Public key encryption, RSA

1
Lecture 5

• Public key encryption, RSA
• Keys, Keytool, Keystore
• OpenSSL
• JAR signing

2
Asymmetric encryption

• A keypair
• java.security.PublicKey
• java.security.PrivateKey
• One for encryption, one for decryption

3
RSA

• Rivest, Shamir, Adleman
• Based on the (assumed) difficulty of factoring
  large integers
• java.security.interfaces.RSAPrivateKey
• java.security.interfaces.RSAPublicKey
• java.security.spec.RSAPrivateKeySpec
• java.security.spec.RSAPublicKeySpec
• Example BaseRSAExmple.java

4
KeyFactory

• java.security.KeyFactory
• getInstance()
• generatePublic()
• generatePrivate()
• getKeySpec()
• translateKey()

5
RSAPublicKeySpec

• RSAPublicKeySpec (RSAPrivateKeySpec) contains
  information needed to generate a public (private)
  key
• Returns a RSAPublicKey (RSAPrivateKey)
• BigInteger getModulus()
• BigInteger getPublicExponent()
• BigInteger getPrivateExponent() in
  RSAPrivateKeySpec
• You can pass this to KeyFactory.generatePublic()
• KeyFactory.generatePrivate() for private key

6
Random RSA keys

• SecureRandom random new SecureRandom()
• KeyPairGenerator generator KeyPairGenerator.getI
  nstance("RSA", "BC")
• generator.initialize(256, random)
• KeyPair pair generator.generateKeyPair()
• Key pubKey pair.getPublic()
• Key privKey pair.getPrivate()
• ExampleRandomRSAKeyExample.java

7
KeyPairGenerator

• static  KeyPairGenerator getInstance(String algori
  thm, Provider provider)
• static KeyPairGenerator getInstance(String algorit
  hm)
• void initialize(AlgorithmParameterSpec params)
• void initialize(AlgorithmParameterSpec params,
  SecureRandom random)
• AlgorithmParameterSpec gives you more control
  over the generated keypair, which is sometimes
  important

8
KeyPairGenerator

• void initialize(int keysize)
• void initialize(int keysize, SecureRandom random)
• KeyPair generateKeyPair()
• KeyPair genKeyPair()

9
RSAKeyGenParameterSpec

• Allows you to control the key generation
• Implements the AlgorithmParameterSpec interface
• RSAKeyGenParameterSpec(int keysize,
  BigInteger publicExponent)
• static BigIntegerF0           The
  public-exponent value F0 3.
• static BigIntegerF4           The public
  exponent-value F4 65537.

10
RSA padding mechanisms

• RSA handles data as BigInteger
• Hence leading zeros tend to disappear
• Example RandomKeyExample.java with added zeros
• Another problem, what if the input is small and
  the public exponent is small?
• A padding scheme is needed

11
PKCS1 v1.5 padding

• Type 1 (when using private key)
• M 0x000x01F0x00M, where F 0xFF, 0xFF
• Type 2 (when using public key)
• M 0x000x02R0x00M, where R is a string of
  random bytes
• Example PKCS1PaddedRSAExample.java
• Cipher cipher Cipher.getInstance("RSA/NONE/PKCS1
  Padding", "BC")

12
OAEP

• Optimal Asymmetric Encryption Padding
• RSAES-OAEP
• Provably secure under the random oracle model
• M1 Mask((H(P)PS0x01M),S)
• M2 Mask(S, M1)
• Msg 0x00M2M1
• where H is a hash function, P is a parameter
  string, S is a random seed, M is the message and
  PS is a padding of zeros. Msg is what is sent.

13
OAEP

• Example OAEPPaddedRSAExample.java
• Cipher cipher Cipher.getInstance("RSA/NONE/OAEP
  WithSHA1AndMGF1Padding", "BC")

14
Handling keys in Java

• Random
• Your own files
• Keystore
• Certificates

15
Keystores

• For storing asymmetric keys
• Store
• Delete
• List
• Export/import
• Make certificate requests
• Etc.

16
Keytool

• Tool for
• Creating
• Storing
• Importing/Exporting
• Managing
• Keys

17
Keytool

• usage keytool command options
• keytool -genkey -keyalg rsa -alias TOHclient
  -keystore client.keystore
• keytool list keystore client.keystore

18
Keystore example