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Cryptography is the practice of protecting information by transforming it into an unreadable format to prevent unauthorized access. It relies on mathematical principles, such as number theory and algebra, to create secure encryption systems. The text explores the evolution of cryptography, its applications in modern technology, and the challenges it faces, including the threat of quantum computing. It also distinguishes between symmetric and asymmetric cryptography, highlighting their roles in digital security.

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## Definition and Importance

### Encryption

Encryption is the process of converting information into an unreadable format to protect it from unauthorized access

### Decryption

Decryption is the process of converting encrypted information back to its original form

### Cryptographic Keys

Cryptographic keys are secret parameters that allow only intended recipients to decrypt and access information

## Mathematical Foundations

### Number Theory

Number theory is a branch of mathematics that provides the theoretical basis for secure encryption systems

### Algebra

Algebra is used in the design of cryptographic algorithms

### Computational Complexity

Computational complexity is integral to the creation of secure cryptographic systems

## Applications

### Internet Security

Cryptography is essential for securing digital communications and protecting data integrity on the internet

### Mobile Devices and Financial Transactions

Cryptography is integral to the security of mobile devices and financial transactions

### Wireless Networks

Cryptography is used to secure wireless network communications

## Types of Cryptography

### Symmetric Cryptography

Symmetric cryptography uses the same key for both encryption and decryption

### Asymmetric Cryptography

Asymmetric cryptography uses a public key for encryption and a private key for decryption

### Hybrid Cryptography

Hybrid cryptography combines the speed of symmetric encryption with the secure key distribution of asymmetric encryption

## Advancements and Challenges

### Computational Problems

Cryptographic strength relies on computational problems that are difficult to solve without a key

### Post-Quantum Cryptography

Post-quantum cryptography is being developed to protect against emerging threats from quantum computing

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