RSA OAEP SHA2 vector creation

This page documents the code that was used to generate the RSA OAEP SHA2 test vectors as well as code used to verify them against another implementation.

Creation

cryptography was modified to allow the use of SHA2 in OAEP encryption. Then the following python script was run to generate the vector files.

# This file is dual licensed under the terms of the Apache License, Version
# 2.0, and the BSD License. See the LICENSE file in the root of this repository
# for complete details.

import binascii
import itertools
import os

from cryptography.hazmat.backends.openssl.backend import backend
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.asymmetric import padding, rsa

from tests.utils import load_pkcs1_vectors, load_vectors_from_file


def build_vectors(mgf1alg, hashalg, filename):
    vectors = load_vectors_from_file(filename, load_pkcs1_vectors)

    output = []
    for vector in vectors:
        # RSA keys for this must be long enough to accommodate the length of
        # the underlying hash function. This means we can't use the keys from
        # the sha1 test vectors for sha512 tests because 1024-bit keys are too
        # small. Instead we parse the vectors for the test cases, then
        # generate our own 2048-bit keys for each.
        private, _ = vector
        skey = rsa.generate_private_key(65537, 2048, backend)
        pn = skey.private_numbers()
        examples = private["examples"]
        output.append(b"# =============================================")
        output.append(b"# Example")
        output.append(b"# Public key")
        output.append(b"# Modulus:")
        output.append(format(pn.public_numbers.n, "x"))
        output.append(b"# Exponent:")
        output.append(format(pn.public_numbers.e, "x"))
        output.append(b"# Private key")
        output.append(b"# Modulus:")
        output.append(format(pn.public_numbers.n, "x"))
        output.append(b"# Public exponent:")
        output.append(format(pn.public_numbers.e, "x"))
        output.append(b"# Exponent:")
        output.append(format(pn.d, "x"))
        output.append(b"# Prime 1:")
        output.append(format(pn.p, "x"))
        output.append(b"# Prime 2:")
        output.append(format(pn.q, "x"))
        output.append(b"# Prime exponent 1:")
        output.append(format(pn.dmp1, "x"))
        output.append(b"# Prime exponent 2:")
        output.append(format(pn.dmq1, "x"))
        output.append(b"# Coefficient:")
        output.append(format(pn.iqmp, "x"))
        pkey = skey.public_key()
        vectorkey = rsa.RSAPrivateNumbers(
            p=private["p"],
            q=private["q"],
            d=private["private_exponent"],
            dmp1=private["dmp1"],
            dmq1=private["dmq1"],
            iqmp=private["iqmp"],
            public_numbers=rsa.RSAPublicNumbers(
                e=private["public_exponent"], n=private["modulus"]
            ),
        ).private_key(backend)
        count = 1

        for example in examples:
            message = vectorkey.decrypt(
                binascii.unhexlify(example["encryption"]),
                padding.OAEP(
                    mgf=padding.MGF1(algorithm=hashes.SHA1()),
                    algorithm=hashes.SHA1(),
                    label=None,
                ),
            )
            assert message == binascii.unhexlify(example["message"])
            ct = pkey.encrypt(
                message,
                padding.OAEP(
                    mgf=padding.MGF1(algorithm=mgf1alg),
                    algorithm=hashalg,
                    label=None,
                ),
            )
            output.append(
                b"# OAEP Example {0} alg={1} mgf1={2}".format(
                    count, hashalg.name, mgf1alg.name
                )
            )
            count += 1
            output.append(b"# Message:")
            output.append(example["message"])
            output.append(b"# Encryption:")
            output.append(binascii.hexlify(ct))

    return b"\n".join(output)


def write_file(data, filename):
    with open(filename, "w") as f:
        f.write(data)


oaep_path = os.path.join(
    "asymmetric", "RSA", "pkcs-1v2-1d2-vec", "oaep-vect.txt"
)
hashalgs = [
    hashes.SHA1(),
    hashes.SHA224(),
    hashes.SHA256(),
    hashes.SHA384(),
    hashes.SHA512(),
]
for hashtuple in itertools.product(hashalgs, hashalgs):
    if isinstance(hashtuple[0], hashes.SHA1) and isinstance(
        hashtuple[1], hashes.SHA1
    ):
        continue

    write_file(
        build_vectors(hashtuple[0], hashtuple[1], oaep_path),
        "oaep-{0}-{1}.txt".format(hashtuple[0].name, hashtuple[1].name),
    )

Download link: generate_rsa_oaep_sha2.py

Verification

A Java 8 program was written using Bouncy Castle to load and verify the test vectors.

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.math.BigInteger;
import java.security.AlgorithmParameters;
import java.security.GeneralSecurityException;
import java.security.KeyFactory;
import java.security.PrivateKey;
import java.security.Security;
import java.security.spec.AlgorithmParameterSpec;
import java.security.spec.MGF1ParameterSpec;
import java.security.spec.RSAPrivateKeySpec;
import java.util.Arrays;

import javax.crypto.Cipher;
import javax.crypto.spec.OAEPParameterSpec;
import javax.crypto.spec.PSource;
import javax.xml.bind.DatatypeConverter;

import org.bouncycastle.jce.provider.BouncyCastleProvider;

class TestVectorData {
    public BigInteger pub_key_modulus;
    public BigInteger pub_key_exponent;
    public BigInteger priv_key_public_exponent;
    public BigInteger priv_key_modulus;
    public BigInteger priv_key_exponent;
    public BigInteger priv_key_prime_1;
    public BigInteger priv_key_prime_2;
    public BigInteger priv_key_prime_exponent_1;
    public BigInteger priv_key_prime_exponent_2;
    public BigInteger priv_key_coefficient;
    public byte[] plaintext;
    public byte[] ciphertext;
}

class TestVectorLoader {
    private static final String FILE_HEADER = "# RSA OAEP SHA2 vectors built";
    private static final String EXAMPLE_HEADER = "# =====";
    private static final String EXAMPLE = "# Example";
    private static final String PUBLIC_KEY = "# Public key";
    private static final String PUB_MODULUS = "# Modulus:";
    private static final String PUB_EXPONENT = "# Exponent:";
    private static final String PRIVATE_KEY = "# Private key";
    private static final String PRIV_MODULUS = "# Modulus:";
    private static final String PRIV_PUBLIC_EXPONENT = "# Public exponent:";
    private static final String PRIV_EXPONENT = "# Exponent:";
    private static final String PRIV_PRIME_1 = "# Prime 1:";
    private static final String PRIV_PRIME_2 = "# Prime 2:";
    private static final String PRIV_PRIME_EXPONENT_1 = "# Prime exponent 1:";
    private static final String PRIV_PRIME_EXPONENT_2 = "# Prime exponent 2:";
    private static final String PRIV_COEFFICIENT = "# Coefficient:";
    private static final String OAEP_EXAMPLE_HEADER = "# OAEP Example";
    private static final String MESSAGE = "# Message:";
    private static final String ENCRYPTION = "# Encryption:";

    private BufferedReader m_reader = null;
    private FileReader m_file_reader = null;
    private TestVectorData m_data = null;

    TestVectorLoader() {

    }

    protected void finalize() {
        close();
    }

    public void open(String path) throws IOException {
        close();
        m_file_reader = new FileReader(path);
        m_reader = new BufferedReader(m_file_reader);
        m_data = new TestVectorData();
    }

    public void close() {
        try {
            if (m_reader != null) {
                m_reader.close();
                m_reader = null;
            }
            if (m_file_reader != null) {
                m_file_reader.close();
                m_file_reader = null;
            }
            m_data = null;
        } catch (IOException e) {
            System.out.println("Exception closing files");
            e.printStackTrace();
        }
    }

    public TestVectorData loadNextTest() throws IOException {
        if (m_file_reader == null || m_reader == null || m_data == null) {
            throw new IOException("A test vector file must be opened first");
        }

        String line = m_reader.readLine();

        if (line == null) {
            // end of file
            return null;
        }

        if (line.startsWith(FILE_HEADER)) {
            // start of file
            skipFileHeader(m_reader);
            line = m_reader.readLine();
        }

        if (line.startsWith(OAEP_EXAMPLE_HEADER)) {
            // Next example, keep existing keys and load next message
            loadMessage(m_reader, m_data);
            return m_data;
        }

        // otherwise it's a new example
        if (!line.startsWith(EXAMPLE_HEADER)) {
            throw new IOException("Test Header Missing");
        }
        startNewTest(m_reader);
        m_data = new TestVectorData();

        line = m_reader.readLine();
        if (!line.startsWith(PUBLIC_KEY))
            throw new IOException("Public Key Missing");
        loadPublicKey(m_reader, m_data);

        line = m_reader.readLine();
        if (!line.startsWith(PRIVATE_KEY))
            throw new IOException("Private Key Missing");
        loadPrivateKey(m_reader, m_data);

        line = m_reader.readLine();
        if (!line.startsWith(OAEP_EXAMPLE_HEADER))
            throw new IOException("Message Missing");
        loadMessage(m_reader, m_data);

        return m_data;
    }

    private byte[] unhexlify(String line) {
        byte[] bytes = DatatypeConverter.parseHexBinary(line);
        return bytes;
    }

    private BigInteger readBigInteger(BufferedReader br) throws IOException {
        return new BigInteger(br.readLine(), 16);
    }

    private void skipFileHeader(BufferedReader br) throws IOException {
        br.readLine(); // # # Derived from the NIST OAEP SHA1 vectors
        br.readLine(); // # # Verified against the Bouncy Castle OAEP SHA2 implementation
        br.readLine(); // #
    }

    private void startNewTest(BufferedReader br) throws IOException {
        String line = br.readLine();
        if (!line.startsWith(EXAMPLE))
            throw new IOException("Example Header Missing");
    }

    private void loadPublicKey(BufferedReader br, TestVectorData data) throws IOException {
        String line = br.readLine();
        if (!line.startsWith(PUB_MODULUS))
            throw new IOException("Public Key Modulus Missing");
        data.pub_key_modulus = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PUB_EXPONENT))
            throw new IOException("Public Key Exponent Missing");
        data.pub_key_exponent = readBigInteger(br);
    }

    private void loadPrivateKey(BufferedReader br, TestVectorData data) throws IOException {
        String line = br.readLine();
        if (!line.startsWith(PRIV_MODULUS))
            throw new IOException("Private Key Modulus Missing");
        data.priv_key_modulus = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_PUBLIC_EXPONENT))
            throw new IOException("Private Key Public Exponent Missing");
        data.priv_key_public_exponent = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_EXPONENT))
            throw new IOException("Private Key Exponent Missing");
        data.priv_key_exponent = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_PRIME_1))
            throw new IOException("Private Key Prime 1 Missing");
        data.priv_key_prime_1 = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_PRIME_2))
            throw new IOException("Private Key Prime 2 Missing");
        data.priv_key_prime_2 = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_PRIME_EXPONENT_1))
            throw new IOException("Private Key Prime Exponent 1 Missing");
        data.priv_key_prime_exponent_1 = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_PRIME_EXPONENT_2))
            throw new IOException("Private Key Prime Exponent 2 Missing");
        data.priv_key_prime_exponent_2 = readBigInteger(br);

        line = br.readLine();
        if (!line.startsWith(PRIV_COEFFICIENT))
            throw new IOException("Private Key Coefficient Missing");
        data.priv_key_coefficient = readBigInteger(br);
    }

    private void loadMessage(BufferedReader br, TestVectorData data) throws IOException {
        String line = br.readLine();
        if (!line.startsWith(MESSAGE))
            throw new IOException("Plaintext Missing");
        data.plaintext = unhexlify(br.readLine());

        line = br.readLine();
        if (!line.startsWith(ENCRYPTION))
            throw new IOException("Ciphertext Missing");
        data.ciphertext = unhexlify(br.readLine());
    }

}

public class VerifyRSAOAEPSHA2 {

    public enum SHAHash {
        SHA1, SHA224, SHA256, SHA384, SHA512
    }

    private SHAHash m_mgf1_hash;
    private SHAHash m_alg_hash;
    private Cipher m_cipher;
    private PrivateKey m_private_key;
    private AlgorithmParameters m_algo_param;

    VerifyRSAOAEPSHA2(SHAHash mgf1_hash, SHAHash alg_hash, TestVectorData test_data) throws Exception {

        m_mgf1_hash = mgf1_hash;
        m_alg_hash = alg_hash;

        MGF1ParameterSpec mgf1_spec = getMGF1ParameterSpec(m_mgf1_hash);
        AlgorithmParameterSpec algo_param_spec = getAlgorithmParameterSpec(m_alg_hash, mgf1_spec);

        m_algo_param = AlgorithmParameters.getInstance("OAEP");
        m_algo_param.init(algo_param_spec);

        m_private_key = loadPrivateKey(test_data);

        m_cipher = getCipher(m_alg_hash);
    }

    private Cipher getCipher(SHAHash alg_hash) throws GeneralSecurityException {
        Cipher cipher = null;

        switch (alg_hash) {

        case SHA1:
            cipher = Cipher.getInstance("RSA/ECB/OAEPwithSHA1andMGF1Padding", "BC");
            break;

        case SHA224:
            cipher = Cipher.getInstance("RSA/ECB/OAEPwithSHA-224andMGF1Padding", "BC");
            break;

        case SHA256:
            cipher = Cipher.getInstance("RSA/ECB/OAEPwithSHA-256andMGF1Padding", "BC");
            break;

        case SHA384:
            cipher = Cipher.getInstance("RSA/ECB/OAEPwithSHA-384andMGF1Padding", "BC");
            break;

        case SHA512:
            cipher = Cipher.getInstance("RSA/ECB/OAEPwithSHA-512andMGF1Padding", "BC");
            break;
        }

        return cipher;
    }

    private MGF1ParameterSpec getMGF1ParameterSpec(SHAHash mgf1_hash) {
        MGF1ParameterSpec mgf1 = null;

        switch (mgf1_hash) {

        case SHA1:
            mgf1 = MGF1ParameterSpec.SHA1;
            break;
        case SHA224:
            mgf1 = MGF1ParameterSpec.SHA224;
            break;

        case SHA256:
            mgf1 = MGF1ParameterSpec.SHA256;
            break;

        case SHA384:
            mgf1 = MGF1ParameterSpec.SHA384;
            break;

        case SHA512:
            mgf1 = MGF1ParameterSpec.SHA512;
            break;
        }

        return mgf1;
    }

    private AlgorithmParameterSpec getAlgorithmParameterSpec(SHAHash alg_hash, MGF1ParameterSpec mgf1_spec) {

        OAEPParameterSpec oaep_spec = null;

        switch (alg_hash) {

        case SHA1:
            oaep_spec = new OAEPParameterSpec("SHA1", "MGF1", mgf1_spec, PSource.PSpecified.DEFAULT);
            break;

        case SHA224:
            oaep_spec = new OAEPParameterSpec("SHA-224", "MGF1", mgf1_spec, PSource.PSpecified.DEFAULT);
            break;

        case SHA256:
            oaep_spec = new OAEPParameterSpec("SHA-256", "MGF1", mgf1_spec, PSource.PSpecified.DEFAULT);
            break;

        case SHA384:
            oaep_spec = new OAEPParameterSpec("SHA-384", "MGF1", mgf1_spec, PSource.PSpecified.DEFAULT);
            break;

        case SHA512:
            oaep_spec = new OAEPParameterSpec("SHA-512", "MGF1", mgf1_spec, PSource.PSpecified.DEFAULT);
            break;
        }

        return oaep_spec;
    }

    private PrivateKey loadPrivateKey(TestVectorData test_data) throws Exception {
        KeyFactory kf = KeyFactory.getInstance("RSA");

        RSAPrivateKeySpec keySpec = new RSAPrivateKeySpec(test_data.priv_key_modulus, test_data.priv_key_exponent);

        return kf.generatePrivate(keySpec);
    }

    public void testDecrypt(byte[] plaintext, byte[] ciphertext) throws Exception {
        System.out.println("Verifying OAEP with mgf1_hash: " + m_mgf1_hash + " alg_hash: " + m_alg_hash + " - "
                + ciphertext.length + " bytes ciphertext - "
                + plaintext.length + " bytes plaintext");

        m_cipher.init(Cipher.DECRYPT_MODE, m_private_key, m_algo_param);
        byte[] java_plaintext = m_cipher.doFinal(ciphertext);

        if (Arrays.equals(java_plaintext, plaintext) == false) {
            throw new Exception("Verification failure - plaintext does not match after decryption.");
        }
    }

    public static void main(String[] args) {
        Security.addProvider(new BouncyCastleProvider());

        // assume current directory if no path given on command line
        String vector_path = "./vectors/cryptography_vectors/asymmetric/RSA/oaep-custom";

        if (args.length > 0) {
            vector_path = args[0];
        }

        System.out.println("Vector file path: " + vector_path);

        try {
            // loop over each combination of hash loading the vector file
            // to verify for each
            for (SHAHash mgf1_hash : SHAHash.values()) {
                for (SHAHash alg_hash : SHAHash.values()) {
                    if (mgf1_hash.name().toLowerCase().equals("sha1") &&
                        alg_hash.name().toLowerCase().equals("sha1")) {
                        continue;
                    }
                    String filename = "oaep-" + mgf1_hash.name().toLowerCase() +
                                          "-" + alg_hash.name().toLowerCase() + ".txt";

                    System.out.println("Loading " + filename + "...");

                    TestVectorLoader loader = new TestVectorLoader();
                    loader.open(vector_path + filename);

                    TestVectorData test_data;

                    // load each test in the file and verify
                    while ((test_data = loader.loadNextTest()) != null) {
                        VerifyRSAOAEPSHA2 verify = new VerifyRSAOAEPSHA2(mgf1_hash, alg_hash, test_data);
                        verify.testDecrypt(test_data.plaintext, test_data.ciphertext);
                    }

                    System.out.println("Verifying " + filename + " completed successfully.");
                }
            }

            System.out.println("All verification completed successfully");

        } catch (Exception e) {
            // if any exception is thrown the verification has failed
            e.printStackTrace();
            System.out.println("Verification Failed!");
        }
    }
}

Download link: VerifyRSAOAEPSHA2.java

Using the Verifier

Download and install the Java SDK. Initial verification was performed using jdk-8u77-macosx-x64.dmg.

Download the latest Bouncy Castle JAR. Initial verification was performed using bcprov-jdk15on-154.jar.

Set the -classpath to include the Bouncy Castle jar and the path to VerifyRSAOAEPSHA2.java and compile the program.

$ javac -classpath ~/Downloads/bcprov-jdk15on-154.jar:./ VerifyRSAOAEPSHA2.java

Finally, run the program with the path to the SHA-2 vectors:

$ java -classpath ~/Downloads/bcprov-jdk15on-154.jar:./ VerifyRSAOAEPSHA2