Modern Cryptography

Presented @ Devoxx UK 2013 (March)

Transcript

1. Modern Cryptography for Java Developers James McGivern
2. About This Talk • Not a treaty in mathematical theory • Rapid fire - please save questions until the end • Looking under the hood • Look at two popular algorithms • Hot cryptographic research
3. Definitions • Cryptography • Plaintext • Cyphertext • Code • Cypher vs Cipher • Encryption / Decryption • Key
4. “Secure Hashes” • A hash function takes an arbitrary length input and returns a fixed sized bit string • Cryptographic hash function obey 3 properties: • Given a hash h it should be hard to find a message m s.t. h = hash(m) • Given an input m1 it should be hard to find an m2 s.t. m1 != m2 and hash(m1 ) = hash(m2 ) • Should be hash collision resistant • MD5, SHA-1, SHA-3, RIPEMD-xxx
5. 1,000,000 BC ~WWII
6. A Challenge Gur Nafjre gb Yvsr, Gur Havirefr, naq Rirelguvat vf sbegl 42.
7. A Challenge The Answer to Life, The Universe, and Everything is 42.
8. The Enigma Machine Simon Singh
9. All Hail Turing and the others at Bletchley Park ©National Portrait Gallery
10. Kerckhoff’s Principle “A cryptosystem should be secure even if everything about the system, except the key, is public knowledge”
11. Symmetric Encryption
12. Background • The only kind of encryption until 1973 • The same cryptographic key for both encryption of plaintext and decryption of ciphertext • This is a “shared secret”
13. Cyphers
14. Cyphers 3-Way Anubis CIPHERUNICORN-A Cobra COCONUT98 Crab Cryptomeria CRYPTON DFC FEAL FROG ICE M6 MARS Mercy MESH Nimbus Threefish Treyfer UES Xenon Zodiac
15. Cyphers 3-Way Anubis CIPHERUNICORN-A Cobra COCONUT98 Crab Cryptomeria CRYPTON DFC FEAL FROG ICE M6 MARS Mercy MESH Nimbus Threefish Treyfer UES Xenon Zodiac Camellia CAST-128 IDEA RC2 RC5 SEED Skipjack TEA XTEA
16. Cyphers 3-Way Anubis CIPHERUNICORN-A Cobra COCONUT98 Crab Cryptomeria CRYPTON DFC FEAL FROG ICE M6 MARS Mercy MESH Nimbus Threefish Treyfer UES Xenon Zodiac Camellia CAST-128 IDEA RC2 RC5 SEED Skipjack TEA XTEA Serpent AES Blowfish DES 3DES Twofish
17. Cypher Types • Block Cyphers • Stream Cyphers
18. All Hail Claude Shannon • Godfather of: • Information Theory • Digital Computing & Digital Circuit Design • Cryptographic Confusion • Cryptographic Diffusion • "the enemy knows the system"
19. S-Boxes • A function which maps an m bit input to an n bit output • Fixed lookup table vs dynamic based on key • Example: 6x4 S-Box:
20. AES • Based on the Rijndael cypher • Block size: 128 bits • Key size: • 128 bit - 10 rounds • 192 bit - 12 rounds • 256 bit - 14 rounds • Block represented as a 4×4 column-major order matrix of bytes called the state
21. AES Recipe • BEGIN • Key Expansion • LOOP (round) • Key XOR • Substitute • Transpose • Mix • END • Key XOR • Substitute • Transpose • Key XOR
22. Key Expansion • Each round of processing uses a round key • Round keys are derived from the primary key • AES uses the Rijndael Key Schedule • Round Keys are the same size as the state
23. Key XOR • Bit-wise XOR the round key with the state
24. Substitute • Replace each byte in the state using an S- box • This process is reversible but non-linear • The S-box is a derangement
25. Transpose
26. Mix • Apply an invertible linear transform to each cell (4 bytes) • This does not change the cell size • Together with Transpose provides cryptographic diffusion
27. AES Recipe • BEGIN • Key Expansion • LOOP (round) • Key XOR • Substitute • Transpose • Mix • END • Key XOR • Substitute • Transpose • Key XOR
28. Weaknesses • Direct Attacks • “Biclique Cryptanalysis of the Full AES” Cracks AES-128 with computational complexity 2126.1 • Side channel attacks • 2005 cache-timing attack (requires root access) • 2009 some hardware implementations found to be susceptible to differential fault analysis allowing key recovery with complexity 232 • 2010 access-driven cache attack, “near realtime” key recovery (requires root access)
29. Asymmetric Encryption
30. Background • 1973 - James H. Ellis, Clifford Cocks, and Malcolm Williamson @GCHQ • 1974/78 - Merkle’s Puzzles • 1976 - Whitfield Diffie and Martin Hellman • 1977/78 - Ron Rivest, Adi Shamir and Leonard Adleman @MIT
31. RSA • Based on the Integer Factorisation Problem • Believed to be in NP and co-NP • => not NP-complete • Is a fundamental part of HTTPS/SSL
32. Key generation • Choose two prime number p and q • Compute n = pq • Compute F(n) = F(p)F(q) = (p - 1)/(q - 1) • Chose an integer e s.t. • 1 < e < F(n) • gcd(e, F(n)) = 1 • Compute d = 1 / e(mod F(n)) • Public Key = (e, n) • Private Key = (e, d)
33. Encryption • Given a message M • Convert M to an integer m s.t. 0 < m < 1 • If necessary use a padding scheme • Computer the cypher text c: c = me (mod n)
34. Decryption • Given a cyphertext c • Compute m = cd (mod n) • Remove padding if present • Convert m in to M
35. Issues • Picking the numbers is hard • If p or q are too small or too close to each other it greatly decreases the security • If p-1 or q-1 only has small prime factors n can be factored in polynomial time • Side-channel attacks • Timing • Differential fault analysis (power)
36. Java Cryptography
37. Cryptographic Libraries • JCA • java.security • javax.security deprcated • JCE Providers • Oracle JCE + policies • The Legion of the Bouncy Castle
38. Useful Utils • Jasypt • Keytool IUI • Spring Crypto Utils • JCE taglib
39. Practical Tips • KISS • Choose the appropriate algorithm for the situation • Cost / benefit analysis • Key size • Hybrid encryption systems • Good quality RNG seeds
40. <Future> Cryptography
41. Quantum Computers @The Pub Explanation
42. The Basics • Binary vectors |0> and |1> • Qubit |q> = x|0> + y|1> where x2 + y2 = 1 • Qubits |q> = a|00> + b|01> + c|11> + d|10>
43. Quantum Operations • An operation on n qubits can be represented by an nxn matrix • Also represented by quantum circuits • Always Reversible...
44. Measuring • Given |q> = -0.2|0> + 0.8|1> • Then the result of measuring q is: • 0 with probability 0.2 • 1 with probability 0.8 |q> = -0.1|00> + 0.4|01> + 0.4|11> + 0.1|10> |q> = -0.2|0> + 0.8|1> • Irreversible
45. Entanglement • Only a quantum effect • An entangled quantum system allows a higher correlation of states than classically possible • Given a qubit system in equal superposition Measuring the first qubit allows us to determine the state of the second without measuring
46. Grover’s Algorithm • Lov Grover 1996 • Given some function f and an value y find x such that f(x) = y • O(N1/2) time complexity • O(log N) space complexity
47. Shor’s Algorithm Don’t leave this blank!
48. Shor’s Algorithm • Peter Shor 1994 • Calculates the factors of a given integer • O((log N)3) • Belongs to BQP
49. Good News • The largest integer factored: 143 • Largest quantum computer: 84 qubits
50. Quantum Cryptography
51. Post-Quantum Cryptography
52. Lattice-Based Cryptography • A lattice L in Rn is a discrete subgroup of Rn which spans the real vector space Rn • Each lattice has a set of bases • A basis is a set of vectors such that any vector is the lattice is a linear combination of the basis vectors • Can be viewed as a regular tiling of a space by a primitive cell
53. Graphical Representation Basis = { [0.5, 0], [0, 1] }
54. Shortest Vector Problem Given a lattice L in Rn find the shortest non- zero vector in L
55. Closest Vector Problem Given a lattice L in Rn and a vector v not in L, find the closest vector in L to v
56. NP-Hard • Non-deterministic polynomial time hard • For all problems in NP, any NP-hard problem is at least as hard as the hardest problem in NP • SVP & CVP are thought to be NP-hard • If we find a polynomial time algorithm for any NP-hard problem then P = NP!
57. Other Approaches • Multivariate Cryptography • Secure Hash Signatures • Lamport signatures • Merkle scheme • McEliece and Niedenrreiter Algorithms based on EEC
58. Summary • Modern cryptography really started ~1937 • Symmetric cyhpers • Asymmetric cyphers • Non-classical cryptography • Post-quantum cryptography
59. Thank You