1. Information Security Methods and Practices in Classical and Quantum Regimes

2. Cryptography What’s that mean? ▫Kryptos: hidden, secret ▫Gráphō: to write What does it do? ▫Encryption: plaintext  ciphertext ▫Decryption: ciphertext  plaintext Why would you want that? ▫Confidentiality ▫Integrity, authentication, signing, interactive proofs, secure multi-party computation

3. Cryptology, Cryptanalysis, Cryptolinguistics Frequency analysis Brute force Differential Integral Impossible differential Boomerang Mod n Related key Slide Timing XSL Linear Multiple linear Davies’ attack Improved Davies’ attack

4. Demands for resilient crypto Auguste Kerckhoff’s principle ▫Cipher practically indecipherable ▫Cipher and keys not required to be secret ▫Key communicable and retainable ▫Applicable to telegraphic communication ▫Portable and human effort efficient ▫Easy to use Bruce Shneier ▫“Secrecy … is a prime cause of brittleness… Conversely, openness provides ductility.” Eric Raymond ▫“Any security software design that doesn't assume the enemy possesses the source code is already untrustworthy; therefore, *never trust closed source.” Shannon’s maxim ▫“The enemy knows the system.”

5. Classical Regime Written language text

6. Transposition Exchange the position of two symbols in the text Like an anagram Scytale E.g. text  cipher Hello world!  eHll oowlr!d

7. Substitution Systematically exchange a symbol in the text with another symbol Caesar cipher, EXCESS-3 E.g. text  cipher Aabcd  Ddefg

8. Poly-Alphabetic Substitution Repeated and dynamic substitution(s) Wehrmacht Enigma Series of rotors

9. One Time Pad Perfect secrecy ▫Coined by Shannon ▫H(M) = H(M|C) Requirements ▫Perfect randomness ▫Secure key generation and exchange ▫Careful adherence to process

10. Classical Regime Binary bit sequence

11. Secret Key Crypto Perfect secrecy ▫Coined by Shannon ▫H(M) = H(M|C) Requirements ▫Perfect randomness ▫Secure key generation and exchange ▫Careful adherence to process

12. Symmetric Key Crypto The same (or similar) key ▫For both encryption and decryption Data Encryption Standard ▫56 bit key ▫Feistel network ▫Broken in 1999 in 22 hours 15 minutes by Deep Crack Triple-DES ▫56 bit keys (3 unique) ▫en-de-en-crypt Advanced Encryption Standard (Rijndael) ▫128-192-256 bit keys ▫Substitution permutation network

13. Feistel Network Expansion Key mixing Substitution Permutation

14. Substitution Permutation Network Substitution ▫1/n input change  1/2 output change ▫confusion Permutation ▫mix up inputs ▫diffusion Round keys

15. Public Key Crypto Asymmetric keys ▫public and private No secret key Multiple use TLS, SSL, PGP, GPG, digital signatures

16. RSA Ron Rivest, Adi Shamir, Leonard Adleman; 1978 Key generation ▫Pick two distinct, large prime numbers: p, q ▫Compute their product: n = pq ▫Compute its totient: phi = (p-1)(q-1) ▫Pick a public key exponent: 1 < e < phi, e and phi coprime ▫Compute private key exponent: de = 1 (mod phi) Encryption ▫Forward padding ▫Cipher = text ^ e (mod n)  Exponentiation by squaring Decryption ▫Text = cipher ^ d (mod n)  = text ^ de (mod n) = text ^ (1+k*phi) (mod n) = text (mod n) ▫Reverse padding

17. Hybrid Crypto Diffe-Hellman key exchange Alice and Bob agree on a finite cyclic group G (Multiplicative group of integers mod p) ▫Period p, prime number ▫Base g, primitive root mod p Alice picks a random natural number a and sends g a mod p to Bob. Bob picks a random natural number b and sends g b mod p to Alice. Alice computes (g b mod p) a mod p Bob computes (g a mod p) b mod p Both know g ab mod p = g ba mod p

18. Quantum Regime Breaking classical crypto

19. Peter Shor’s Factorization Algorithm Polynomial time in log N: O( (log N) 3 ) Polynomial gates in log N: O( (log N) 2 ) Complexity class Bounded-Error Quantum Polynomial (BQP) Transform from to periodicity ▫Pick 1 < r < N: a r = 1 mod N ▫a r -1 = (a r/2 +1)(a r/2 -1) = 0 mod N ▫N = (a r/2 +1)(a r/2 -1) = pq Quantum Fourier Transform ▫Map x-space to ω-space ▫Measure with 1/r 2 probability

20. Factor 15 In 2001 IBM demonstrated Shor’s Algorithm and factored 15 into 3 and 5 NMR implementation with 7 qubits pentafluorobutadienyl cyclopentadienyldicarbon yl-iron complex (C11H5F5O2Fe)

21. DWave Superconducting processors Adiabatic quantum algorithms Solving Quantum Unconstrained Binary Optimization problems (QUBO is in NP)

22. Quantum Regime Future proof cryptography

23. Quantum Key Distribution Quantum communication channel ▫Single photon, entangled photon pair Preparation ▫Alice prepares a state, sends to Bob, measures Entanglement ▫Alice and Bob each receive half the pair, measure

24. Non-Orthogonal Bases Complementary bases ▫Basis A: { |0>, |1> } ▫Basis B: { |+>, |-> } Indistinguishable transmission states ▫|+> = 0.5 |0> + 0.5 |1> ▫|-> = 0.5 |0> - 0.5 |1> Random choice of en-de-coding bases ▫Succeeds ~ p = 0.5

25. True Random Number Generation Quantum mechanics at < atomic scale ▫Shot noise ▫Nuclear decay ▫Optics Thermal noise ▫Resistor heat ▫Avalanche/Zener diode breakdown noise ▫Atmospheric noise

26. EPR Einstein, Podolsky, Rosen (1935) Entangled qubits Violation of Bell Inequality

27. BB84 Charles A Bennett, Gilles Brassard (1984) Single photon source, polarization One way, Alice prepares sends to Bob ▫Psi encoded as random bits a, random bases b Bob measures ▫Decoded in random bases b’ ▫50% successfully measured bits a’ = a Measurement bases are shared publicly ▫Throw away a, a’ for b != b’

28. E91 Artur Ekert (1991) Entangled photon source ▫Perfect correlation, 100% a = a’ if b = b’ ▫Non-locality, > 50% a a’ ▫Eve measurement reduces correlation

29. B92 Charles A. Bennett (1992) Dim signal pulse, bright reference pulse ▫Maintains phase with a single qubit transmitted Bases: rectilinear, circular ▫P 0 = 1 - |u 1 ><u 1 |  P 0 |u 0 > = 1 ; p= 1 - | | 2 > 0  P 0 |u 1 > = 0 ▫P 1 = 1 - |u 0 ><u 0 |  P 1 |u 0 > = 0  P 1 |u 1 > = 1 ; p= 1 - | | 2 > 0 Throw away measurements != 1

30. SARG04 Scarani et. al. (2004) Attenuated laser pulses

31. Information Reconciliation 1992 Bennett, Bessette, Brassard, Salvail, Smolin Cascade protocol, repititious Compare block parity bits ▫Odd 1 count: parity = 1; even 1 count transmitted ▫Even 1 count: parity = 0; even 1 count transmitted Two-out-of-five code ▫Every transmission has two 1s and three 0s Hamming codes ▫Additional bits used to identify and correct errors

32. Privacy Amplification Shortened key length Universal hash function ▫Range r ▫Collision probability p < 1/r

33. Quantum Regime Attacks

34. Intercept and Resend Eve measures the qubit in basis b’’ ▫50% probability of correct measurement Eve sends to a’’ Bob ▫25% probability of correct measurement Probability of detection ▫P = 1 – (0.75) n ▫99% in n = 16 bits

35. Security Proofs BB84 is proven unconditionally secure against unlimited resources, provided that: ▫Eve cannot access Alice and Bob's encoding and decoding devices ▫The random number generators used by Alice and Bob must be trusted and truly random ▫The classical communication channel must be authenticated using an unconditionally secure authentication scheme

36. Man in the Middle Senders and recipients are indistinguishable on public channels Eve could pose as Bob ▫Receiving some large portion of messages ▫Responding promptly, at least before Bob Wegman-Carter authentication ▫Alice and Bob share a secret key

37. Photon Number Splitting No true single photon sources Attenuated laser pulses ▫Some small number of photons per pulse, i.e. 0.1 If > 1 photon are present, splitting can occur without detection during reconciliation A secure key is still possible, but requires additional privacy amplification

38. Hacking Gain access to security equipment ▫Foil random number generation ▫Plant Trojan horse Faked state attack ▫Eve - actively quenched detector module Phase remapping attack ▫Move from { |0>, |1>, |+>, |-> } to { |0>, |δ/2>, |δ>, |3δ/2> } Time-shift attack ▫Demonstrated to have ~ 4% mutual information gathered from the idQuantique ID-500 QKD

39. Denial of Service Stop Alice and Bob from communicating ▫Via Classical channel(s) ▫Via Quantum channel(s) Physically block transmissions Introduce large volume of errors

40. Quantum Regime Commercially available devices

41. MagiQ – QPN 8505 “Any sufficiently advanced technology is indistinguishable from magic.” –Arthur C Clarke Transmits qubit polarization over optical fiber 256 bit AES; 1,000 keys per second 140 km range, more with repeaters

42. idQuantique – Cerberis, Centauris Transmits qubit phase over optical fiber High speed layer 2 encryption 256 bit AES; 12 key-devices per minute, 100 km range

43. SmartQuantum – KeyGen, Defender Generate and distribute secret keys over quantum channel Use classical encryption and communication

44. Quintessence Labs G2 QKD Continuous variable brightness laser beams ▫Cheaper than SPS Dense wavelength division multiplexing ▫Erbium doped fiber amplifiers ~ 1550 nm

45. BBN Technologies DARPA QNet ▫Fully operational October 23, 2003 ▫Harvard University ▫Boston University ▫BBN Technologies QKD ▫Weak coherence ▫5 MHz pulse rate ▫0.1 mean photons/pulse

46. John Krah University of Washington Physics Department