Introduction to Cryptography: Understanding Encryption and OpenPGP/GnuPG

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2. OpenPGP/GnuPG Encryption Tanner Lovelace Triangle Linux Users Group 11-April-2002

3. What is Cryptography? • Cryptography • The science of using mathematics to encrypt and decrypt data. • A method of securely sending data over an insecure communications medium. • Cryptanalysis • The science of analyzing and breaking secure communications. • Cryptology is the combination of the two.

4. There are two kinds of cryptography in this world: cryptography that will stop your kid sister from reading your files, and cryptography that will stop major governments from reading your files. -- Bruce Schneier, Applied Cryptography

5. Why do you need cryptography? • Privacy • Keep communications secret • Integrity • Keep communications secure • Authentication • Know who you’re communicating with • Nonrepudiation • A sender shouldn’t be able to deny that they sent a message

6. Cryptography Background • Two main types of cryptography • Symmetric • Same key encrypts/decrypts • DES, AES, IDEA • Asymmetric • Different keys for encryption/decryption • Also called public key cryptography • RSA, Diffie-Hellman, ElGamal

7. Bits, bytes, and Key Lengths, oh my! • Which is better? • 128 bit keys? • 1024 bit keys? • Answer: neither • Symmetric encryption is much faster than asymmetric • Asymmetric makes communicating with people you don’t know much easier

8. Symmetric Key Key Original Plaintext Plaintext Ciphertext Encryption Decryption • Asymmetric Decryption Key Encryption Key Original Plaintext Plaintext Ciphertext Encryption Decryption How does encryption work?

9. How do I know this is secure? • Symmetric • The only way to decrypt without the key is to try all possible combinations. • With a 128 bit key, there are 2128 possible combinations • Comparison • Our sun should go nova in approximately 230 years • The universe is only 234 years old. • Asymmetric • You don’t, but smart people think it is.

10. Not Secure?!? What’s up? • Asymmetric algorithms are built upon certain assumptions that have not been proved • Factoring large numbers • Computing discrete logrithms • These are similar to the P vs. NP problem in classical computer science • Which is why you hear the press talking about the possibility of codes being broken easily.

11. Public Key Algorithms • Diffie-Hellman (key exchange) • First public key algorithm published (1976) • Whitfield Diffie and Martin Hellman • Alice and Bob chose a large prime n and another number g. • Alice chooses a random large integer a and sends Bob X = ga mod n. • Bob chooses a random large integer b and sends Alice Y = gb mod n. • Alice computes k = Yamod n. • Bob computes k’ = Xbmod n. • k and k’ are equal (gab mod n) and cannot be computed by someone watching the exchange!

12. Public Key Algorithms • RSA (Rivest, Shamir, and Adleman) [1977] • Choose two random large prime numbers p and q. • Compute n = pq. • Choose a number e such that e is between 1 and pq and e is relatively prime to (p – 1)(q – 1). • Compute d from e (d = e-1 mod ((p-1)(q-1))) • Multiplicative inverse • To encrypt, calculate c = me mod n. • To decrypt, calculate m = cd mod n.

13. What is OpenPGP/GnuPG • Pretty Good Privacy • Encryption program written by Phill Zimmerman in 1991. • Zimmerman was later criminally charged with releasing it on the Internet. (Charges were eventually dropped.) • OpenPGP • A standard for encrypted/signed messages. • RFC 2440, November 1998 • Gnu Privacy Guard • An implementation of OpenPGP. • Does not use patented algorithms.

14. What can PGP/GnuPG do? • Encrypt / Decrypt • Messages • Files • Digital Signatures • Key management • Create secret and public keys • Manage a list of keys • Certify keys • Revoke or disable keys

15. Encryption • PGP uses multiple forms of encryption to encrypt different parts of a message • Symmetric encryption fast • Asymmetric encryption easy to distribute • Message is encrypted with a symmetric algorithm • Symmetric session key is encrypted with an asymmetric algorithm. • In addition, the message is compressed beforehand, just to remove redundancy that could help cryptanalysis.

16. Encryption

17. Encryption • To encrypt a file, you need to specify options • Recepient (can be yourself) • Binary or ascii mode • Output filename • Input filename % gpg -r [UID]-a –o [outname] –e [file] • Will also work with streams.

18. Decryption • Only need to specify the decrypt option % gpg -d [file] • Will prompt for pass phrase

19. Signature • Integrity • Message is hashed • Hash is encrypted with private key • Message can be hashed again to prove it hasn’t changed. • Authentication • Hash can be decrypted with a public key • Proves that the private key was used to encrypt. • But not necessarily that a particular person encrypted the message. What?!?

20. Signature • Can be combined with encryption • Can be integrated or detached % gpg –a --sign[file] % gpg –a --detach-sign[file] • Detached signatures are useful for signing binary packages. • Used with rpm (--addsign and –resign options)

21. Key Management • Session keys • Created at use • Only used once • Need a very good source of randomness • Asymmetric keys • GPG allows you to create and manage • Public portion of key can be published

22. Web of Trust • How do you know what keys to trust? • You can only physically check a finite number of keys • PGP allows you to sign someone elses key. • Done when you have verified that a key is valid. • Allows you to accept the validity of a key of someone you’ve never met. • If Alice trusts Bob and Bob trusts Charles, then Alice can also trust Charles.

23. Web of Trust

24. GPG Key Creation % gpg --gen-key • Generates a public/private key pair. • Because of the RSA patent, it defaults to using DH/ElGamal (Discrete Logorithm Problem) • Choose a key length (use at least 1024 bits) • User data (name, e-mail) • Pass phrase

25. Key revocation • Always generate a revocation certificate after creating a key! • If you lose your pass phrase, will allow you to cancel your key. % gpg --gen-revoke [UID] • Need the pass phrase (to get to the secret key)

26. Key functions • List keys and signatures % gpg --list-keys % gpg --list-sigs % gpg --fingerprint • Import % gpg --import [filename] • Export % gpg --export [UID] • By default export is binary. Use “-a” to do ascii-armor.

27. Key servers • You could exchange keys by e-mail or web page, but there is a better way. • PGP and GnuPG support a remote key server • Send % gpg --keyserver [ks] --send-key [UID] • Receive % gpg --keyserver [ks] --recv-key [UID] • Default key server can be put in options file. • If default server set, gpg will automatically look there for new keys.

28. Key signing • ONLY SIGN A KEY WHEN YOU ARE ABSOLUTELY SURE IT IS AUTHENTIC!!! • Use the edit key function % gpg --edit-key [UID] • Will bring up a command prompt • Can sign, revoke, change trust, delete, etc… >sign • Make sure you send the newly signed key to a key server.

29. Conclusion • GPG is a tool you can use to improve communication security. • Don’t consider it an end result, but a link in a chain. • It is integrated into a few packages, but the interface could be better • Barrier to use • Better when used all the time.

30. References • Garfinkel, Simson, PGP, Pretty Good Privacy, 1995, O’Reilly & Associates. • Schneier, Bruce, Applied Cryptography, 1996, Wiley. • Various crypto links • http://www.x5.net/faqs/crypto/ • http://www.pgpi.org/doc/guide/6.5/en/intro/ • http://www.dewinter.com/gnupg_howto/english/GPGMiniHowto-1.html • http://www.mcc.ac.uk/cos/security/PGP_why_and_how.html • http://www.wired.com/wired/archive/people/whitfield_diffie/ • http://www.iae.nsk.su/pages/CRYPTO/rsafaq.html • http://www.philzimmermann.com/ • http://www.openpgp.org/ • http://www.gnupg.org/