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

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information security

Information Security

Methods and Practices in

Classical and Quantum Regimes

cryptography
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
cryptology cryptanalysis cryptolinguistics
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
demands for resilient crypto
Demands for resilient crypto
  • AugusteKerckhoff’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.”
classical regime

Classical Regime

Written language text

transposition
Transposition
  • Exchange the position of two symbols in the text
  • Like an anagram
  • Scytale

E.g. text  cipher

Hello world!  eHll oowlr!d

substitution
Substitution
  • Systematically exchange a symbol in the text with another symbol
  • Caesar cipher, EXCESS-3

E.g. text  cipher

Aabcd  Ddefg

poly alphabetic substitution
Poly-Alphabetic Substitution
  • Repeated and dynamic substitution(s)
  • Wehrmacht Enigma
  • Series of rotors
one time pad
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
classical regime10

Classical Regime

Binary bit sequence

secret key crypto
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
symmetric key crypto
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
feistel network
Feistel Network
  • Expansion
  • Key mixing
  • Substitution
  • Permutation
substitution permutation network
Substitution Permutation Network
  • Substitution
    • 1/n input change  1/2 output change
    • confusion
  • Permutation
    • mix up inputs
    • diffusion
  • Round keys
public key crypto
Public Key Crypto
  • Asymmetric keys
    • public and private
  • No secret key
  • Multiple use
  • TLS, SSL, PGP, GPG, digital signatures
slide16
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
hybrid crypto
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 gamod p to Bob.
  • Bob picks a random natural number b and sends gbmod p to Alice.
  • Alice computes (gb mod p)a mod p
  • Bob computes (ga mod p)b mod p
  • Both know gab mod p = gba mod p
quantum regime

Quantum Regime

Breaking classical crypto

peter shor s factorization algorithm
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: ar = 1 mod N
    • ar -1 = (ar/2 +1)(ar/2 -1) = 0 mod N
    • N = (ar/2 +1)(ar/2 -1) = pq
  • Quantum Fourier Transform
    • Map x-space to ω-space
    • Measure with 1/r2 probability
factor 15
Factor 15
  • In 2001 IBM demonstrated Shor’s Algorithm and factored 15 into 3 and 5
  • NMR implementation with 7 qubits
  • pentafluorobutadienylcyclopentadienyldicarbonyl-iron complex (C11H5F5O2Fe)
dwave
DWave
  • Superconducting processors
  • Adiabatic quantum algorithms
  • Solving Quantum Unconstrained Binary Optimization problems (QUBO is in NP)
quantum regime22

Quantum Regime

Future proof cryptography

quantum key distribution
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
non orthogonal bases
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
true random number generation
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
slide26
EPR
  • Einstein, Podolsky, Rosen (1935)
  • Entangled qubits
  • Violation of Bell Inequality
slide27
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’
slide28
E91
  • Artur Ekert (1991)
  • Entangled photon source
    • Perfect correlation, 100% a = a’ if b = b’
    • Non-locality, > 50% a <--> a’
    • Eve measurement reduces correlation
slide29
B92
  • Charles A. Bennett (1992)
  • Dim signal pulse, bright reference pulse
    • Maintains phase with a single qubit transmitted
  • Bases: rectilinear, circular
    • P0 = 1 - |u1><u1|
      • P0 |u0> = 1 ; p= 1 - |< u0 | u1 >|2 > 0
      • P0 |u1> = 0
    • P1 = 1 - |u0><u0|
      • P1 |u0> = 0
      • P1 |u1> = 1 ; p= 1 - |< u0 | u1 >|2 > 0
  • Throw away measurements != 1
sarg04
SARG04
  • Scarani et. al. (2004)
  • Attenuated laser pulses
information reconciliation
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
privacy amplification
Privacy Amplification
  • Shortened key length
  • Universal hash function
    • Range r
    • Collision probability p < 1/r
intercept and resend
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
security proofs
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
man in the middle
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
photon number splitting
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
hacking
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
denial of service
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
quantum regime40

Quantum Regime

Commercially available devices

magiq qpn 8505
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
idquantique cerberis centauris
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
smartquantum keygen defender
SmartQuantum – KeyGen, Defender
  • Generate and distribute secret keys over quantum channel
  • Use classical encryption and communication
quintessence labs
Quintessence Labs
  • G2 QKD
  • Continuous variable brightness laser beams
    • Cheaper than SPS
  • Dense wavelength division multiplexing
    • Erbium doped fiber amplifiers ~ 1550 nm
bbn technologies
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
john krah university of washington physics department
John Krah

University of Washington

Physics Department

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