Telegram Cloud Storage: Data Encryption

End-to-End Encryption
- Used in Secret Chats.
- Messages are encrypted on the sender's device and decrypted on the recipient's device.
- No intermediary can access the content.
Cloud Chats Encryption
- Regular chats in Telegram (non-Secret Chats) are not end-to-end encrypted.
- These messages are encrypted in transit and stored in the cloud.
Encryption Standards
- Telegram uses its own encryption protocol called MTProto.
- MTProto is designed for speed and security, incorporating multiple encryption layers.
Data Security Measures
- Telegram employs AES (Advanced Encryption Standard) with 256-bit keys for message encryption.
- The Diffie-Hellman key exchange protocol is used for secure key generation.
User Control
- Users can choose between regular chats (cloud storage) and Secret Chats (end-to-end encryption).
- Secret Chats are device-specific and do not utilize Telegram's cloud storage.
Privacy Features
- Self-destruct timers for messages in Secret Chats.
- Users can delete messages from both ends in Secret Chats.
Data Storage
- Regular messages, media, and files are stored in Telegram’s cloud.
- Users can access their data from multiple devices after logging in.
Risks and Considerations
- While cloud storage is convenient, it may expose messages to potential server-side vulnerabilities.
- Users should be aware of the differences in security between cloud chats and Secret Chats.
Compliance and Data Retention
- Telegram’s privacy policy emphasizes minimal data retention.
- Users' messages in the cloud are typically stored until deleted or until the account is inactive for an extended period.

Data Encryption in Telegram

End-to-End Encryption
- Implemented exclusively in Secret Chats for enhanced security.
- Messages encrypted on the sender's device, decrypted solely on the recipient's device.
- Content remains inaccessible to intermediaries.
Cloud Chats Encryption
- Standard chats are not protected by end-to-end encryption.
- These messages are encrypted during transit and stored in Telegram’s cloud system.
Encryption Standards
- Utilizes the MTProto encryption protocol developed by Telegram.
- MTProto emphasizes both speed and security, featuring multiple encryption layers for added protection.
Data Security Measures
- Employs the Advanced Encryption Standard (AES) with 256-bit keys to encrypt messages.
- Incorporates the Diffie-Hellman key exchange protocol for secure encryption key generation.
User Control
- Users can opt for either regular cloud storage chats or Secret Chats for end-to-end encryption.
- Secret Chats are device-specific, preventing access to Telegram’s cloud storage.
Privacy Features
- Self-destruct timers can be set for messages in Secret Chats.
- Users have the ability to delete messages from both ends in Secret Chats, enhancing privacy.
Data Storage
- Regular messages, media, and files stored in Telegram’s cloud for user convenience.
- Provides access to data across multiple devices upon logging in.
Risks and Considerations
- While cloud storage offers convenience, it presents potential vulnerabilities linked to server-side security.
- Awareness of security differences is crucial between regular cloud chats and Secret Chats for users.
Compliance and Data Retention
- Telegram’s privacy policy focuses on minimizing data retention.
- Cloud-stored messages remain until either deleted by the user or if the account remains inactive for a significant duration.

Definition

Algebra involves symbols and rules to solve equations and understand relationships in mathematics.

Key Concepts

Variables and Constants
- Variables are symbols (usually letters like x, y) representing unknown values.
- Constants are fixed values that remain unchanged, such as 3, -7, or π.
Expressions
- Combinations of variables, constants, and operators; can be simplified or evaluated (e.g., 2x + 5).
Equations
- Statements where two expressions are claimed to be equal (e.g., 2x + 5 = 11); solvable for variables.
Inequalities
- Indicate one expression is greater or less than another (e.g., x + 2 > 5); solutions define a range of values.
Functions
- Relations that assign each input exactly one output (e.g., f(x) = 2x + 3); can be classified as linear, quadratic, polynomial, etc.

Operations

Addition/Subtraction of Polynomials
- Combine like terms, e.g., (3x² + 2x) + (4x² + 5) = 7x² + 2x + 5.
Multiplication of Polynomials
- Use the distributive property, e.g., (x + 2)(x + 3) = x² + 5x + 6.
Factoring
- Rewrite expressions as products of factors, e.g., x² - 9 = (x - 3)(x + 3).

Types of Equations

Linear Equations
- Standard form: Ax + B = C; graphs as straight lines.
Quadratic Equations
- Standard form: Ax² + Bx + C = 0; solvable by factoring, completing the square, or quadratic formula.
Exponential Equations
- Standard form: a^x = b; features variables as exponents.
Logarithmic Equations
- Standard form: log_a(b) = x; these equations invert exponential forms.

Key Techniques

Solving Systems of Equations
- Employ methods such as graphing, substitution, and elimination for multi-variable equations.
Using the Quadratic Formula
- Formula x = (-B ± √(B² - 4AC)) / (2A) to solve Ax² + Bx + C = 0.
Completing the Square
- Rearranging a quadratic equation to ensure it fits the format (x - p)² = q.

Graphing

Familiarity with the coordinate plane (x-y axes) is essential.
Identify crucial elements like intercepts, slope (for linear functions), and vertex (for quadratic functions).

Applications

Algebra is utilized in diverse fields such as physics, engineering, economics, and statistics.
It serves as a foundation for problem-solving and modeling real-world situations.