Basic definitions

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layout: page title: Basic Definitions

The goal of this chapter is to define used functions related to cryptography and data manipulation. The definitions crafted in this chapter are then used in pseudo-codes in documentation. You can learn more about actual implementation of following functions in the "Implementation Notes" section.

Cryptographic Functions

Following basic cryptography algorithms and parameters are used in the PowerAuth 2.0 cryptography description:

• AES - A symmetric key encryption algorithm, uses CBC mode of operation. It defines four methods:

  • byte[] encrypted = AES.encrypt(byte[] original, byte[] iv, SecretKey key) - encrypt bytes using symmetric key with given initialization vector and PKCS7 padding.
  • byte[] original = AES.decrypt(byte[] encrypted, byte[] iv, SecretKey key) - decrypt bytes using symmetric key with given initialization vector and PKCS7 padding.
  • byte[] encrypted = AES.encrypt(byte[] original, byte[] iv, SecretKey key, String padding) - encrypt bytes using symmetric key with given initialization vector and given padding.
  • byte[] original = AES.decrypt(byte[] encrypted, byte[] iv, SecretKey key, String padding) - decrypt bytes using symmetric key with given initialization vector and given padding.

• PBKDF2 - An algorithm for key stretching, converts a short password into long key by performing repeated hash iteration on the original data, HMAC-SHA1 algorithm is used for a pseudo-random function. Implementations must make sure resulting key is converted in format usable by AES algorithm. One method is defined for this algorithm:

  • SharedKey expandedKey = PBKDF2.expand(char[] password, byte[] salt, long iterations, long lengthInBits) - stretch the password using given number of iterations to achieve key of given length in bits, use given salt.

• ECDSA - An algorithm for elliptic curve based signatures, uses SHA256 hash algorithm. It defines two operations:

  • byte[] signature = ECDSA.sign(byte[] data, PrivateKey privateKey) - compute signature of given data and private key.
  • boolean isValid = ECDSA.verify(byte[] data, byte[] signature, PublicKey publicKey) - verify the signature for given data using a given public key.

• ECDH - An algorithm for elliptic curve with Diffie-Helman key exchange, uses P256r1 curve. We define single operation on ECDH, a symmetric key deduction between parties A and B:

  • SecretKey secretKey = ECDH.phase(PrivateKey privateKeyA, PublicKey publicKeyB)

• KDF - A key derivation function used to derive a symmetric key with specific "index" from a given master key. Uses AES algorithm with zero initialization vector to derive the new key in following way: index is converted to bytes, XORed with a 16 byte long zero array (to get 16 byte long array with bytes from the index) and AES encrypted using provided symmetric key masterKey.

  • SecretKey derivedKey = KDF.derive(SecretKey masterKey, long index)

• KDF_INTERNAL - A second key derivation function for the algorithm internal purposes used to derive a symmetric key with specific "index" (in this case, byte[16]) from a given master key. Uses HMAC-SHA256 to derive the new key in following way: index used as HMAC-SHA256 key, provided symmetric key masterKey is converted to key bytes used as HMAC-SHA256 data, resulting 32B long byte array is then XORed on per-byte basis to obtain 16B ling byte array (0th with 16th, 1st with 17th, etc.).

  • SecretKey derivedKey = KDF_INTERNAL.derive(SecretKey masterKey, byte[] index)

Helper Functions

These functions are used in the pseudo-codes:

• Key generators.

  • KeyPair keyPair = KeyGenerator.randomKeyPair() - Generate a new ECDH key pair using P256r1 elliptic curve.

• Key conversion utilities.

  • byte[] privateKeyBytes = KeyConversion.getBytes(PrivateKey privKey) - Get bytes from the ECDH key pair private key by encoding the D value (the number defining the ECDH private key).
  • byte[] publicKeyBytes = KeyConversion.getBytes(PublicKey pubKey) - Get bytes from the ECDH key pair public key by encoding the Q value (the point defining the ECDH public key).
  • byte[] secretKeyBytes = KeyConversion.getBytes(SecretKey secretKey) - Get bytes from the symmetric key (using getEncoded).
  • PrivateKey privateKey = KeyConversion.privateKeyFromBytes(byte[] privKeyBytes) - Get ECDH key pair private key by decoding the bytes into the original D value (the number defining the ECDH private key).
  • PublicKey publicKey = KeyConversion.publicKeyFromBytes(byte[] pubKeyBytes) - Get ECDH key pair public key by decoding the bytes into the original Q value (the point defining the ECDH public key).
  • SecretKey secretKey = KeyConversion.secretKeyFromBytes(byte[] secretKeyBytes) - Create a symmetric key using provided bytes.

• Random data generators.

  • byte[] randomBytes = Generator.randomBytes(int N) - Generate N random bytes using a secure random generator.
  • String randomBase32 Generator.randomBase32String(int N) - Generate string in Base32 encoding with N characters using a secure random generator.
  • String uuid = Generator.randomUUUD() - Generate a new UUID level 4 and return it in string representation.

• Hashing and MAC functions.

  • byte[] signature = Mac.hmacSha256(SharedKey key, byte[] message) - Compute HMAC-SHA256 signature for given message using provided symmetric key.
  • byte[] hash = Hash.sha256(byte[] original) - Compute SHA256 hash of a given input.

• Utility functions.

  • byte[] zeroBytes = ByteUtils.zeroBytes(int N) - Generate buffer with N zero bytes.
  • byte[] truncatedBytes = ByteUtils.truncate(byte[] bytes, int N) - Get last N bytes of given byte array.
  • int integer = ByteUtils.getInt(byte[4] bytes) - Get integer from 4 byte long byte array.
  • byte[] result = ByteUtils.concat(byte[] a, byte[] b) - Concatenate two byte arrays - append b after a.
    • byte[] result = ByteUtils.convert32Bto16B(byte[] bytes32, byte[] b) - Converts 32b long byte array to 16b long array by xor-ing the first 16b with the second 16b, byte-by-byte.