I found an answer. The class org.bouncycastle.cms.CMSSignedHelper from Bouncy Castle Library has the mapping. I extracted the required snippet from there and copied here.
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private static final Map encryptionAlgs = new HashMap();
private static final Map digestAlgs = new HashMap();
static
{
encryptionAlgs.put(X9ObjectIdentifiers.id_dsa_with_sha1.getId(), "DSA");
encryptionAlgs.put(X9ObjectIdentifiers.id_dsa.getId(), "DSA");
encryptionAlgs.put(OIWObjectIdentifiers.dsaWithSHA1.getId(), "DSA");
encryptionAlgs.put(PKCSObjectIdentifiers.rsaEncryption.getId(), "RSA");
encryptionAlgs.put(PKCSObjectIdentifiers.sha1WithRSAEncryption.getId(), "RSA");
encryptionAlgs.put(TeleTrusTObjectIdentifiers.teleTrusTRSAsignatureAlgorithm, "RSA");
encryptionAlgs.put(X509ObjectIdentifiers.id_ea_rsa.getId(), "RSA");
encryptionAlgs.put(CMSSignedDataGenerator.ENCRYPTION_ECDSA, "ECDSA");
encryptionAlgs.put(X9ObjectIdentifiers.ecdsa_with_SHA2.getId(), "ECDSA");
encryptionAlgs.put(X9ObjectIdentifiers.ecdsa_with_SHA224.getId(), "ECDSA");
encryptionAlgs.put(X9ObjectIdentifiers.ecdsa_with_SHA256.getId(), "ECDSA");
encryptionAlgs.put(X9ObjectIdentifiers.ecdsa_with_SHA384.getId(), "ECDSA");
encryptionAlgs.put(X9ObjectIdentifiers.ecdsa_with_SHA512.getId(), "ECDSA");
encryptionAlgs.put(CMSSignedDataGenerator.ENCRYPTION_RSA_PSS, "RSAandMGF1");
encryptionAlgs.put(CryptoProObjectIdentifiers.gostR3410_94.getId(), "GOST3410");
encryptionAlgs.put(CryptoProObjectIdentifiers.gostR3410_2001.getId(), "ECGOST3410");
encryptionAlgs.put("1.3.6.1.4.1.5849.1.6.2", "ECGOST3410");
encryptionAlgs.put("1.3.6.1.4.1.5849.1.1.5", "GOST3410");
digestAlgs.put(PKCSObjectIdentifiers.md5.getId(), "MD5");
digestAlgs.put(OIWObjectIdentifiers.idSHA1.getId(), "SHA1");
digestAlgs.put(NISTObjectIdentifiers.id_sha224.getId(), "SHA224");
digestAlgs.put(NISTObjectIdentifiers.id_sha256.getId(), "SHA256");
digestAlgs.put(NISTObjectIdentifiers.id_sha384.getId(), "SHA384");
digestAlgs.put(NISTObjectIdentifiers.id_sha512.getId(), "SHA512");
digestAlgs.put(PKCSObjectIdentifiers.sha1WithRSAEncryption.getId(), "SHA1");
digestAlgs.put(PKCSObjectIdentifiers.sha224WithRSAEncryption.getId(), "SHA224");
digestAlgs.put(PKCSObjectIdentifiers.sha256WithRSAEncryption.getId(), "SHA256");
digestAlgs.put(PKCSObjectIdentifiers.sha384WithRSAEncryption.getId(), "SHA384");
digestAlgs.put(PKCSObjectIdentifiers.sha512WithRSAEncryption.getId(), "SHA512");
digestAlgs.put(TeleTrusTObjectIdentifiers.ripemd128.getId(), "RIPEMD128");
digestAlgs.put(TeleTrusTObjectIdentifiers.ripemd160.getId(), "RIPEMD160");
digestAlgs.put(TeleTrusTObjectIdentifiers.ripemd256.getId(), "RIPEMD256");
digestAlgs.put(CryptoProObjectIdentifiers.gostR3411.getId(), "GOST3411");
digestAlgs.put("1.3.6.1.4.1.5849.1.2.1", "GOST3411");
}
String getDigestAlgName(String digestAlgOID) {
String algName = (String)digestAlgs.get(digestAlgOID);
if (algName != null)
{
return algName;
}
return digestAlgOID;
}
String getEncryptionAlgName(String encryptionAlgOID) {
String algName = (String)encryptionAlgs.get(encryptionAlgOID);
if (algName != null)
{
return algName;
}
return encryptionAlgOID;
}
MessageDigest getDigestInstance(String algorithm, String provider)
throws NoSuchProviderException, NoSuchAlgorithmException {
if (provider != null)
{
try
{
return MessageDigest.getInstance(algorithm, provider);
}
catch (NoSuchAlgorithmException e)
{
return MessageDigest.getInstance(algorithm); // try rolling back
}
}
else
{
return MessageDigest.getInstance(algorithm);
}
}