RSA Encryption Maximum Number of Bytes

The maximum number of bytes you can encrypt using RSA depends on the key size and the padding scheme.

1. Key Size

The RSA key size determines the maximum size of the plaintext that can be encrypted. The larger the key size (e.g., 1024, 2048, 4096 bits), the larger the block of plaintext that can be encrypted. However, the actual size of the plaintext is limited by the key size minus the padding overhead.

• Key size in bytes =  key size in bits /  8.
  • For a 2048-bit key, the modulus size is  2048 / 8 = 256  bytes.
  • For a 1024-bit key, the modulus size is  1024 / 8 = 128  bytes.

2. Padding Schemes

RSA does not encrypt raw data directly but applies a padding scheme to ensure security. Padding reduces the maximum size of the plaintext block.

PKCS#1 v1.5 Padding

• Padding Overhead: At least 11 bytes.
• Maximum Plaintext Size: Max Size  =  Key Size in Bytes  – 11
• For a 2048-bit key:  256 – 11 = 245  bytes.
• For a 1024-bit key:  128 – 11 = 117  bytes.

OAEP Padding

• Padding Overhead: Varies depending on the hash function used.
  • Commonly uses SHA-1 or SHA-256 in the padding process.
• Approximate Padding Overhead: Hash size (e.g., 20 bytes for SHA-1) + 2.
• Maximum Plaintext Size: Max Size  =  Key Size in Bytes – 2 × Hash Size – 2
• For a 2048-bit key and SHA-1: 256 – 2 × 20 – 2 = 214 bytes
• For a 2048-bit key and SHA-256: 256 – 2 × 32 – 2 = 190 bytes

Example

• Key Size: 2048 bits (256 bytes modulus).
• PKCS#1 v1.5: Max plaintext size =  256 – 11 = 245  bytes.
• OAEP with SHA-1: Max plaintext size =   256 – 42 = 214   bytes.
• OAEP with SHA-256: Max plaintext size =  256 – 66 = 190  bytes.

Note on Best Practices

1. Encrypting Large Data:
   • RSA is not designed for encrypting large messages. Instead, use RSA to encrypt a small symmetric key (e.g., AES), and then use AES for the actual message.
2. Padding Matters for Security:
   • Always use padding (e.g., OAEP) for encryption to prevent vulnerabilities.

By considering key size and padding, you can determine the maximum data you can encrypt with RSA.