diff --git a/src/main/java/net/schmizz/sshj/transport/KeyExchanger.java b/src/main/java/net/schmizz/sshj/transport/KeyExchanger.java
index cd1694b1..d654799c 100644
--- a/src/main/java/net/schmizz/sshj/transport/KeyExchanger.java
+++ b/src/main/java/net/schmizz/sshj/transport/KeyExchanger.java
@@ -47,6 +47,7 @@ import net.schmizz.sshj.transport.verification.HostKeyVerifier;
 import org.slf4j.Logger;
 import org.slf4j.LoggerFactory;
 
+import java.security.GeneralSecurityException;
 import java.security.PublicKey;
 import java.util.Arrays;
 import java.util.LinkedList;
@@ -228,8 +229,12 @@ final class KeyExchanger
         log.debug("Negotiated algorithms: {}", negotiatedAlgs);
         kex = Factory.Named.Util.create(transport.getConfig().getKeyExchangeFactories(), negotiatedAlgs
                 .getKeyExchangeAlgorithm());
-        kex.init(transport, transport.getServerID().getBytes(), transport.getClientID().getBytes(), buf
-                .getCompactData(), clientProposal.getPacket().getCompactData());
+        try {
+            kex.init(transport, transport.getServerID().getBytes(), transport.getClientID().getBytes(), buf
+                    .getCompactData(), clientProposal.getPacket().getCompactData());
+        } catch (GeneralSecurityException e) {
+            throw new TransportException(DisconnectReason.KEY_EXCHANGE_FAILED, e);
+        }
     }
 
     /**
@@ -347,10 +352,14 @@ final class KeyExchanger
             case FOLLOWUP:
                 ensureKexOngoing();
                 log.info("Received kex followup data");
-                if (kex.next(msg, buf)) {
-                    verifyHost(kex.getHostKey());
-                    sendNewKeys();
-                    expected = Expected.NEWKEYS;
+                try {
+                    if (kex.next(msg, buf)) {
+                        verifyHost(kex.getHostKey());
+                        sendNewKeys();
+                        expected = Expected.NEWKEYS;
+                    }
+                } catch (GeneralSecurityException e) {
+                    throw new TransportException(DisconnectReason.KEY_EXCHANGE_FAILED, e);
                 }
                 break;
 
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/AbstractDHG.java b/src/main/java/net/schmizz/sshj/transport/kex/AbstractDHG.java
index 6f8f4ec2..624e8829 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/AbstractDHG.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/AbstractDHG.java
@@ -51,6 +51,7 @@ import org.slf4j.Logger;
 import org.slf4j.LoggerFactory;
 
 import java.math.BigInteger;
+import java.security.GeneralSecurityException;
 import java.security.PublicKey;
 
 /**
@@ -81,6 +82,10 @@ public abstract class AbstractDHG
         return ByteArrayUtils.copyOf(H);
     }
 
+    public byte[] getK() {
+        return ByteArrayUtils.copyOf(K);
+    }
+
     public Digest getHash() {
         return sha;
     }
@@ -89,12 +94,8 @@ public abstract class AbstractDHG
         return hostKey;
     }
 
-    public byte[] getK() {
-        return ByteArrayUtils.copyOf(K);
-    }
-
     public void init(Transport trans, byte[] V_S, byte[] V_C, byte[] I_S, byte[] I_C)
-            throws TransportException {
+            throws GeneralSecurityException, TransportException {
         this.trans = trans;
         this.V_S = ByteArrayUtils.copyOf(V_S);
         this.V_C = ByteArrayUtils.copyOf(V_C);
@@ -109,7 +110,7 @@ public abstract class AbstractDHG
     }
 
     public boolean next(Message msg, SSHPacket packet)
-            throws TransportException {
+            throws GeneralSecurityException, TransportException {
         if (msg != Message.KEXDH_31)
             throw new TransportException(DisconnectReason.KEY_EXCHANGE_FAILED, "Unexpected packet: " + msg);
 
@@ -139,7 +140,8 @@ public abstract class AbstractDHG
         signature.init(hostKey, null);
         signature.update(H, 0, H.length);
         if (!signature.verify(sig))
-            throw new TransportException(DisconnectReason.KEY_EXCHANGE_FAILED, "KeyExchange signature verification failed");
+            throw new TransportException(DisconnectReason.KEY_EXCHANGE_FAILED,
+                                         "KeyExchange signature verification failed");
         return true;
     }
 
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/DH.java b/src/main/java/net/schmizz/sshj/transport/kex/DH.java
index dcf79b97..ef672acc 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/DH.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/DH.java
@@ -56,17 +56,16 @@ public class DH {
     private BigInteger e; // my public key
     private BigInteger f; // your public key
     private BigInteger K; // shared secret key
-    private final KeyPairGenerator myKpairGen;
-    private final KeyAgreement myKeyAgree;
+    private final KeyPairGenerator generator;
+    private final KeyAgreement agreement;
 
     public DH() {
         try {
-            myKpairGen = SecurityUtils.getKeyPairGenerator("DH");
-            myKeyAgree = SecurityUtils.getKeyAgreement("DH");
+            generator = SecurityUtils.getKeyPairGenerator("DH");
+            agreement = SecurityUtils.getKeyAgreement("DH");
         } catch (GeneralSecurityException e) {
             throw new SSHRuntimeException(e);
         }
-
     }
 
     public void setF(BigInteger f) {
@@ -81,33 +80,25 @@ public class DH {
         this.p = p;
     }
 
-    public byte[] getE() {
+    public byte[] getE()
+            throws GeneralSecurityException {
         if (e == null) {
-            DHParameterSpec dhSkipParamSpec = new DHParameterSpec(p, g);
-            KeyPair myKpair;
-            try {
-                myKpairGen.initialize(dhSkipParamSpec);
-                myKpair = myKpairGen.generateKeyPair();
-                myKeyAgree.init(myKpair.getPrivate());
-            } catch (GeneralSecurityException e) {
-                throw new SSHRuntimeException(e);
-            }
-            e = ((javax.crypto.interfaces.DHPublicKey) myKpair.getPublic()).getY();
+            generator.initialize(new DHParameterSpec(p, g));
+            final KeyPair kp = generator.generateKeyPair();
+            agreement.init(kp.getPrivate());
+            e = ((javax.crypto.interfaces.DHPublicKey) kp.getPublic()).getY();
         }
         return e.toByteArray();
     }
 
-    public byte[] getK() {
+    public byte[] getK()
+            throws GeneralSecurityException {
         if (K == null) {
-            try {
-                KeyFactory myKeyFac = SecurityUtils.getKeyFactory("DH");
-                DHPublicKeySpec keySpec = new DHPublicKeySpec(f, p, g);
-                PublicKey yourPubKey = myKeyFac.generatePublic(keySpec);
-                myKeyAgree.doPhase(yourPubKey, true);
-            } catch (GeneralSecurityException e) {
-                throw new SSHRuntimeException(e);
-            }
-            K = new BigInteger(myKeyAgree.generateSecret());
+            final KeyFactory keyFactory = SecurityUtils.getKeyFactory("DH");
+            final DHPublicKeySpec keySpec = new DHPublicKeySpec(f, p, g);
+            final PublicKey yourPubKey = keyFactory.generatePublic(keySpec);
+            agreement.doPhase(yourPubKey, true);
+            K = new BigInteger(agreement.generateSecret());
         }
         return K.toByteArray();
     }
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/DHG1.java b/src/main/java/net/schmizz/sshj/transport/kex/DHG1.java
index 1bf61a05..2336fd87 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/DHG1.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/DHG1.java
@@ -59,8 +59,8 @@ public class DHG1
 
     @Override
     protected void initDH(DH dh) {
-        dh.setG(DHGroupData.getG());
-        dh.setP(DHGroupData.getP1());
+        dh.setG(DHGroupData.G);
+        dh.setP(DHGroupData.P1);
     }
 
 }
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/DHG14.java b/src/main/java/net/schmizz/sshj/transport/kex/DHG14.java
index 2b3ef47c..cb3694d3 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/DHG14.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/DHG14.java
@@ -60,8 +60,8 @@ public class DHG14
 
     @Override
     protected void initDH(DH dh) {
-        dh.setG(DHGroupData.getG());
-        dh.setP(DHGroupData.getP14());
+        dh.setG(DHGroupData.G);
+        dh.setP(DHGroupData.P14);
     }
 
 }
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/DHGroupData.java b/src/main/java/net/schmizz/sshj/transport/kex/DHGroupData.java
index 1dc74233..46dae607 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/DHGroupData.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/DHGroupData.java
@@ -40,74 +40,23 @@ import java.math.BigInteger;
 /** Simple class holding the data for DH group key exchanges. */
 public final class DHGroupData {
 
-    private static final BigInteger G = new BigInteger(new byte[]{2});
+    public static final BigInteger G =
+            new BigInteger("2");
 
-    private static final BigInteger P1 = new BigInteger(new byte[]{
-            (byte) 0x00, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF,
-            (byte) 0xFF, (byte) 0xC9, (byte) 0x0F, (byte) 0xDA, (byte) 0xA2, (byte) 0x21, (byte) 0x68, (byte) 0xC2,
-            (byte) 0x34, (byte) 0xC4, (byte) 0xC6, (byte) 0x62, (byte) 0x8B, (byte) 0x80, (byte) 0xDC, (byte) 0x1C,
-            (byte) 0xD1, (byte) 0x29, (byte) 0x02, (byte) 0x4E, (byte) 0x08, (byte) 0x8A, (byte) 0x67, (byte) 0xCC,
-            (byte) 0x74, (byte) 0x02, (byte) 0x0B, (byte) 0xBE, (byte) 0xA6, (byte) 0x3B, (byte) 0x13, (byte) 0x9B,
-            (byte) 0x22, (byte) 0x51, (byte) 0x4A, (byte) 0x08, (byte) 0x79, (byte) 0x8E, (byte) 0x34, (byte) 0x04,
-            (byte) 0xDD, (byte) 0xEF, (byte) 0x95, (byte) 0x19, (byte) 0xB3, (byte) 0xCD, (byte) 0x3A, (byte) 0x43,
-            (byte) 0x1B, (byte) 0x30, (byte) 0x2B, (byte) 0x0A, (byte) 0x6D, (byte) 0xF2, (byte) 0x5F, (byte) 0x14,
-            (byte) 0x37, (byte) 0x4F, (byte) 0xE1, (byte) 0x35, (byte) 0x6D, (byte) 0x6D, (byte) 0x51, (byte) 0xC2,
-            (byte) 0x45, (byte) 0xE4, (byte) 0x85, (byte) 0xB5, (byte) 0x76, (byte) 0x62, (byte) 0x5E, (byte) 0x7E,
-            (byte) 0xC6, (byte) 0xF4, (byte) 0x4C, (byte) 0x42, (byte) 0xE9, (byte) 0xA6, (byte) 0x37, (byte) 0xED,
-            (byte) 0x6B, (byte) 0x0B, (byte) 0xFF, (byte) 0x5C, (byte) 0xB6, (byte) 0xF4, (byte) 0x06, (byte) 0xB7,
-            (byte) 0xED, (byte) 0xEE, (byte) 0x38, (byte) 0x6B, (byte) 0xFB, (byte) 0x5A, (byte) 0x89, (byte) 0x9F,
-            (byte) 0xA5, (byte) 0xAE, (byte) 0x9F, (byte) 0x24, (byte) 0x11, (byte) 0x7C, (byte) 0x4B, (byte) 0x1F,
-            (byte) 0xE6, (byte) 0x49, (byte) 0x28, (byte) 0x66, (byte) 0x51, (byte) 0xEC, (byte) 0xE6, (byte) 0x53,
-            (byte) 0x81, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF,
-            (byte) 0xFF
-    });
+    public static final BigInteger P1 =
+            new BigInteger("1797693134862315907708391567937874531978602960487560117064444236841971802161585193" +
+                           "6894783379586492554150218056548598050364644054819923910005079287700335581663922955" +
+                           "3136239076508735759914822574862575007425302077447712589550957937778424442426617334" +
+                           "727629299387668709205606050270810842907692932019128194467627007");
 
-    private static final BigInteger P14 = new BigInteger(new byte[]{
-            (byte) 0x00, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF,
-            (byte) 0xFF, (byte) 0xC9, (byte) 0x0F, (byte) 0xDA, (byte) 0xA2, (byte) 0x21, (byte) 0x68, (byte) 0xC2,
-            (byte) 0x34, (byte) 0xC4, (byte) 0xC6, (byte) 0x62, (byte) 0x8B, (byte) 0x80, (byte) 0xDC, (byte) 0x1C,
-            (byte) 0xD1, (byte) 0x29, (byte) 0x02, (byte) 0x4E, (byte) 0x08, (byte) 0x8A, (byte) 0x67, (byte) 0xCC,
-            (byte) 0x74, (byte) 0x02, (byte) 0x0B, (byte) 0xBE, (byte) 0xA6, (byte) 0x3B, (byte) 0x13, (byte) 0x9B,
-            (byte) 0x22, (byte) 0x51, (byte) 0x4A, (byte) 0x08, (byte) 0x79, (byte) 0x8E, (byte) 0x34, (byte) 0x04,
-            (byte) 0xDD, (byte) 0xEF, (byte) 0x95, (byte) 0x19, (byte) 0xB3, (byte) 0xCD, (byte) 0x3A, (byte) 0x43,
-            (byte) 0x1B, (byte) 0x30, (byte) 0x2B, (byte) 0x0A, (byte) 0x6D, (byte) 0xF2, (byte) 0x5F, (byte) 0x14,
-            (byte) 0x37, (byte) 0x4F, (byte) 0xE1, (byte) 0x35, (byte) 0x6D, (byte) 0x6D, (byte) 0x51, (byte) 0xC2,
-            (byte) 0x45, (byte) 0xE4, (byte) 0x85, (byte) 0xB5, (byte) 0x76, (byte) 0x62, (byte) 0x5E, (byte) 0x7E,
-            (byte) 0xC6, (byte) 0xF4, (byte) 0x4C, (byte) 0x42, (byte) 0xE9, (byte) 0xA6, (byte) 0x37, (byte) 0xED,
-            (byte) 0x6B, (byte) 0x0B, (byte) 0xFF, (byte) 0x5C, (byte) 0xB6, (byte) 0xF4, (byte) 0x06, (byte) 0xB7,
-            (byte) 0xED, (byte) 0xEE, (byte) 0x38, (byte) 0x6B, (byte) 0xFB, (byte) 0x5A, (byte) 0x89, (byte) 0x9F,
-            (byte) 0xA5, (byte) 0xAE, (byte) 0x9F, (byte) 0x24, (byte) 0x11, (byte) 0x7C, (byte) 0x4B, (byte) 0x1F,
-            (byte) 0xE6, (byte) 0x49, (byte) 0x28, (byte) 0x66, (byte) 0x51, (byte) 0xEC, (byte) 0xE4, (byte) 0x5B,
-            (byte) 0x3D, (byte) 0xC2, (byte) 0x00, (byte) 0x7C, (byte) 0xB8, (byte) 0xA1, (byte) 0x63, (byte) 0xBF,
-            (byte) 0x05, (byte) 0x98, (byte) 0xDA, (byte) 0x48, (byte) 0x36, (byte) 0x1C, (byte) 0x55, (byte) 0xD3,
-            (byte) 0x9A, (byte) 0x69, (byte) 0x16, (byte) 0x3F, (byte) 0xA8, (byte) 0xFD, (byte) 0x24, (byte) 0xCF,
-            (byte) 0x5F, (byte) 0x83, (byte) 0x65, (byte) 0x5D, (byte) 0x23, (byte) 0xDC, (byte) 0xA3, (byte) 0xAD,
-            (byte) 0x96, (byte) 0x1C, (byte) 0x62, (byte) 0xF3, (byte) 0x56, (byte) 0x20, (byte) 0x85, (byte) 0x52,
-            (byte) 0xBB, (byte) 0x9E, (byte) 0xD5, (byte) 0x29, (byte) 0x07, (byte) 0x70, (byte) 0x96, (byte) 0x96,
-            (byte) 0x6D, (byte) 0x67, (byte) 0x0C, (byte) 0x35, (byte) 0x4E, (byte) 0x4A, (byte) 0xBC, (byte) 0x98,
-            (byte) 0x04, (byte) 0xF1, (byte) 0x74, (byte) 0x6C, (byte) 0x08, (byte) 0xCA, (byte) 0x18, (byte) 0x21,
-            (byte) 0x7C, (byte) 0x32, (byte) 0x90, (byte) 0x5E, (byte) 0x46, (byte) 0x2E, (byte) 0x36, (byte) 0xCE,
-            (byte) 0x3B, (byte) 0xE3, (byte) 0x9E, (byte) 0x77, (byte) 0x2C, (byte) 0x18, (byte) 0x0E, (byte) 0x86,
-            (byte) 0x03, (byte) 0x9B, (byte) 0x27, (byte) 0x83, (byte) 0xA2, (byte) 0xEC, (byte) 0x07, (byte) 0xA2,
-            (byte) 0x8F, (byte) 0xB5, (byte) 0xC5, (byte) 0x5D, (byte) 0xF0, (byte) 0x6F, (byte) 0x4C, (byte) 0x52,
-            (byte) 0xC9, (byte) 0xDE, (byte) 0x2B, (byte) 0xCB, (byte) 0xF6, (byte) 0x95, (byte) 0x58, (byte) 0x17,
-            (byte) 0x18, (byte) 0x39, (byte) 0x95, (byte) 0x49, (byte) 0x7C, (byte) 0xEA, (byte) 0x95, (byte) 0x6A,
-            (byte) 0xE5, (byte) 0x15, (byte) 0xD2, (byte) 0x26, (byte) 0x18, (byte) 0x98, (byte) 0xFA, (byte) 0x05,
-            (byte) 0x10, (byte) 0x15, (byte) 0x72, (byte) 0x8E, (byte) 0x5A, (byte) 0x8A, (byte) 0xAC, (byte) 0xAA,
-            (byte) 0x68, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF, (byte) 0xFF,
-            (byte) 0xFF
-    });
-
-    public static BigInteger getG() {
-        return G;
-    }
-
-    public static BigInteger getP1() {
-        return P1;
-    }
-
-    public static BigInteger getP14() {
-        return P14;
-    }
+    public static final BigInteger P14 =
+            new BigInteger("3231700607131100730033891392642382824881794124114023911284200975140074170663435422" +
+                           "2619689417363569347117901737909704191754605873209195028853758986185622153212175412" +
+                           "5149017745202702357960782362488842461894775876411059286460994117232454266225221932" +
+                           "3054091903768052423551912567971587011700105805587765103886184728025797605490356973" +
+                           "2561526167081339361799541336476559160368317896729073178384589680639671900977202194" +
+                           "1686472258710314113364293195361934716365332097170774482279885885653692086452966360" +
+                           "7725026895550592836275112117409697299806841055435958486658329164213621823107899099" +
+                           "9448652468262416972035911852507045361090559");
 
 }
diff --git a/src/main/java/net/schmizz/sshj/transport/kex/KeyExchange.java b/src/main/java/net/schmizz/sshj/transport/kex/KeyExchange.java
index 0fd4c46a..09a78fde 100644
--- a/src/main/java/net/schmizz/sshj/transport/kex/KeyExchange.java
+++ b/src/main/java/net/schmizz/sshj/transport/kex/KeyExchange.java
@@ -41,6 +41,7 @@ import net.schmizz.sshj.transport.Transport;
 import net.schmizz.sshj.transport.TransportException;
 import net.schmizz.sshj.transport.digest.Digest;
 
+import java.security.GeneralSecurityException;
 import java.security.PublicKey;
 
 /** Key exchange algorithm. */
@@ -55,14 +56,18 @@ public interface KeyExchange {
      * @param I_S   the server key init packet
      * @param I_C   the client key init packet
      *
-     * @throws TransportException if there is an error sending a packet
+     * @throws GeneralSecurityException
+     * @throws TransportException       if there is an error sending a packet
      */
     void init(Transport trans, byte[] V_S, byte[] V_C, byte[] I_S, byte[] I_C)
-            throws TransportException;
+            throws GeneralSecurityException, TransportException;
 
     /** @return the computed H parameter */
     byte[] getH();
 
+    /** @return the computed K parameter */
+    byte[] getK();
+
     /**
      * The message digest used by this key exchange algorithm.
      *
@@ -73,9 +78,6 @@ public interface KeyExchange {
     /** @return the host key determined from server's response packets */
     PublicKey getHostKey();
 
-    /** @return the computed K parameter */
-    byte[] getK();
-
     /**
      * Process the next packet
      *
@@ -84,9 +86,10 @@ public interface KeyExchange {
      *
      * @return a boolean indicating if the processing is complete or if more packets are to be received
      *
-     * @throws TransportException if there is an error sending a packet
+     * @throws GeneralSecurityException
+     * @throws TransportException       if there is an error sending a packet
      */
     boolean next(Message msg, SSHPacket buffer)
-            throws TransportException;
+            throws GeneralSecurityException, TransportException;
 
 }