RSA???????

1
RSA???????

• ????????,?????????RSA???,???????
• ???????p,q(??512bit)
• ??????????(?????????).
• ??npq
• ??
• ????e,?
• ?????? n,e
• ?????? d ( )

2
RSA???????

• KeyPairGenerator
• The KeyPairGenerator class is an engine class
  used to generate pairs of public and private keys
  
• Creating the Key Pair Generator
• try
• //??KeyPairGenerator??
• KeyPairGenerator keyGenKeyPairGenerator.getIns
  tance("RSA")
• System.out.println("Key Test program is ok")
• catch(NoSuchAlgorithmException e)
• System.out.println("Error "e.getMessage())

3
RSA???????

• Initializing the Key Pair Generator
• SecureRandom random SecureRandom.getInstance(S
  HA1PRNG, SUN) random.setSeed(userSeed)
  //????????,???????
• keyGen.initialize(1024, random) //???

4
RSA???????

• The KeyPair Class
• KeyPair???????????.
• KeyPair pair keyGen.generateKeyPair()

5
RSA???????

• The PublicKey Class
• ???????????(n,e)

6
RSA???????

• The PrivateKey Class
• ???????????(n,d,p,q)

7
RSA?????????

• ??????????????????,??????????????(?10???)?
• KeyFactory
• ???????????????????????.
• //??KeyFactory ??????????
• RSAPublicKeySpec
• RSAPrivateKeySpec

8
????RSA??????

• // ??KeyPairGenerator??
• KeyPairGenerator keyGen KeyPairGenerator.getInst
  ance("RSA")
• // ???????
• SecureRandom random SecureRandom.getInstance("SH
  A1PRNG", "SUN")
• // ???keyGen?????1024???????
• keyGen.initialize(1024, random)
• // ?????
• KeyPair pair keyGen.generateKeyPair()
• // ???????????
• PublicKey puKey pair.getPublic()
• PrivateKey prKey pair.getPrivate()
• //????????
• System.out.println(puKey.toString())
• System.out.println(prKey.toString())

9
Java???????API

• Sun RSA public key, 1024 bits
• modulus( n) 14533458076675335296827162414322
  76429031800268580705381780938426546551318964885088
  59021170467602039725331815700222176862989556902870
  84482393294066468420852304195235606106267419032473
  38842105945430257490034420087727308742868108451005
  51163211606567048423518752061867186661617099735966
  587084128589872797083364747
• public exponent( e) 65537
• Sun RSA private CRT(??????) key, 1024 bits
• modulus(n ) 1453345807667533529682716
  24143227642903180026858070538178093842654655131896
  48850885902117046760203972533181570022217686298955
  69028708448239329406646842085230419523560610626741
  90324733884210594543025749003442008772730874286810
  84510055116321160656704842351875206186718666161709
  9735966587084128589872797083364747
• public exponent( e ) 65537
• private exponent( d ) 123650928314896931628818
  18652978058410727398442985115489375977802738781908
  56508959133033468743308685634798161592487962479734
  30327100346926738740536218117730278249237671789995
  77581947427302758151178755242699163508625431533367
  68729876006408930991684033761163675165176902364959
  72293965947291133168132306425021585
• prime p 128361932237935582979273054284
  96631019420276059582307483685094836716895113592759
  86555886052041544399610367440155992619595177767984
  3538568226126094329161913
• prime q 113222493797738064807993294815
  84580801659487779713145666093610874564424578061919
  18369426328690536495749517578643835275222390603246
  5534494985244811289566819
• prime exponent p 914811597881693894168623303857
  04585962748193221372787225609918754068086740402678
  64575090381418803770786186738386857391005381389023
  790468073571745545755305
• prime exponent q 684497066811141777279628657689
  33987814906169846043386855714322666755735875519370
  73365433353532774844453001508071379135387084866751
  864476949057550209865067
• crt coefficient 122151313758391817686507891258
  52251387959893277517099645583985397510200970338820
  22847578024232819508295582798491689735541362335865
  4311131059893783646946460

10
??????(???)???

• //??KeyFactory ??????????
• KeyFactory keyFactory
• RSAPublicKeySpec rsaPublicKeySpec
• RSAPrivateKeySpec rsaPrivateKeySpec
• //??KeyFactory??
• keyFactory KeyFactory.getInstance("RSA")
• //??KeySpec??
• rsaPublicKeySpec (RSAPublicKeySpec)keyFactory.ge
  tKeySpec(puKey,RSAPublicKeySpec.class)
• rsaPrivateKeySpec (RSAPrivateKeySpec)keyFactory.g
  etKeySpec(prKey,RSAPrivateKeySpec.class)

11
??????(???)???

• //??RSA????n,e,d
• BigInteger nrsaPublicKeySpec.getModulus()
• BigInteger ersaPublicKeySpec.getPublicExponent()
  
• BigInteger drsaPrivateKeySpec.getPrivateExponent(
  )
• byte array_nn.toByteArray()
• byte array_ee.toByteArray()
• byte array_dd.toByteArray()

12
??????(???)???

• FileOutputStream osnew FileOutputStream("keypair.
  dat")
• BufferedOutputStream bosnew BufferedOutputStream(
  os)
• bos.write(array_n.length)
• bos.write(array_n)
• bos.write(array_e.length)
• bos.write(array_e)
• bos.write(array_d.length)
• bos.write(array_d)
• bos.close()

13
RSA??????????

• //???????
• FileInputStream isnew FileInputStream("keypair.da
  t")
• BufferedInputStream bisnew BufferedInputStream(is
  )
• int rnbis.read()
• byte arr_nnew bytern
• bis.read(arr_n)
• rnbis.read()
• byte arr_enew bytern
• bis.read(arr_e)
• rnbis.read()
• byte arr_dnew bytern
• bis.read(arr_d)
• BigInteger bndnew BigInteger(arr_d)
• ????,????????????

14

• package digitalSignature
• import java.security.
• import java.security.spec.
• import java.math.
• public class TestKeyFactory
• /
• _at_param args
• /
• public static void main(String args)
• // TODO Auto-generated method stub
• KeyFactory keyFactory
• RSAPublicKeySpec rsaPublicKeySpec
• RSAPrivateKeySpec rsaPrivateKeySpec
• PublicKey puKey
• PrivateKey prKey

15

• // ?RSAPublicKeySpec ??
• rsaPublicKeySpec new RSAPublicKeySpec(modulus,
  publicExponent)
• // ?RSAPrivateKeySpec??
• rsaPrivateKeySpec new RSAPrivateKeySpec(modulus,
  privateExponent)
• // ??PublicKey??
• puKey keyFactory.generatePublic(rsaPublicKeySpec
  )
• // ??PrivateKey??
• prKey keyFactory.generatePrivate(rsaPrivateKeySp
  ec)
• System.out.println(puKey.toString())

16

• System.out.println(prKey.toString())
• System.out.println(keyFactory.getProvider().getNam
  e())
• System.out.println("bit count "
  modulus.bitCount())
• System.out.println("bit length "
  modulus.bitLength())
• catch (NoSuchAlgorithmException e)
• System.out.println(e.getMessage())
• catch (InvalidKeySpecException e)
• System.out.println(e.getMessage())

17
SHA???????

• import java.io.
• import java.security.
• import tool.Tools
• public class TestSHA
• public static void main(String args)
• try
• byte a new byte512
• int len
• // ????????
• FileInputStream in new FileInputStream("GEF-ALL-
  3.2M3.zip")
• BufferedInputStream read new BufferedInputStream
  (in)

18
SHA???????

• // ??MessageDigest??
• MessageDigest sha MessageDigest.getInstance("SHA
  ")
• while ((len read.read(a, 0, 512)) gt 0)
• sha.update(a, 0, len)
• byte hash sha.digest()
• System.out
• .println("???????" sha.getDigestLength() 8
  " bits")
• System.out.println(Tools.toHexString(hash))
• // ???????
• in.close()

19
SHA???????

• System.out.println(sha.getAlgorithm())
• catch (FileNotFoundException e)
• System.out.println(e.getMessage())
• catch (NoSuchAlgorithmException e)
• System.out.println(e.getMessage())
• catch (IOException e)
• System.out.println(e.getMessage())