BigIntegers and RSA in JavaScript

Demos

• RSA Encryption Demo - simple RSA encryption of a string with a public key
• RSA Cryptography Demo - more complete demo of RSA encryption, decryption, and key generation

Source Code

  x = new BigInteger("abcd1234", 16);
  y = new BigInteger("beef", 16);
  z = x.mod(y);
  alert(z.toString(16));

• jsbn.js - basic BigInteger implementation, just enough for RSA encryption and not much more.
• jsbn2.js - the rest of the library, including most public BigInteger methods.
• rsa.js - implementation of RSA encryption, does not require jsbn2.js.
• rsa2.js - rest of RSA algorithm, including decryption and keygen.
• rng.js - rudimentary entropy collector and RNG interface, requires a PRNG backend to define prng_newstate().
• prng4.js - ARC4-based PRNG backend for rng.js, very small.
• base64.js - Base64 encoding and decoding routines.

Interoperability

1. Generate a new public/private keypair:

   $ openssl genrsa -out key.pem
   Generating RSA private key, 512 bit long modulus
   ..++++++++++++
   ..............++++++++++++
   e is 65537 (0x10001)
   $
   

2. Extract the modulus from your key:

   $ openssl rsa -in key.pem -noout -modulus
   Modulus=DA3BB4C40E3C7E76F7DBDD8BF3DF0714CA39D3A0F7F9D7C2E4FEDF8C7B28C2875F7EB98950B22AE82D539C1ABC1AB550BA0B2D52E3EF7BDFB78A5E817D74BBDB
   $
   

3. Go to the RSA Encryption demo and paste the modulus value into the "Modulus (hex)" field at the bottom.
4. Make sure the value in the "Public exponent" field is "10001", or whatever value your public key uses.
5. Type in a short string (e.g. testing) into the "Plaintext (string)" field and click on "encrypt". The result should appear in the "Ciphertext" fields.
6. Copy the base64 version of the ciphertext and paste it as the input of the following command:

   $ openssl base64 -d | openssl rsautl -inkey key.pem -decrypt
   1JW24UMKntVhmmDilAYC1AjLxgiWHBzTzZsCVAejLjVri92abLHkSyLisVyAdYVr
   fiS7FchtI9vupe9JF/m3Kg==
   

   Hit ctrl-D or whatever your OS uses for end-of-file. Your original plaintext should appear:

   testing$
   

Performance

On similar hardware, running IE6:

Key type	Encryption time	Decryption time
RSA 512-bit (e=3)	50ms	0.7s
RSA 512-bit (e=F4)	60ms	0.7s
RSA 1024-bit (e=3)	60ms	4.3s
RSA 1024-bit (e=F4)	220ms	4.3s

Timing measurememnts, especially under IE, appear to have limited precision for faster operations.

Licensing