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Cryptography, quantum computing, and evolutionary computation Thijs - - PowerPoint PPT Presentation

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Cryptography, quantum computing, and evolutionary computation Thijs Laarhoven mail@thijs.com http://www.thijs.com/ CFMAI 2019, Bangkok, Thailand (December 13, 2019) Cryptography History Cryptography Classical cryptography Some operations

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SLIDE 1

Cryptography, quantum computing, and evolutionary computation

Thijs Laarhoven

mail@thijs.com http://www.thijs.com/

CFMAI 2019, Bangkok, Thailand

(December 13, 2019)

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SLIDE 2

Cryptography

History

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SLIDE 3

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 714881 × 448843 =

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SLIDE 4

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 =

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SLIDE 5

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 = 320869332683,

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SLIDE 6

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 = 320869332683, ...but are difficult to “invert”, or compute in the reverse direction 143 = 188629334237 =

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SLIDE 7

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 = 320869332683, ...but are difficult to “invert”, or compute in the reverse direction 143 = 11 × 13, 188629334237 =

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SLIDE 8

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 = 320869332683, ...but are difficult to “invert”, or compute in the reverse direction 143 = 11 × 13, 188629334237 = 214729 × 878453.

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SLIDE 9

Cryptography

Classical cryptography

Some operations are easy to perform in one direction... 7 × 17 = 119, 714881 × 448843 = 320869332683, ...but are difficult to “invert”, or compute in the reverse direction 143 = 11 × 13, 188629334237 = 214729 × 878453. The security of modern cryptography depends on the hardness of such problems.

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SLIDE 10

Cryptography

Protocols

Example: Suppose Bob wishes to send a private message to Alice across the world.

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SLIDE 11

Cryptography

Protocols

Example: Suppose Bob wishes to send a private message to Alice across the world. Insecure solution:

  • Bob sends Alice the message in the clear over the internet.
  • Problem: Others can see the contents of the message.
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SLIDE 12

Cryptography

Protocols

Example: Suppose Bob wishes to send a private message to Alice across the world. Insecure solution:

  • Bob sends Alice the message in the clear over the internet.
  • Problem: Others can see the contents of the message.

More secure solution:

  • Alice sends Bob a product (323), for which only she knows the factors (17,19).
  • Bob computes some function of his message modulo 323 and sends it to Alice.

◮ This function is easy to compute but hard to invert without the prime factors

  • Alice, knowing the prime factors, can invert and recover Bob’s message.
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SLIDE 13

Quantum computing

Overview

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SLIDE 14

Quantum computing

Applications to cryptography

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SLIDE 15

Post-quantum cryptography

Ongoing efforts

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SLIDE 16

Post-quantum cryptography

Candidates

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SLIDE 17

O

Lattices

Basics

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SLIDE 18

b1 b2 O

Lattices

Basics

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SLIDE 19

b1 b2 O

Lattices

Basics

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SLIDE 20

b1 b2 O

Lattices

Shortest Vector Problem (SVP)

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SLIDE 21

b1 b2 O

Lattices

Shortest Vector Problem (SVP)

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SLIDE 22

b1 b2 O

Lattices

Evolutionary approach to SVP

Basic lattice tools

  • Given a lattice basis, sampling a (long) lattice vector v ∈ L(B) is easy
  • If v1 and v2 are lattice points, then so is w = v1 − v2
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SLIDE 23

b1 b2 O

Lattices

Evolutionary approach to SVP

Basic lattice tools

  • Given a lattice basis, sampling a (long) lattice vector v ∈ L(B) is easy
  • If v1 and v2 are lattice points, then so is w = v1 − v2

Evolutionary approach

  • Construct random initial population of lattice vectors
  • Combine parent vectors vi,vj to produce offspring w
  • Select the fittest parents and children for the next generation
  • Repeat until the population contains a shortest non-zero lattice vector
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SLIDE 24

O

Lattices

Sample a list of random lattice vectors

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SLIDE 25

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Sample a list of random lattice vectors

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SLIDE 26

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Collect all short difference vectors

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SLIDE 27

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Collect all short difference vectors

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SLIDE 28

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Repeat same procedure with difference vectors

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SLIDE 29

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Repeat same procedure with difference vectors

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SLIDE 30

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Repeat same procedure with difference vectors

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SLIDE 31

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 O

Lattices

Repeat same procedure with difference vectors

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SLIDE 32

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 O

Lattices

Repeat same procedure with difference vectors

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SLIDE 33

Summary

  • Cryptography:

◮ Methods for secure communication over insecure (public) channels ◮ More applications every day with an interconnected world ◮ Security currently relies on number-theoretic problems, like factoring

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SLIDE 34

Summary

  • Cryptography:

◮ Methods for secure communication over insecure (public) channels ◮ More applications every day with an interconnected world ◮ Security currently relies on number-theoretic problems, like factoring

  • Quantum computing:

◮ Offers new opportunities in many areas, to solve harder problems ◮ Poses threat to currently-deployed cryptographic schemes

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SLIDE 35

Summary

  • Cryptography:

◮ Methods for secure communication over insecure (public) channels ◮ More applications every day with an interconnected world ◮ Security currently relies on number-theoretic problems, like factoring

  • Quantum computing:

◮ Offers new opportunities in many areas, to solve harder problems ◮ Poses threat to currently-deployed cryptographic schemes

  • Post-quantum cryptography:

◮ Relies on different hard problems, such as lattice problems ◮ Transitions are gradually happening, standardization in progress

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SLIDE 36

Summary

  • Cryptography:

◮ Methods for secure communication over insecure (public) channels ◮ More applications every day with an interconnected world ◮ Security currently relies on number-theoretic problems, like factoring

  • Quantum computing:

◮ Offers new opportunities in many areas, to solve harder problems ◮ Poses threat to currently-deployed cryptographic schemes

  • Post-quantum cryptography:

◮ Relies on different hard problems, such as lattice problems ◮ Transitions are gradually happening, standardization in progress

  • Artificial intelligence:

◮ Offers new powerful algorithmic tools and capabilities ◮ Evolutionary techniques improve state-of-the-art for lattice problems ◮ Only scratching the surface – more applications possible?