Mat 140 Cryptology Day 4
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CryptologyDay 4: Going public
MAT 140: Introduction to the Mathematical Sciences24 September 2008
Robert Talbert, PhDAssociate Professor of Mathematics and Computing Science [email protected]
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Recap of Day 3
•Bits, bytes, and binary representation of text using ASCII
•The XOR operation
•The Simple XOR cipher
•Perfect security and one-time pads
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Alice
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Alice Bob
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Alice Bob
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Enc
rypt
ion
func
tion
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
Dec
rypt
ion
func
tion
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Original plaintext
Dear Bob - The meeting will be at the embassy.
Alice Bob
Enc
rypt
ion
func
tion
Dec
rypt
ion
func
tion
![Page 13: Mat 140 Cryptology Day 4](https://reader034.fdocuments.net/reader034/viewer/2022042513/549327f2ac7959342e8b47c4/html5/thumbnails/13.jpg)
Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Original plaintext
Dear Bob - The meeting will be at the embassy.
Alice Bob
Enc
rypt
ion
func
tion
Dec
rypt
ion
func
tion
How are these communicated?
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The key distribution problem
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The key distribution problem
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The key distribution problem
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The key distribution problem
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The key distribution problem
Insecure channel
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The key distribution problem
Insecure channel
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The key distribution problem
Insecure channel
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The key distribution problem
Insecure channel
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The key distribution problem
Insecure channel
CENSORED
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
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The key distribution problem
Insecure channel
CENSORED
Anonymity
Many-to-many communication
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Activity: A “public-key” cipher
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Why does Kid Crypto work? Can an adversary find the private key from the public key? How does this solve the key distribution problem?
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
One-way trapdoor function
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Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Enc
rypt
ion
func
tion
(ex)
mod
n
Public(e,n)
PrivatedOne-way trapdoor function
![Page 40: Mat 140 Cryptology Day 4](https://reader034.fdocuments.net/reader034/viewer/2022042513/549327f2ac7959342e8b47c4/html5/thumbnails/40.jpg)
Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
(ex)
mod
n
Public(e,n)
PrivatedOne-way trapdoor function
![Page 41: Mat 140 Cryptology Day 4](https://reader034.fdocuments.net/reader034/viewer/2022042513/549327f2ac7959342e8b47c4/html5/thumbnails/41.jpg)
Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
(ex)
mod
n
Public(e,n)
PrivatedOne-way trapdoor function
![Page 42: Mat 140 Cryptology Day 4](https://reader034.fdocuments.net/reader034/viewer/2022042513/549327f2ac7959342e8b47c4/html5/thumbnails/42.jpg)
Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Alice Bob
Enc
rypt
ion
func
tion
(ex)
mod
n
Dec
rypt
ion
func
tion
(dy)
mod
nPublic(e,n)
PrivatedOne-way trapdoor function
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Plaintext
Dear Bob - The meeting will be at
the embassy.
Ciphertext
Qrne Obo - Gur zrrgvat jvyy or ng gur rzonffl.
Original plaintext
Dear Bob - The meeting will be at the embassy.
Alice Bob
Enc
rypt
ion
func
tion
(ex)
mod
n
Dec
rypt
ion
func
tion
(dy)
mod
nPublic(e,n)
PrivatedOne-way trapdoor function
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RSA
Alice
Choose two large prime numbers p, qCalculate n = pq and m = (p-1)(q-1)
Choose e such that gcd(e, (p-1)(q-1)) = 1Choose d such that ed = 1 mod (p-1)(q-1)
Publicize e, n. Keep d private.
To encrypt x: calculate y = xe mod n
Bob
To decrypt y: calculate z = yd mod n.
Fermat’s Little Theorem: xed = x mod n.
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74037563479561712828046796097429573142593188889231289084936232638972765034028266276891996419625117843995894330502127585370118968098286733173273108930900552505116877063299072396380786710086096962537934650
563796359
This number is a product of two primes:
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Modulus (1024 bits):9d 88 94 32 62 30 a3 3b 0f 5b 30 7c d5 69 75 21 25 99 0f e1 a8 c2 7d 5b 2b e9 24 72 48 fa 13 47 7c 53 8b 6a 56 be 66 5a 93 7c 3b bb 84 d4 90 4e ab d5 aa f1 33 de 93 2a 1c 80 e3 f5 19 25 a8 69 d3 55 44 fd 7f 76 bb 28 f5 90 62 69 57 eb 82 ba dd 73 40 c0 dd fb 7e 2b ea 86 8e 83 eb e1 5f cc f4 a5 a4 be 99 4f 90 ff 66 79 b1 44 d4 13 60 96 80 00 3d f8 49 b5 e7 82 54 b3 9d 17 56 cc 90 bb
Exponent (24 bits):01 00 01
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Cutting edge
Design/analysis of block ciphers
Elliptic curve cryptography
Quantum cryptography
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Cryptology at Franklin College
MAT 135 MAT 140
MAT 142Calculus II
MAT 240Methods of
Problem Solving
MAT 233Linear Algebra
MAT 361Modern Algebra
CMP 141Computing I
MAT 300Topics in
Mathematics
MAT 490Individualized
Study
Careers: NSA and other government; network security
and CISSP license; more
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For more information
http://delicious.com/robert.talbert/cryptohttp://www.slideshare.net/rtalbert
http://en.wikipedia.org/wiki/Portal:Cryptography
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