used to create passwords, such as lowercase letters, uppercase letters, numbers, and special symbols. The choice of character sets directly impacts the total number of possible passwords. By expanding the character set, the bank can significantly increase the complexity and security of the passwords, making them harder to guess.