Good day,
There is another third party that need my web application to send them some data in encrypt format. Thus they send me some guide to do so, however, I am not familiar with it, I am trying to google around but looks like I am google wrong way.
The guide is something as follow:
Run openssl command to generate a privatekey:
openssl ecparam -name prime256v1 -genkey -out myprivate.pem
After run this command, I output a priv.pem file, and I saw inside got some key end with '==', which is as follow:
-----BEGIN EC PARAMETERS-----
BggqhkjOPQMBBw==
-----END EC PARAMETERS-----
-----BEGIN EC PRIVATE KEY-----
MHcCAQEEILefWfeuZOgnbDlxpwo3uQ2xQXfhXHUPTS+vKzvVZdCToAoGCCqGSM49
AwEHoUQDQgAE4MeQspGRJ1qdpweBfiaT5P84alZdga1f7mSpa5HqXTH58u0ZWJUQ
J7ToU/bUOPITh4FX07AV6wrgFCmwtUenDQ==
-----END EC PRIVATE KEY-----
Second one is run openssl command to generate the public key, and then send them:
openssl ec -in myprivate.pem -pubout -out mypublic.pem
Convert the private key to pkcs8 format:
openssl pkcs8 -topk8 -nocrypt -in myprivate.pem -out mypkcs8.pem
The third party will give me a public key in string format, then ask me to generate a secret key, and provide me some java code as follow:
first is to generate secret key and second one is encrypt:
public static SecretKey generateSharedSecret(PrivateKey privateKey,
PublicKey publicKey) {
try {
KeyAgreement keyAgreement = KeyAgreement.getInstance( "ECDH" );
keyAgreement.init( privateKey );
keyAgreement.doPhase( publicKey, true );
SecretKeySpec key = new SecretKeySpec(
keyAgreement.generateSecret( ), "AES" );
return key;
} catch ( Exception e ) {
// TODO Auto-generated catch block
e.printStackTrace( );
return null;
}
}
public static String encryptString(SecretKey key, String plainText) {
try {
String myIv = "Testing # IV!";
byte[] iv = myIv.getBytes( "UTF-8" );
IvParameterSpec ivSpec = new IvParameterSpec( iv );
Cipher cipher = Cipher.getInstance( "AES / CBC / PKCS5Padding" );
byte[] plainTextBytes = plainText.getBytes( "UTF-8" );
byte[] cipherText;
cipher.init( Cipher.ENCRYPT_MODE, key, ivSpec );
cipherText = new byte[cipher.getOutputSize( plainTextBytes.length )];
int encryptLength = cipher.update( plainTextBytes, 0,
plainTextBytes.length, cipherText, 0 );
encryptLength += cipher.doFinal( cipherText, encryptLength );
return bytesToHex( cipherText );
} catch ( Exception e ) {
e.printStackTrace( );
return null;
}
}
and also the bytes to hex string method:
public static String bytesToHex(byte[] byteArray) {
StringBuffer hexStringBuffer = new StringBuffer( );
for ( int i = 0; i < byteArray.length; i++ ) {
hexStringBuffer.append( String.format( "%02X", byteArray[ i ] ) );
}
return hexStringBuffer.toString( );
}
I have self gen a private key and also a public key by using openssl command, but the 4th step telling me that they will give me a public key as well, thus I am not understand, which public key should I use.
And also, how can I convert a String into java PrivateKey and PublicKey object?
* add on *
I try to convert the der file to java PublicKey object, it looks work. Before this, I convert the pem to der using openssl command:
openssl pkey -pubin -in ecpubkey.pem -outform der -out ecpubkey.der
Here is the java code:
File f = new File("/home/my/Desktop/key/ecpubkey.der");
FileInputStream fis = new FileInputStream(f);
DataInputStream dis = new DataInputStream(fis);
byte[] keyBytes = new byte[(int) f.length()];
dis.readFully(keyBytes);
dis.close();
KeyFactory fact = KeyFactory.getInstance("EC");
PublicKey theirpub = fact.generatePublic(new X509EncodedKeySpec(keyBytes));
However, I am hitting java.security.spec.InvalidKeySpecException: java.io.IOException: insufficient data when I try to convert der file to java PrivateKey object, the following is what I did:
openssl ecparam -name prime256v1 -genkey -out priv.pem
openssl pkcs8 -topk8 -nocrypt -in priv.pem -outform der -out priv.der
And the following is my java code:
File f2 = new File("/home/my/Desktop/key/priv.der");
FileInputStream fis2 = new FileInputStream(f2);
DataInputStream dis2 = new DataInputStream(fis2);
byte[] keyBytes2 = new byte[(int) f.length()];
dis2.readFully(keyBytes2);
dis2.close();
KeyFactory fact2 = KeyFactory.getInstance("EC");
PrivateKey pKey = fact2.generatePrivate( new PKCS8EncodedKeySpec(keyBytes2) ); // this line hit insufficient data
Diffie-Hellman is well-explained in wikipedia -- and probably some of the hundreds of Qs here, and crypto.SX and security.SX, about it, but I can't easily find which. In brief:
you generate a keypair, keep your privatekey, and provide your publickey to the other party
the other party does the same thing (or its reflection): generate a keypair, keep their privatekey, and provide their publickey to you
you use your privatekey and their publickey to compute the 'agreement' value
they similarly use their privatekey and your publickey to compute the same 'agreement' value. This is also called a shared secret, because you and the other party know it, but anyone eavesdropping on your traffic does not.
The 'provide' in that synopsis omits a lot of very important details. It is vital that when you provide your publickey to the other party they actually get your publickey and not a value altered or replaced by an adversary, and similarly when they provide their publickey to you it is vital you get the real one and not a modified or fake one. This is where actual DH systems mostly break down, and the fact you mention none of the protections or complications needed here suggests your scheme will be insecure and easily broken -- if used for anything worth stealing.
Note you should NEVER disclose or 'send' your privatekey to anyone, and they should similarly not disclose theirs. That's the main basis for public-key (or 'asymmetric') cryptography to be of any value or use at all.
There are numerous ways that keys can be represented, but only some are relevant to you.
Public keys are often represented either in
the ASN.1 structure SubjectPublicKeyInfo defined in X.509 and more conveniently in PKIX, primarily in rfc5280 #4.1 and #4.1.2.7 and rfc3279 2.3, encoded in DER, which has the limitation that many of the bytes used in this encoding are not valid characters and cannot be correctly displayed or otherwise manipulated and sometimes not transmitted or even stored; or
that same ASN.1 DER structure 'wrapped' in 'PEM' format, which converts the troublesome binary data to all displayable characters in an easily manipulable form. PEM format was originally created for a secure-email scheme call Privacy Enhanced Mail which has fallen by the wayside, replaced by other schemes and technologies, but the format it defined is still used. The publickey PEM format was recently re-standardized by rfc7468 #13 (which as you see referenced rfc5280).
OpenSSL supports both of these, but the commandline utility which you are using mostly defaults to PEM -- and since you need to convey your key to 'them', and they need to convey their key to you, PEM may well be the most reliable and/or convenient way of doing so. (Although other formats are possible, if you and they agree -- and if they require something else you'll have to agree for this scheme to work at all.)
Java directly supports only DER, thus assuming you receive their publickey in SPKI PEM, to use it in Java you need to convert it to DER. You can either do this in OpenSSL
openssl pkey -pubin -in theirpub.pem -outform der -out theirpub.der
and then read the DER into a Java crypto KeyFactory:
byte[] theirpubder = Files.readAllBytes(Paths.get(whatever));
KeyFactory fact = KeyFactory.getInstance("EC");
PublicKey theirpub = fact.generatePublic(new X509EncodedKeySpec(theirpubder));
// can downcast to ECPublicKey if you want to be more specific
Alternatively you can have Java convert the PEM which isn't too hard; there are several variations but I like:
String theirpubpem = new String(Files.readAllBytes(Paths.get(whatever)));
// IN GENERAL letting new String(byte[]) default the charset is dangerous, but PEM is OK
byte[] theirpubder = Base64.getMIMEDecoder().decode(theirpubpem.replaceAll("-----[^\\n]*\\n","") );
// continue as for DER
For private keys
there are significantly more representations, but only one (or two-ish) that Java shares with OpenSSL. Since you only need to store the private key locally and not 'send' it, PEM may not be needed; if so you can just add -outform der to your pkcs8 -topk8 -nocrypt command, adjusting the name appropriately, and read the result directly in a Java KeyFactory in the same fashion as above except with PKCS8EncodedKeySpec and generatePrivate and [EC]PrivateKey. If you do want to store it in (PKCS8-clear) PEM, you can also combine the above.
Using the DH agreement value directly as a symmetric cipher (e.g. AES) key is nonstandard and generally not considered good practice, although for ECDH with prime256v1 (aka secp256r1 or P-256) it is technically possible. AFAIK all good standards use a key-derivation step (aka Key Derivation Function or KDF) in between. Since you haven't shown us their 'guide' I can't say if this is correct -- for at least small values of correct.
To be sure you know, using CBC with a fixed IV more than once for the same key (which in this case is the same DH result) is insecure. I assume 'Testing' means you plan to replace it with something better.
Also FYI you don't need to use the full complication of the Cipher.init,update,doFinal API. When the data is small enough to fit in memory, as here, you can just do:
cipher.init(ENCRYPT_MODE, key, parms);
byte[] encrypted = cipher.doFinal (plainbytes);
// or since you want to hexify it
... bytesToHex (cipher.doFinal (plainbytes)) ...
Finally because Java byte is signed, your bytesToHex will output almost exactly half of all bytes with FFFFFF prefixed. This is very unusual, and phenomenally ugly, but again I don't know if it is 'correct' for you.
Base on dave_thompson_085 explanation and code, I manage to create my java PublicKey and Privatekey with following:
public static PublicKey getPublicKey(String filename) throws IOException, GeneralSecurityException {
String publicKeyPEM = getKey(filename);
return getPublicKeyFromString(publicKeyPEM);
}
private static String getKey(String filename) throws IOException {
// Read key from file
String strKeyPEM = "";
BufferedReader br = new BufferedReader(new FileReader(filename));
String line;
while ((line = br.readLine()) != null) {
strKeyPEM += line + "\n";
}
br.close();
return strKeyPEM;
}
public static PublicKey getPublicKeyFromString(String key) throws IOException, GeneralSecurityException {
String publicKeyPEM = key;
publicKeyPEM = publicKeyPEM.replace("-----BEGIN PUBLIC KEY-----\n", "");
publicKeyPEM = publicKeyPEM.replace("-----END PUBLIC KEY-----", "");
BASE64Decoder b = new BASE64Decoder();
byte[] encoded = b.decodeBuffer(publicKeyPEM);
KeyFactory kf = KeyFactory.getInstance("EC");
PublicKey pubKey = (PublicKey) kf.generatePublic(new X509EncodedKeySpec(encoded));
return pubKey;
}
and this is for private key
public static PrivateKey getPrivateKey(String filename) throws IOException, GeneralSecurityException {
String privateKeyPEM = getKey(filename);
return getPrivateKeyFromString(privateKeyPEM);
}
public static PrivateKey getPrivateKeyFromString(String key) throws IOException, GeneralSecurityException {
String privateKeyPEM = key;
privateKeyPEM = privateKeyPEM.replace("-----BEGIN PRIVATE KEY-----\n", "");
privateKeyPEM = privateKeyPEM.replace("-----END PRIVATE KEY-----", "");
BASE64Decoder b = new BASE64Decoder();
byte[] encoded = b.decodeBuffer(privateKeyPEM);
KeyFactory kf = KeyFactory.getInstance("EC");
PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(encoded);
PrivateKey privKey = (PrivateKey) kf.generatePrivate(keySpec);
return privKey;
}
Many thanks to #dave_thompson_085 explanation.
Adapting the directions at Creating a DSA Signature from the Linux command line I created a DSA signed message:
echo "foobar" > foo.txt
openssl dgst -dss1 -sign dsa_priv.pem foo.txt > sigfile.bin
The directions actually used foo.sha1 instead of foo.txt, where foo.sha1 was generated by sha1sum but signing a hash seems a bit redundant since DSA is, itself, supposed to do hashing.
So, anyway, I did that. Here's the private key I used (I generated it specifically for testing purposes):
-----BEGIN DSA PRIVATE KEY-----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-----END DSA PRIVATE KEY-----
Here's the hex encoded output of sigfile.bin:
302c021456d7e7da10d1538a6cd45dcb2b0ce15c28bac03402147e973a4de1e92e8a87ed5218c797952a3f854df5
I'm now trying to verify this in Java with BouncyCastle and am unable to do so. Here's my Java code:
import java.io.StringReader;
import org.bouncycastle.openssl.PEMReader;
import java.security.interfaces.DSAPublicKey;
import org.bouncycastle.crypto.params.DSAPublicKeyParameters;
import org.bouncycastle.crypto.signers.DSADigestSigner;
import org.bouncycastle.crypto.signers.DSASigner;
import org.bouncycastle.crypto.digests.SHA1Digest;
import org.bouncycastle.crypto.params.DSAParameters;
public class DSA
{
public static void main(String[] args)
throws Exception
{
byte[] message = "foobar".getBytes();
byte[] signature = hexStringToByteArray("302c021456d7e7da10d1538a6cd45dcb2b0ce15c28bac03402147e973a4de1e92e8a87ed5218c797952a3f854df5");
String key = "-----BEGIN PUBLIC KEY-----\n" +
"MIIBuDCCASwGByqGSM44BAEwggEfAoGBAOwYAcAzXpuw+XCXuNp5zhAzKdhrRguI\n" +
"uI5kLia8fhRb+1EnFPNpXt4fUS2c/0P0nvzH/TvApizzMkRYJea6rRSW5B+MDjv6\n" +
"lvrxv+5xBM15kdug033mgSL7wEJIrTLwbe5/djz2oe+pr1KLqs/fvgyKcQyttUWb\n" +
"5SmwZ+UVx3zfAhUAu0kA2L6VgbvEwpD9sTj5tLyB6Y0CgYEA5GjC+KsPsAH3HZKl\n" +
"2IwTjX47iNVHyuzr4ZcyXceJ/pi3WR6bQJ6tpf1I2jIE0DOMPlNUwYh0aWBGvoY2\n" +
"t4d5cwZaW90OS8IAIRFkQS0ywpmJyb7KXqRHwAYdMID88GW0d/KsVB3if0j/9QOo\n" +
"jhGOrO+kJcZBxUSxINgIIEYFAlEDgYUAAoGBALnHTAZlpoLJZuSBVtnMuRM3cSX4\n" +
"3IkE9w9FveDV1jX5mmfK7yBVpQFV8eVJfk91ERQ4Dn6ePLUv2dRIt4a0S0qHqadg\n" +
"zyoFyqkmmUi1kNLyixtRqh+m2gXx0t63HEpZDbEPppdpnlppZquVQh7TyrKSXW9M\n" +
"TzUkQjFI9UY7kZeK\n" +
"-----END PUBLIC KEY-----";
PEMReader reader = new PEMReader(new StringReader(key));
DSAPublicKey decoded = (DSAPublicKey) reader.readObject();
DSADigestSigner dsa = new DSADigestSigner(new DSASigner(), new SHA1Digest());
DSAParameters params = new DSAParameters(
decoded.getParams().getP(),
decoded.getParams().getQ(),
decoded.getParams().getG()
);
DSAPublicKeyParameters publickey = new DSAPublicKeyParameters(decoded.getY(), params);
dsa.init(false, publickey);
dsa.update(message, 0, message.length);
boolean result = dsa.verifySignature(signature);
System.out.println(result ? "good" : "bad");
}
public static byte[] hexStringToByteArray(String s)
{
int len = s.length();
byte[] data = new byte[len / 2];
for (int i = 0; i < len; i += 2)
{
data[i / 2] = (byte) ((Character.digit(s.charAt(i), 16) << 4)
+ Character.digit(s.charAt(i+1), 16));
}
return data;
}
}
The signature is not validating. Is there something wrong with my Java code? Maybe OpenSSL is doing something weird with dss1?
I was able to validate the signature just fine with OpenSSL:
openssl dgst -dss1 -verify dsa_pub.pem -signature sigfile.bin foo.txt
(Unix) echo outputs its arguments, space-separated if more than one, PLUS A NEWLINE. Use "foobar\n" as the data to verify. Alternatively sign the result of printf '%s' foobar >foo.txt which portably omits the newline; some versions of echo support -n for this purpose, some older ones use \c, and some don't support it at all.
FYI BouncyCastle as of version 150 (2013) no longer has org.bouncycastle.openssl.PEMReader; instead you need PEMParser which returns org.bouncycastle.asn1.x509.SubjectPublicKeyInfo which can be converted to key object by org.bouncycastle.openssl.jcajce.JcaPEMKeyConverter or KeyFactory.getInstance(alg).generatePublicKey(new X509EncodedKey(spki.getEncoded())) which is what JcaPEMKeyConverter actually does.
OTOH you can use org.bouncycastle.jcajce.provider.asymmetric.dsa.DSAUtil.generatePublicKeyParameter to replace that fiddling with the parameter pieces; that's what the BC provider interface (as opposed to the lightweight interface) does. Or of course you could just use JCA in the first place and you don't really need BC at all, since OpenSSL publickey formats (unlike privatekey) are consistently compatible with basic Java crypto.
Also BTW openssl dgst needed the -dss1 hack only through version 0.9.8; since version 1.0.0 released 2010 (but not immediately upgraded by many distros and products due to actual or feared incompatibility) you only need -sha1 and a DSA pubkey.
I'm trying to sign a string using BouncyCastle library.
My code works, but the resulting string is full of weird characters and my instinct says something is wrong about it.
My code looks like this
Security.addProvider(new BouncyCastleProvider());
FileReader fileReader = new FileReader(new File("certs/private.pem"));
PEMReader r = new PEMReader(fileReader);
PrivateKey privateKey = (PrivateKey) r.readObject();
r.close()
String toSign = "hello world";
Signature signature = Signature.getInstance("SHA1withRSA","BC");
signature.initSign(privateKey);
signature.update(toSign.getBytes("UTF-8"));
byte[] signedArray = signature.sign();
String signedString = new String(signedArray, "UTF-8");
And the resulting string (signedString) looks (awfully) like this:
�����jc.������c�1�#�ٶ����E8����a��f8���t�~W�{%��\Z#��it��ҽ;�n��k�n{U>&�d�_���&�?�N��g�
z\�k�g���e~�S4��ƎG�g��U�:��s>i�%YL�n3�����Y��9����T���}�Usb���&�����eշѾUr�Y�ڝ[j�h~mu\3U��j���c�U�ac����t��No-��1J�B]�
The private.pem was generated with this command
openssl req -new -x509 -days 3652 -nodes -out private.crt -keyout private.pem.
Any help or hint will be very appreciated.
SOLVED
What I did was to encode de byte array to Base64 using this line
byte[] encodedArray = org.bouncycastle.util.encoders.Base64.encode(signedArray);
and voalá!
Your signature is a byte[], it is not a string. Attempting to treat a byte array as a string gives you what you have found. Either retain and store the signature as a byte array, or else convert the byte array to a string-compatible format, such as Base64. Java 8 contains the Base64 class which will do the conversion for you. If you do use Base64, then remember to convert back to bytes before checking the signature.
I have the following code in bash:
signed_request = $(printf "PLAIN TEXT REQUEST" |
openssl rsautl -sign -inkey "keyfile.pem" | openssl enc -base64 | _chomp )
Basically, this code takes a plain text, signs it with a private key and encodes using Base64
How could I do a code with exactly the same functionality in Java?
You can use JDK security API. Take a look at this working sample, hope it can get you started:
public static void main(String[] args) throws Exception {
KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
kpg.initialize(1024);
KeyPair keyPair = kpg.genKeyPair();
byte[] data = "test".getBytes("UTF8");
Signature sig = Signature.getInstance("MD5WithRSA");
sig.initSign(keyPair.getPrivate());
sig.update(data);
byte[] signatureBytes = sig.sign();
System.out.println("Singature:" + new BASE64Encoder().encode(signatureBytes));
sig.initVerify(keyPair.getPublic());
sig.update(data);
System.out.println(sig.verify(signatureBytes));
}
EDIT:
The example above uses internal Sun's encoder (sun.misc.BASE64Encoder). It is best to use something like Base64 from Commons Codec.
Also, you can use not-yet-commons-ssl to obtain the private key from a file and encode using org.apache.commons.ssl.Base64. Using Max's example:
import java.security.Signature;
import org.apache.commons.ssl.Base64;
import org.apache.commons.ssl.PKCS8Key;
// [...]
PKCS8Key pkcs8 = new PKCS8Key(new FileInputStream("keyfile.pem"),
"changeit".toCharArray());
Signature sig = Signature.getInstance("MD5WithRSA");
sig.initSign(pkcs8.getPrivateKey());
sig.update(data);
byte[] signatureBytes = sig.sign();
System.out.println("Singature: " +
Base64.encodeBase64String(signatureBytes));
I copy the link #Aqua posted as a new answer, because I think it's FAR more useful than any of the answers given yet. Use THIS to read/write private/public keys from files:
http://codeartisan.blogspot.ru/2009/05/public-key-cryptography-in-java.html
The link doesn't say anythig about signing and verifying, but signing is a lot easier. I used this code to sign:
Signature signature = Signature.getInstance("SHA256WithRSA");
signature.initSign(privateKey);
signature.update("text to sign".getBytes());
signature.sign();
And to verify:
Signature signature = Signature.getInstance("SHA256WithRSA");
signature.initVerify(publicKey);
signature.update("text to sign".getBytes);
signature.verify(signatureMadeEarlier);
I'm trying to encrypt some binary data in Java with a public key as described on this useful page:
http://www.junkheap.net/content/public_key_encryption_java
As directed by the page, I created public and private keys using the commands:
openssl genrsa -aes256 -out private.pem 2048
openssl rsa -in private.pem -pubout -outform DER -out public.der
Now I save encrypt some data with a small program:
public class Rsa {
public static void main(String[] args) throws Exception, IOException {
File keyFile = new File("public.der");
byte[] encodedKey = new byte[(int) keyFile.length()];
new FileInputStream(keyFile).read(encodedKey);
X509EncodedKeySpec publicKeySpec = new X509EncodedKeySpec(encodedKey);
KeyFactory kf = KeyFactory.getInstance("RSA");
PublicKey pk = kf.generatePublic(publicKeySpec);
Cipher rsa = Cipher.getInstance("RSA");
rsa.init(Cipher.ENCRYPT_MODE, pk);
FileOutputStream fileOutputStream = new FileOutputStream(
"encrypted.rsa");
OutputStream os = new CipherOutputStream(fileOutputStream, rsa);
byte[] raw = new byte[245];
raw[0] = 4;
os.write(raw);
os.flush();
os.close();
}
}
The above code works, but when I change the size of the byte array to 246, it produces a zero-length file!
What am I doing wrong?
CipherOutputStream tends to swallow exceptions generated by the Cipher and OutputStream objects it wraps. The Sun RSA implementation will not encrypt more than than M-11 bytes, where M is the length in bytes of the modulus. This is true for the default PKCS1Padding, which is what you should always use unless you really know what you are doing. You can specify NoPadding and thereby get the full M bytes.
RSA is not the correct choice for encrypting bulk data. The generally accepted method for encrypting data with RSA is to generate a random symmetric session key K. e.g. an AES key, encrypt the data with the symmetric algorithm with K, then encrypt K using the RSA keys of all the receipients.