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Essential Concepts

• Cryptography involves using techniques to obscure a message so that unauthorized individuals cannot read it. It consists of two main steps: encryption and decryption.
  • Encryption is the process of converting plain text or data into an encoded format that can only be read by authorized parties who possess the appropriate decryption key.
  • Decryption is the process of converting the encrypted data back into its original, readable form using the appropriate decryption key. Only authorized parties who possess the correct key can decrypt the information and access the original plain text or data.
• A substitution cipher is a type of encryption where each letter in a message is replaced with a different letter or symbol based on a special pattern or rule. It’s kind of like creating a secret code where each letter has a special substitute.
• A brute force attack is a way to crack encryption by trying out all possible keys until the right one is found. It’s like trying every possible combination to unlock a lock.
• A transposition cipher is a type of encryption where the order of letters in a message is changed to make it harder to understand.
• Public key cryptography helps two parties agree on a secret key without others being able to figure it out, using special math and two keys (a public one and a private one) to encrypt and decrypt the information, making sure it’s secure and authentic.
• The modulus refers to the remainder obtained when one number is divided by another. It tells us what is left over after the division.
• RSA is a popular method for keeping messages secure. It uses two special keys: a public key that anyone can use to lock up messages and a private key that only the intended recipient has to unlock them. RSA’s security is based on the difficulty of factoring large numbers.

Glossary

brute force attack

a method for breaking encryption by trying all possible encryption keys

cryptography

using techniques to obscure a message so outsiders cannot read the message

decryption

the process of converting the encrypted data back into its original, readable form using the appropriate decryption key

digital signatures

created by applying a mathematical algorithm to the data using the sender’s private key

encryption

the process of converting plain text or data into an encoded format that can only be read by authorized parties who possess the appropriate decryption key

key pairs

consist of a public key and a private key

modulus

another name for the remainder after division

public key cryptography

a method of securing digital communication by using two mathematically related keys: a public key and a private key

RSA

distributing a public encryption key, which anyone can use to encrypt messages to you, but which can only be decrypted using a separate private key

substitution cipher

a method of encryption that involves replacing each letter in a message with a different letter or symbol according to a predetermined pattern or rule

transposition cipher

where the order of characters are changed to obscure the message

Key Equations

modular exponentiation rule

[latex]\left(a^{b} \bmod n\right)=(a \bmod n)^{b} \bmod n[/latex]

modular exponent power rule

[latex]\left(a^{b} \bmod n\right)^{c} \bmod n=\left(a^{b c} \bmod n\right)=\left(a^{c} \bmod n\right)^{b} \bmod n \nonumber[/latex]