Fun with Certificates part I - IAS Security · 5/13/2019  · Fun with Certificates part I RSA...

Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

Fun with Certificates part Ia Deep Dive into Cryptography and RSA for all ages

Brian Epstein(he/him/his)

Institute for Advanced Study

Computer Manager, Network and Security

Information Security Officer

bepstein@ias.edu - @epepepep

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

The Institute for Advanced Study

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

Topics● Cryptography

● History and Concepts● Symmetric and Asymmetric (RSA/ECC)

● Certificates● Trust● Key Size (bit-length)

● Lab and Demonstrations

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

Cryptography

Goal: pass messages secretly between entities through an insecure medium

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Symmetric Cryptography● Cereal box decoder ring/Cryptograms● Decode secret message (“zsad”).● Translate each letter with decoder ring● Secret message is (“easy”).● Reverse to encode.● Fast.

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

tpuud JimmyJimmJimJiJttptputpuutpuud

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Symmetric Box Demo

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Symmetric Key Cryptography

n*(n-1)/2 = 6*(5-1)/2 = 30/2 = 15 unique keys

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

One way function

X

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Asymmetric Keys● Private key that you keep to yourself● Public key that you give to everyone

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

Asymmetric Box Demo

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Math

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

51

3 17

1 3 1 17

41

1 41

Prime Numbers

1 * 41 = 41

1 * 3 * 1 * 17 = 3 * 17 = 51

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Exponents

27 = 2*2*2*2*2*2*2 = 128

2^7 = 128

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Fun with Certificates part IRSA Cryptography

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Modulus

55 1282

11018

r 18 128 ÷ 55 = 2 r 18128 mod 55 = 18128 ≡ 18 (mod 55)

55 1282

11018

r 18

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

Modulus 5 r 05 25 25 0

5 r 15 26 25 1

5 r 25 27 25 2

5 r 35 28 25 3

5 r 45 29 25 4

6 r 05 30 30 0

6 r 15 31 30 1

mod 5

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Modulus● Think of modulus like a circle● Examples

● clock - 59 minutes becomes 0 minutes : (mod 60)● date - 365th day of the year becomes the 1st : (mod

365)● numbers - ones column goes from 9 to 0 : (mod 10)● circular degrees - 359° goes to 0° : (mod 360)

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

RSA Private Key Contents● Two large Prime Numbers (p and q)● Modulus (n = p*q)● Private exponent (d)

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Private Exponent● Private exponent (d) must solve

(d*e) mod φ(n) = 1

Fun with Certificates

Fun with Certificates

Fun with Certificates

Fun with Certificates

Fun with Certificates

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RSA Public Key Contents● Modulus (n)● Public exponent (e)

Fun with Certificates

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Public Exponent● Public exponent (e) must be relatively

prime to p-1 for all primes p which divide the modulus

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Jimmy 1414 1314 13 1814 13 18 1814 13 18 18 36

One way function for RSA

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

14 13 18 18 36

One way function for RSA

14 13 18 18 36

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

14 13 18 18 36

One way function for RSA

14

13

18

18

36

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

One way function for RSA

14

13

18

18

36

147 mod 55

137 mod 55

187 mod 55

187 mod 55

367 mod 55

= 105413504 mod 55= 9 = “g”

= 7

= 17

= 17

= 31

= “e”

= “l”

= “l”

= “v”

E(Jimmy) = gellv

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Fun with Certificates part IRSA Cryptography

May 13, 2019

Network SecurityInstitute for Advanced Study

One way function for RSA

9

7

17

17

31

923 mod 55

723 mod 55

1723 mod 55

1723 mod 55

3123 mod 55

= 14 = “J”

= 13

= 18

= 18

= 36

= “i”

= “m”

= “m”

= “y”

D(gellv) = Jimmy

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Fun with Certificates part IRSA Cryptography

May 13, 2019

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Asymmetric Key Demo

Modulo Calculatorhttps://tinyurl.com/rsacalc

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Fun with Certificates part IRSA Cryptography

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Network SecurityInstitute for Advanced Study

Asymmetric Key Cryptography

2*n = 2 * 6 = 12 unique keys