mat 140 cryptology day 4
DESCRIPTION
An overview of public-key cryptography and a wrap-up of this minicourse. For MAT 140: Introduction to the Mathematical Sciences at Franklin College.TRANSCRIPT
CryptologyDay 4: Going public
MAT 140: Introduction to the Mathematical Sciences24 September 2008
Robert Talbert, PhDAssociate Professor of Mathematics and Computing Science [email protected]
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
Alice
Alice Bob
Alice Bob
Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Enc
rypt
ion
func
tion
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
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
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
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
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?
The key distribution problem
The key distribution problem
The key distribution problem
The key distribution problem
The key distribution problem
Insecure channel
The key distribution problem
Insecure channel
The key distribution problem
Insecure channel
The key distribution problem
Insecure channel
The key distribution problem
Insecure channel
CENSORED
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
The key distribution problem
Insecure channel
CENSORED
Anonymity
Many-to-many communication
Activity: A “public-key” cipher
Why does Kid Crypto work? Can an adversary find the private key from the public key? How does this solve the key distribution problem?
Alice Bob
Alice Bob
Alice Bob
Alice Bob
One-way trapdoor function
Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
Plaintext
Dear Bob - The meeting will be at
the embassy.
Alice Bob
Public(e,n)
PrivatedOne-way trapdoor function
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
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
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
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
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
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.
74037563479561712828046796097429573142593188889231289084936232638972765034028266276891996419625117843995894330502127585370118968098286733173273108930900552505116877063299072396380786710086096962537934650
563796359
This number is a product of two primes:
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
Cutting edge
Design/analysis of block ciphers
Elliptic curve cryptography
Quantum cryptography
Cryptology at Franklin College
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Mathematics
MAT 490Individualized
Study
Careers: NSA and other government; network security
and CISSP license; more
For more information
http://delicious.com/robert.talbert/cryptohttp://www.slideshare.net/rtalbert
http://en.wikipedia.org/wiki/Portal:Cryptography