RSA Signature performance

When I run the following code on my machine using a key generated from KeyPairGenerator I get around 31 milliseconds.

import java.security.KeyPairGenerator;
import java.security.PrivateKey;
import java.security.Signature;

public class Crypto {

    public static void main(String[] args){
        final String PROVIDER_NAME = "SunRsaSign";
        final String SIGNATURE_ALGORITHM_NAME = "SHA1withRSA";

        try {
            byte[] bytesToSign = "TEST".getBytes();

            KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
            kpg.initialize(4096);
            PrivateKey privateKey = kpg.genKeyPair().getPrivate();

            Signature rsaSign = Signature.getInstance(SIGNATURE_ALGORITHM_NAME, PROVIDER_NAME);
            rsaSign.initSign(privateKey);
            rsaSign.update(bytesToSign);
            long start = System.currentTimeMillis();
            rsaSign.sign();
            long end = System.currentTimeMillis();
            System.out.println(end-start);
        } catch (Exception e) {
            System.out.print(e.toString());
        }
    }
}

However when I run the following code using a KeySpec I get 328 milliseconds.

import java.security.PrivateKey;
import java.security.Signature;
import java.security.spec.RSAPrivateKeySpec;
import java.math.BigInteger;
import java.security.KeyFactory;

public class Crypto {

    public static void main(String[] args){
        final String PROVIDER_NAME = "SunRsaSign";
        final String SIGNATURE_ALGORITHM_NAME = "SHA1withRSA";

        try {
            byte[] bytesToSign = "TEST".getBytes();
            BigInteger n = new BigInteger("597587226679466141124693638138125299950880068828254488555957644249281492201151725373904252242430008473810144110612094128024063578707460431712823842235991465354560187737393879297229743260146710677226117056578671416566287740136599124897385892941425870120428978181352342388371378999775548901123514895501669300647274487518472636693700503555192766931023284431580962701846364239256545481706926550688122371316117197948006216002474377830241838340355035516984862145128976925834940027104794937790806573064454303239801464883574025970986374457025729491416244044251160491275299917049444537591955178699287053624986215597863163779443074749369005932415039400383140953067480491452272333580572932227865814237470887152932057448674357000903536202101025652676188117995296037813643835836244002726526603485151069928993258393018157442284327764913186610742443124225235294325533610789139086190718423569760575759726606015005217606970790315033865732422275945142140911185854993011517078112760033989491003743777970147736937449399489701150359137542465776194778304313471540815791992057968970251791757741455255986669925249397189780062920148823884414124748384210776408299989145375246596521057664660283677204196251491406330933981965200587649372807527331850099013257897");
            BigInteger d = new BigInteger("4595632425140774449957208807568475077822353093511150376614777190009275250154576339906430613701950413824256719589674465424479729674360438494030291537405430497866828426990044023464665617942749014775195126363972265955863237881331857713173970276980616118233916795144751523013552268426795194259216190965909964257232194664224944823437524662279584883855466917214959567904093375903463675828620336322181571862357493748047593464230085088216456147268549642195406724768375183035854704573917278005501724412537726304726489438047535118930941799690876415821196987935099026314948062288370234324829415598279455498832614441633322162210880362668225335174174254925331410135687428608342277292478555925249301141034109001860652817038518162426120218303741256538573731958165872030034502507324328196680907973846309670995934916630480379153721692432821724120534768708296475728203534373370163067285835785480486327238089504618803125757317740030708309519453831883949072027340057586476480382666523830109818313596509315892976057010736043565833515535051861285267156916096112209738518894413968197350931670388334238393788649720192047074674730303813328065901384401315536207657662831106566630368281509079558729496437617044484467087495574832015312198202479584112626996225");

            RSAPrivateKeySpec rsaPrivateKeySpec = new RSAPrivateKeySpec(n,d);
            KeyFactory keyFactory = KeyFactory.getInstance("RSA");
            PrivateKey privateKey = keyFactory.generatePrivate(rsaPrivateKeySpec);

            Signature rsaSign = Signature.getInstance(SIGNATURE_ALGORITHM_NAME, PROVIDER_NAME);
            rsaSign.initSign(privateKey);
            rsaSign.update(bytesToSign);
            long start = System.currentTimeMillis();
            rsaSign.sign();
            long end = System.currentTimeMillis();
            System.out.println(end-start);
        } catch (Exception e) {
            System.out.print(e.toString());
        }
    }
}

I can't figure out why the second option is so much slower. Any ideas?

Benchmarking is a science unto itself, especially with an environment as complex as the JVM. However, in your case, one significant difference between your two examples is that in the KeyPairGenerator case the private key has all of its optional components, permitting chinese remainder theorem (CRT) speedups, whereas in the second case using the RSAPrivateKeySpec you have only the minimal private key which admits no such speedup. You might try a third case using RSAPrivateCrtKeySpec to compare with.

I might expect this difference to account for a factor of 2-4, not a factor of 10 however.