Post on 12-Jan-2016
CRYPTOGRAPHY
Presented by: Noushin Ranjkesh
Olinka Bedroya
Sharif University of Technology-1391
Department of Physics, Tehran, Iran
CHAPTER 4THE LANGUAGE BARRIER
The impenetrability of
unknown languages, the Navajo
code talkers of World War II
and the decipherment of
Egyptian hieroglyphs
PURPLE CODE , BATTLE OF MIDWAY
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رمزنگاری، های ماشین بنیادی بیهودگینبردهای در اطالعات انتقال پایین سرعت
اقیانوس های جنگ ویژه به محدود، مناطقگوهای کد از استفاده موجب نهایت در آرام،
. گردید ناواجو
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ناواجو زبان از استفاده های کاستیجنگ در اطالعات رمزگذاری برای
دوم جهانی
های واژه ناواجو،برای زبان در معادل های واژه نبودننظامی
حیوانات نام با جنگ در کاربردی های واژه سازی معادلناواجو زبان در اصیل واژهای و
ادا مشابه صورت به زبانی، هر در که افراد و ها مکان نامشود می
زبان معادل،در دارای های واژه از ای نامه واژه ی تهیهالفبا حرف هر برای ناواجو
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The military terms The Navajo terms
fighter plane amphibious vehicle Submarine
owl (Da-he-tih-hi) frog (Chal) iron fish (Besh-lo)
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PACIFIC Pig Ant Cat Ice Fox Ice Cat
Bi-sodih Wol-la-chee Moasi Tkin Ma-e Tkin Moasi
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DECIPHERING LOST LANGUAGE AND ANCIENT SCRIPTS
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HIEROGLYPH
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HIEROGLYPH از پیش سال هزار سه حدود از ن باستا مصریان زبان
میالد معابد برای کاربردی و زینتی بسیار زبان یک
و هیراتیک زبان به کم کم زبان این نوشتار سختی دلیل بهتر مناسب روزمره در استفاده برای که دموتیک سپس
. اند شده تبدیل است،مسیحیت گسترش مسیح،با میالد از پس قرن چهار حدود در
و شد غالب یونانی کلیسا،زبان نفوذ قدرت افزایش وترکیب از جدیدی و 24الفبای یونانی زبان از 6حرف
شکل قبطی زبان و شد ساخته دموتیک زبان از نشانهگرفت. 11
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HIERATIC
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DEMOTIC
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COPTIC
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THE ROSETTA STONE
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روزتا سنگ روزتا شهر در اسکندر اعزامی شناس باستان گروه توسط
. شد کشف. شود می داری نگه بریتانیا ی موزه در و دموتیک یونانی، زبان سه به ثابت متن یک شامل
. است هیروگلیف
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THOMAS YOUNG
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KARNAK TEMPLE
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Jean-François Champollion
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Berenika
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Ptolemaios
Cleopatra
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RAگفته ) خورشید به درقبطی
شود (می
RAMSS( رامسس)
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CHAPTER 5ALICE AND BOB GO PUBLIC
Modern cryptography,the solution to the so-calledkey-distribution problemand the secret history ofnonsecret encryption
ENTERING THE COMPUTER AGE
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Break of lorenz cypher: sending a same 4000 characters message twice (slightly different)
Bill Tutte
John TiltmanA Lorenz cypher machine
ENTERING THE COMPUTER AGE
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Colossus,delivered 1943
Max Newman
Thomas H. FlowersENIAC ,1945
ENTERING THE COMPUTER AGE
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Differences between computer and mechanical encryption: complexity speed Computers deal with binary numbers
e.g. computer version of a substitution cipher:
ASCII table
Message HELLOMessage in ASCII 10010001000101100110010011001001111Key(DAVID) 10001001000001101011010010011000100Ciphertext 00011000000100001101000001010001011
ENTERING THE COMPUTER AGE
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1947, invention of transistor 1951, Ferranti began to make computers to order. 1953, IBM launched its first computer 1957, introduction of Fortran 1959, invention of the integrated circuit
First transistor Ferranti’s computer IBMs first computer
KEY DISTRIBUTION
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Vigenère key
Delivering the Enigma monthly code book
1970s, Banks needed to deliver keys to customers
KEY DISTRIBUTION
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Quadratic gap is best possible if we treat cipher as a black box oracle[B. Barak and M. Mahmoody-Ghidary. Merkle Puzzles are Optimal]
Merkle puzzles
KEY DISTRIBUTION
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Whitfield Diffie
connections of the world wide web. Colors represent different domains.
KEY DISTRIBUTION
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Martin Hellman
Ralph Merkle
Exchanging keys in person
No key sharing - double locked
Asymmetric key…
ASYMMETRIC KEY
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What symmetric and asymmetric indicate
To build an asymmetric cipher: Alice publishes a public key People lookup for Alice’s Public key They use the public key and encryption method to send
Alice messages Alice uses her private key to decrypt
ONE WAY FUNCTIONS
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Mixing colors
ONE WAY FUNCTIONS
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Modular Exponentiation
Diffie-Hellman
Agree on a public modulus N and a base g Alice chooses a private key x between 1 and N -1 She constructs a public key by computing X=g x mod N Bob chooses a random y and calculate K= X y. Bob sends Alice the enciphered text and Y=g y
Alice calculates the K= Y x and deciphers the text
ONE WAY FUNCTIONS
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RSA CRYPTOSYSTEM
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Ronald Rivest, Adi Shamir and Leonard Adleman.
RSA CRYPTOSYSTEM
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RSA CRYPTOSYSTEM
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N = 114,381,625,757,888,867,669,235,779,976,146,612,010, 218,296,721,242,362,562,561,842,935,706,935,245,733,897, 830,597,123,563,958,705,058,989,075,147,599,290,026,879, 543,541
q = 3,490,529,510,847,650,949,147,849,619,903,898,133,417, 764,638,493,387,843,990,820,577
p = 32,769,132,993,266,709,549,961,988,190,834,461,413,177, 642,967,992,942,539,798,288,533
Thus far, the best way known to invert RSA is to factor N. The best running time for a fully proved algorithm is Dixon’s
Random squares which runs in time It took 2 years to factor a 232 digit number, using hundreds of
machines P should have 1024 bits
THE SECRET HISTORY OF PUBLIC KEY CRYPTOGRAPHY
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James Ellis, joined GCHQ in 1965
Clifford Cocks , joined GCHQ in 1973 Malcolm Williamson , joined GCHQ in 1974Both new and old GCHQbuildings
Brief review of chapter 5
• Birth of computer encryption• Key distribution problem• Asymmetric encryption• Diffie-Hellman cryptosystem• RSA crypto system
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APPENDIX
NUMBER THEORY BASIS FORRSA CRYPTOSYSTEM
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Number Theory Background
is the number of elements in relatively prime to forms an Abeliangroup
Theorem: If then
HOW TO FIND PRIME NUMBERS
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AKS primality test Fermat primality test Miller–Rabin primality test Solovay-strassen primality test
take a preselected random number of the desired length apply a Fermat primality test apply a certain number of Miller–Rabin tests (depending on
the length and the allowed error rate) to get a number which is very probably a prime number.
Deterministic
Probabilistic
HOW TO FIND PRIME NUMBERS
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AKS primality test
Input: integer n > 1.If n = ab for integers a > 0 and b > 1, output composite.
Find the smallest r such that or(n) > log2(n).
If 1 < gcd(a,n) < n for some a ≤ r, output composite. If n ≤ r, output prime. For a = 1 to do if (X+a)n≠ Xn+a (mod Xr − 1,n),
output composite; Output prime.
HOW TO FIND PRIME NUMBERS
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Fermat primality test
Choose random
If so output p as prime; else go back to first step and choose another random number