Introduction

If you’ve ever been asked to create a password for an account, you know how hard it can be to remember which letter or number goes where. But if you’re serious about securing your online funds and protecting yourself from hackers, you need to understand some basic concepts in the field of mathematics. This article will explain four critical mathematical concepts related to password security: entropy, randomness, collision resistance, and vital stretching.

Password entropy is the most basic mathematical concept to understand regarding password security.

Password entropy is the most basic mathematical concept to understand regarding password security. It’s a measure of password strength, and you’ll see it everywhere, from security experts’ blogs to your browser’s password manager.

Password entropy is “the number of bits of information in a password.” If you have a four-character alphanumeric password with no special characters or spaces (like “abc123”), its entropy is 4 x 8 = 32 bits. But what does this mean? How can we use it?

Understanding this concept is so important because it helps us quantify how secure our passwords are–and thus, how much effort we should put into protecting them with backup systems and other safeguards.

The critical space is another crucial concept in understanding how cryptographic algorithms and security protocols work.

The critical space is another crucial concept in understanding how cryptographic algorithms and security protocols work. The critical area is the set of all possible keys that can be used with a given algorithm, and it depends on both the algorithm and its length. For example, if you were using an encryption algorithm with a 128-bit key (a standard size), then your total possible number of keys would be 2^128 – 1: that’s about 3 billion billion billion billion trillion trillion trillion trillion trillion trillion trillion times more than our current population of 7 billion people!

The larger your crucial size, the more secure your system will be because there are many more possible combinations for attackers to try before they find one that works. It also means less work for them when they do finally see one; instead of having to brute force every single possibility out there until they get lucky enough with one combination (and then start over again when we update our security measures), all they need now is just one — which makes things easier for everyone involved!

Randomness is an essential part of password entropy, and one-way functions are a way to generate truly random numbers.

One-way functions are a type of algorithm that is used to generate truly random numbers. They can be used to create password entropy, an essential part of password security.

One-way hashes, also known as one-way functions, are used in cryptography to generate random numbers. The SHA256 algorithm was designed specifically for use with Bitcoin mining!

Two-factor authentication uses multiple pieces of information to verify user account ownership.

Two-factor authentication (also known as 2FA) is a security method that requires users to provide two pieces of information to prove they are who they are. The two factors can be something you know (like a password), something you have (like a token or physical device), or something you are (like your fingerprint). For someone else to access your account, they would need both pieces of this information.

Two-factor authentication is commonly used by companies like Google and Facebook, as well as banks and other financial institutions. It’s also available for individual accounts on websites such as Dropbox and Amazon Prime Video–you need to turn it on in your account settings before using it for those apps on iOS devices like iPhones or iPads.*

A rainbow table is a specialized table that can crack passwords quickly.

A rainbow table is a specialized table that can crack passwords quickly. Rainbow tables are not a security measure, but they help attackers with access to them and a list of usernames and passwords. Rainbow tables can be used by anyone who has access to the table, including you!

Rainbow tables are massive databases of common passwords, organized into rows based on their first letter (A through Z) or digit (0 through 9). When an attacker finds out your username/email address pair from somewhere else (like LinkedIn), he’ll use it as input data for his rainbow table lookup tool, which will give him all possible combinations of letters/digits from A-Z or 0-9 that match with what he knows about your account–and then try each one until he gets lucky with one that matches.*

Salting is a technique for increasing the complexity of password hashes by adding random bits before hashing them.

Salting is a technique for increasing the complexity of password hashes by adding random bits before hashing them. This prevents attackers from using rainbow tables to crack passwords, as they must first retrieve and then decrypt all possible salts before attempting to break each hash individually. The salt should be long enough that it would be impractical for an attacker to store all possible values in memory (and thus use brute force attacks) but short enough that it only adds a little additional time or memory usage during authentication requests.

The best practice for salting is:

• Use a unique salt per user account; even if two users share a password, their hashes will still be different because of their individual salts.* Make sure your application stores these salts in its database so they can easily be retrieved when needed again later on down the line when authentication attempts occur.*

Critical stretching increases the time for automated attacks like dictionary attacks or brute force spells to find the correct answer by making each guess take longer.

To understand how key stretching works, let’s look at an example. Let’s say that you have a password of “password.” In this case, the attacker will try to guess your password by guessing every word in its dictionary and seeing if it matches. However, if we add some steps to the algorithm (making each step take longer), their automated attack will take longer than before–and thus be less effective.

How does critical stretching work?

Collision resistance means that two different inputs cannot produce the same output value when running an algorithm repeatedly on them – even if they’re close enough together.

Collision resistance means that two different inputs cannot produce the same output value when running an algorithm repeatedly on them – even if they’re close enough together.

This property is essential for password security because it makes it harder for attackers to guess the correct password.

The problem with a password-based system is that it’s only as secure as the password. If someone guesses your password, they can get into your account. This is why many websites now use two-factor authentication (2FA). Two-factor authentication requires you to enter a password and an additional code provided by another device – usually via text message or an app on your phone.

Conclusion

We hope this article has given you a better understanding of the mathematical concepts behind password security. When someone asks you what entropy is or how two-factor authentication works, refer them here!