**The Key Points Discussed in This Chapter is as Follows:**

- A
**prime number** is an integer that can only be divided without remainder by positive and negative values of itself and 1. Prime numbers play a critical role both in number theory and in cryptography.
- Two theorems that play important roles in public-key cryptography are
**Fermat’s theorem** and **Euler’s theorem**.
- Asymmetric encryption is a form of cryptosystem in which encryption and decryption are performed using the different keys—one a
**public key** and one a **private key.** It is also known as public-key encryption.
- Asymmetric encryption transforms plaintext into ciphertext using a one of two keys and an encryption algorithm. Using the paired key and a decryp-tion algorithm, the plaintext is recovered from the ciphertext.
- Asymmetric encryption can be used for
**confidentiality, authentication,or both**.
- The most widely used public-key cryptosystem is RSA. The difficulty of attacking RSA is based on the difficulty of finding the prime factors of a composite number

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