1. The Hard Size Limit of RSA

A common beginner mistake when implementing cryptography is attempting to encrypt an entire 50MB PDF document or a 1GB database backup directly with an RSA public key. The result? An immediate exception: Data too long for key size.

For a standard 2048-bit RSA key using RSA-OAEP with SHA-256, the absolute maximum message length you can encrypt in a single block is exactly 190 bytes.

2. The Mathematical Limit: Modulus & Padding

RSA operates on numbers smaller than its modulus ( n ):

• A 2048-bit key has a 256-byte modulus.
• To prevent mathematical chosen-ciphertext attacks, RSA requires secure padding (OAEP).
• OAEP with SHA-256 consumes ( 2 imes 32 + 2 = 66 ) bytes for hash overhead.
• ( 256 - 66 = 190 ) bytes of maximum plaintext payload.

3. How Hybrid Encryption Solves the Problem

To encrypt arbitrarily large files without size limits and with maximum speed, modern systems use Hybrid Encryption:

1. Generate a fast, single-use random AES-256-GCM symmetric key (32 bytes).
2. Encrypt the 500MB file using AES-256-GCM (which processes gigabytes per second with zero payload length limitations).
3. Encrypt the tiny 32-byte AES key using the recipient's RSA Public Key (easily fits within the 190-byte limit).
4. Package the encrypted AES key together with the encrypted file payload.

4. How HTTPS Secures Your Web Browser

Every time you connect to DailyTool or your online bank, your browser performs this exact dance: Asymmetric cryptography (RSA or ECDHE) is used for the first fraction of a second to verify identity and securely exchange a symmetric key. Once agreed upon, high-speed symmetric AES-GCM takes over to encrypt every video frame, picture, and webpage.