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PBKDF2

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PBKDF2 (Password-Based Key Derivation Function 2) is a key derivation function that is part of RSA Laboratories' Public-Key Cryptography Standards (PKCS) series, specifically PKCS #5 v2.0, also published as Internet Engineering Task Force's RFC 2898. It replaces an earlier standard, PBKDF1, which could only produce derived keys up to 160 bits long.

PBKDF2 applies a pseudorandom function, such as a cryptographic hash, cipher, or HMAC to the input password or passphrase along with a salt value and repeats the process many times to produce a derived key, which can then be used as a cryptographic key in subsequent operations. The added computational work makes password cracking much more difficult, and is known as key stretching. When the standard was written in 2000, the recommended minimum number of iterations was 1000, but the parameter is intended to be increased over time as CPU speeds increase. Having a salt added to the password reduces the ability to use precomputed hashes (rainbow tables) for attacks, and means that multiple passwords have to be tested individually, not all at once. The standard recommends a salt length of at least 64 bits.

Key derivation process

The PBKDF2 key derivation function has five input parameters: 

DK = PBKDF2(PRF, Password, Salt, c, dkLen)

where:

  • PRF is a pseudorandom function of two parameters with output length hLen (e.g. a keyed HMAC)
  • Password is the master password from which a derived key is generated
  • Salt is a cryptographic salt
  • c is the number of iterations desired
  • dkLen is the desired length of the derived key
  • DK is the generated derived key

Each hLen-bit block Ti of derived key DK, is computed as follows: 

DK = T1 || T2 || ... || Tdklen/hlen
Ti = F(Password, Salt, c, i)

The function F is the xor (^) of c iterations of chained PRFs. The first iteration of PRF uses Password as the PRF key and Salt concatenated with i encoded as a big-endian 32-bit integer. (Note that i is a 1-based index.) Subsequent iterations of PRF use Password as the PRF key and the output of the previous PRF computation as the salt: 

F(Password, Salt, c, i) = U1 ^ U2 ^ ... ^ Uc

where: 

U1 = PRF(Password, Salt || INT_32_BE(i))
U2 = PRF(Password, U1)
...
Uc = PRF(Password, Uc-1)

For example, WPA2 uses: 

 DK = PBKDF2(HMAC−SHA1, passphrase, ssid, 4096, 256)

Implementations

Systems that use PBKDF2


Disk encryption software

Alternatives to PBKDF2

One weakness of PBKDF2 is that while its number of iterations can be adjusted to make it take an arbitrarily large amount of computing time, it can be implemented with a small circuit and very little RAM, which makes brute-force attacks using ASICs or GPUs relatively cheap.[17] The bcrypt key derivation function requires a larger (but still fixed) amount of RAM and is slightly stronger against such attacks,[18] while the more modern scrypt key derivation function can use arbitrarily large amounts of memory and is therefore more resistant to ASIC and GPU attacks.[17]

References

  1. ^ "Windows Data Protection". NAI Labs, Network Associates, Inc.; Microsoft Corporation. October 2001. Archived from the original on 2007-04-16.
  2. ^ "AES Coding Tips for Developers". WinZip. 2008-07-21. Retrieved 2013-09-07.
  3. ^ "BRG Main SIte". Winzip.com. Retrieved 2013-09-07.
  4. ^ "Security". LastPass: How We Do It. LastPass. Retrieved 2013-06-13.
  5. ^ "LastPass Security Notification". LastPass. 2011-05-04. Retrieved 2013-06-13.
  6. ^ "Defending against crackers, PBKDF2". Agilebits, Inc. 2014. Retrieved 2014-11-14.
  7. ^ "Our security model in a nutshell". Dashlane, Inc. 2014. Retrieved 2014-03-09.
  8. ^ "Protection of User Data in Dashlane" (PDF). Dashlane Security Whitepaper. Dashlane, Inc. November 2011. Retrieved 2014-03-09.
  9. ^ iOS security, May 2012, Apple inc.
  10. ^ "How Django stores passwords". Django 1.4 documentation. 2012-03-23. Retrieved 31 July 2012.
  11. ^ Encrypt/decrypt using block ciphers, Programmer’s Reference Guide of Zend Framework 2.
  12. ^ Worldwide. "Cisco Security Response: Cisco IOS and Cisco IOS XE Type 4 Passwords Issue". Tools.cisco.com. Retrieved 2013-09-07.
  13. ^ Notes on the implementation of encryption in Android 3.0, September 2012, Android Open Source Project.
  14. ^ http://crypto.nsa.org/vilefault/23C3-VileFault.pdf[dead link]
  15. ^ "Header Key Derivation, Salt, and Iteration Count". TrueCrypt User’s Guide. TrueCrypt Foundation. 2012-02-07. Retrieved 2013-06-08.
  16. ^ "CipherShed User's Guide, Techincal Details" (PDF). CipherShed User’s Guide. CipherShed Project. 2014-12-19. Retrieved 2014-12-27.
  17. ^ a b Colin Percival. scrypt. As presented in "Stronger Key Derivation via Sequential Memory-Hard Functions". presented at BSDCan'09, May 2009.
  18. ^ "New 25 GPU Monster Devours Passwords In Seconds". The Security Ledger. 2012-12-04. Retrieved 2013-09-07.
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