Slides from the presentation "Modern Cryptography" delivered at Deovxx UK 2013. See Parleys.com for the full video https://www.parleys.com/speaker/5148920c0364bc17fc5697a5

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
©National Portrait Gallery
and the others at Bletchley Park

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
Camellia Cobra CAST-COCONUT98 128 IDEA
Crab
Cryptomeria CRYPTON DFC
FEAL FROG ICE M6 MARS
RC2 RC5 SEED
Skipjack TEA XTEA
Mercy MESH Nimbus Threefish
Treyfer UES Xenon Zodiac

16. Cyphers
Serpent AES
3-Way Anubis CIPHERUNICORN-A
Cobra COCONUT98 Crab
Cryptomeria CRYPTON DFC
FEAL FROG ICE M6 MARS
Blowfish
DES 3DES
Camellia CAST-128 IDEA
RC2 RC5 SEED
Skipjack TEA XTEA
Mercy MESH Nimbus Threefish
Twofish
Treyfer UES Xenon Zodiac

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