Sobre el Dinámico y Salvaje Mundo de la Criptología Matemática

Transcription

UNIVERSIDAD NACIONAL DE TRUJILLO - IV FAST WORKSHOP ON APPLIED AND COMPUTATIONAL MATHEMATICS
Sobre el Dinámico y Salvaje Mundo de la
Criptología Matemática
Adler Rensso Chung Gonzalez
∗ Universidad
Nacional de Trujillo
IV FAST WORKSHOP ON APPLIED AND
COMPUTATIONAL MATHEMATICS
Trujillo-Perú
Enero 5-6, 2011
UNT
...Salvaje Mundo de la Criptología Matemática
CRYPTOGRAPHY
Cryptography is the study of the processes of encryption
(mapping the original message, plaintext, into a secret form,
ciphertext, using the encryption key), and decryption (inverting
the ciphertext back to the plaintext, using the corresponding
decryption key).
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CRYPTOGRAPHY
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CRYPTOSYSTEMS
Modern cryptography is the study of the mathematical systems
of encryption and decryption.Such mathematical system is
called the cryptographic system, or cryptosystems for short.
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CRYPTANALYSIS
Cryptanalysis is the study of breaking the encryptions without
the knowledge of the key, i.e., the study of the cryptanalytic
attacks on cryptosystems, aiming at breaking the
cryptosystems without using/knowing the keys.
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THE KERCKHOFFS PRINCIPLE
A cryptosystem should be secure even if the attacker knows all
details about the system, with the exception of the secret key.
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SHANNON’S MAXIM
The enemy knows the system being used.
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Shift Cipher (or Caesar Cipher)
Encoding of letters for the shift cipher:
A ↔ 0, B ↔ 1, C ↔ 2, · · · , Z ↔ 25
Now, the ciphertext letters are now elements of the ring Z26
Let x, y , k ∈ Z26
Encryption: ek (x) = x + k mod 26.
Decryption: dk (y ) = y − k mod 26.
Example:
Let the key be k = 17, and the plaintext is:
ATTACK = x1 , x2 , · · · , x6 = 0, 19, 19, 0, 2, 10.
The ciphertext is then computed as:
y1 , y2 , · · · , y3 = 17, 10, 10, 17, 19, 1 =rkkrtb
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Turing was a quite brilliant mathematician, most famous for his
work on breaking the German Enigma codes. It is no
exaggeration to say that, without his outstanding contribution,
the history of World War Two could well have been very
different.
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Cryptography concentrates on three fundamental
paradigms:
Confidentiality. The information should not leak to any
unexpected party.
Integrity. The information must be protected against any
malicious modification.
Authentication. The information should make clear who the
author of it is.
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Some modern cryptographic problems:
Nonrepudiation. In the case of a dispute on the origin of
the document, someone should be able to formally prove
that he is not the author. This repudiation proof should be
made impossible if he actually is the author.
Electronic payment. The notion of electronic coin should
be protected against, for instance, double spending,
because it is easy to copy digital information.
Anonymity. Privacy protection may require anonymity
enforcement.
Electronic votes. Democracy protection requires that
ballots should be anonymous, that a single person should
not vote more than once, and that people should not be
able to prove for whom they voted afterwards.
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CRYPTOLOGY
EN BREF
def
Cryptography = Encryption
L
Decription
def
Cryptanalysis = Cryptanalytic Attacks on Encryption
def
Cryptology = Cryptography
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L
Cryptanalysis
RSA
Rivest,Shamir,Adleman
RSA was invented in 1978 by Ron Rivest, Adi Shamir, and
Leonard Adleman, and takes its name from their initials.
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Elliptic Curve Cryptography
The idea to use elliptic curves in cryptography was
independently proposed by Neil Koblitz and Victor Miller in the
mid 1980s.
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On cryptanalytic attacks
It is impossible to foresee the consequences of being clever.
CHRISTOPHER STRACHEY
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Ciphertext-only attack.Eve has the ability to obtain
ciphertexts.
Known-plaintext attack.Eve has the ability to obtain
plaintext-ciphertext pairs.
Chosen-plaintext attack.Eve has the ability to obtain
ciphertexts for plaintexts of her choosing.
Adaptively-chosen-plaintext attack. This is the same as the
previous attack, except now Eve may do some analysis on
the plaintext-ciphertext pairs, and subsequently get more
pairs.
Chosen- and adaptively-chosen-ciphertext attack.These
two attacks are similar to the above plaintext attacks.
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A PLAINTEXT
ODQSOCL OW GIU BOEE QRROHOCS QV GIUR KIA QF Q
DQCQSLR WIR ICL IW CQFQF EIYQE YIDJUVLR FGFVLDF
GIU SLV OCVI GIUR IWWOYL IC VXQV DICPQG DIRCOCS
VI WOCP VXL JXICLF ROCSOCS LHLRG YQEELR OF Q
POFVRQUSXV YICWUFLP CQFQ BIRMLR QCP LHLRG
YQEELR QFFURLF GIU VXQV XOF IR XLR WOEL IR
QYYIUCVOCS RLYIRP IR RLFLQRYX JRIKLYV LHLRG ICL
IW BXOYX OF DOFFOCS WRID VXL YIDJUVLR FGFVLD OF
QAFIEUVLEG HOVQE
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DISTRIBUTION OF THE CHARACTERS IN A
TYPICAL ENGLISH TEXT
Letter
A
B
C
D
E
F
G
H
I
Probability
8.2%
1.5%
2.8%
4.3%
12.7%
2.2 %
2.0%
6.1%
6.0%
Letter
J
K
L
M
N
O
P
Q
R
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Probability
0.2 %
0.8 %
4.2 %
2.4%
6.7%
7.5%
1.9 %
0.1 %
6.0%
Letter
S
T
U
V
W
X
Y
Z
Probability
6.3%
9.1%
2.8%
1.0%
2.3%
0.1%
2.0%
0.1%
DECRYPTED SECRET
IMAGINE IF YOU WILL ARRIVING AT YOUR JOB AS A
MANAGER FOR ONE OF NASAS LOCAL COMPUTER
SYSTEMS YOU GET INTO YOUR OFFICE ON THAT
MONDAY MORNING TO FIND THE PHONES RINGING
EVERY CALLER IS A DISTRAUGHT CONFUSED NASA
WORKER AND EVERY CALLER ASSURES YOU THAT HIS
OR HER FILE OR ACCOUNTING RECORD OR RESEARCH
PROJECT EVERY ONE OF WHICH IS MISSING FROM THE
COMPUTER SYSTEM IS ABSOLUTELY VITAL
Imagine, if you will, arriving at your job as a manager for one of NASA’s local computer systems. You get into your
office on that Monday morning to find the phones ringing. Every caller is a distraught, confused NASA worker. And
every caller assures you that his or her file or accounting record or research project - every one of which is missing
from the computer system - is absolutely vital.
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Social Engineering Attacks
For instance, forcing someone to reveal his/her secret key, e.g.,
by holding a gun to his/her head can be quite successful.
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CRYPTANALYSIS
Classical cryptanalysis
1
2
Mathematical analysis
Brute-Force Attacks: which treat the encryption algorithm
as a black box and test all possible keys
Implementation Attacks: side-channel analysis can be
used to obtain a secret key, for instance, by measuring the
electrical power consumption of a processor which
operates on the secret key.
Social Engineering
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QUANTUM CRYPTOGRAPHY
I think that it is safe to say that nobody understands quantum
mechanics.
Richard Feynman
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WIKILEAKS
The Chaos Computer Club (CCC)
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Sobre el Dinámico y Salvaje Mundo de la Criptología Matemática

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