fun with certificates part i - ias security · 5/13/2019 · fun with certificates part i rsa...
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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
[email protected] - @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
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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
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
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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
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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
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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Symmetric Box Demo
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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
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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
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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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One way function
X
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Fun with Certificates part IRSA Cryptography
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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
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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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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
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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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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
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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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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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Fun with Certificates part IRSA Cryptography
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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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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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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
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
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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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Asymmetric Key Cryptography
2*n = 2 * 6 = 12 unique keys