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암호학 (Cryptology)

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  1. 암호학(Cryptology) 평문 암호문 평문 Bob Alice 공격자 Prof. Jk LEE/security

  2. 1st 16th 비자카드 번호 확인 0699 0043 1313 9642 Select odd numbers 0699 0043 1313 9642 Select even numbers After * 2, if  9 then -9 0699 0083 2323 9682 *10 0+6+9+9+0+0+8+3+2+3+2+3+9+6+8+2 = 70 Prof. Jk LEE/security

  3. 암호학(Cryptology)이란? • 암호화 기법과 암호분석기법에 관한 원리,수단,방법을 연구하는 학문 • 평문의 해독 불가하도록 하는 방법과 해독 불가능한 메시지를 해독 가능하도록 형태를 바꾸는 방법으로 구성 Prof. Jk LEE/security

  4. Basic Encryption and Decryption • S R sender message receiver • S T R sender transmission medium receiver • S R senderaccessreceiver O interceptor/intruder Prof. Jk LEE/security

  5. S T R senderaccessreceiver O interceptor/intruder - block - intercept - modify - fabricate Prof. Jk LEE/security

  6. Terminology • Encryption • Decryption • Cryptosystem: system for encryption and decryption • Plaintext • Ciphertext Prof. Jk LEE/security

  7. Original plaintext plaintext ciphertext decryption encryption Encryption Algorithms Encryption Prof. Jk LEE/security

  8. Original plaintext Original plaintext plaintext plaintext ciphertext ciphertext decryption decryption encryption encryption key key Symmetric cryptosystem Encryption Key:KE Decryption Key:KD Asymmetric cryptosystem Prof. Jk LEE/security

  9. Cryptanalysis • Cryptography: hidden writing • cryptanalyst: studies encryption,encryption message • cryptology: research of encryption and decryption Prof. Jk LEE/security

  10. Cryptanalyst’s chore: - attempt to break a single message - attempt to recognize patterns in encrypted message - attempt to find general weaknesses in an encryption algorithm break an encryption ! Prof. Jk LEE/security

  11. 암호시스템의 설계요건 • 난이도가 클 것 • 키의 크기가 작을 것 • 암.복호화 여건의 간결성과 처리속도의 효율성 • 에러 전파율이 적을 것 Prof. Jk LEE/security

  12. 암호시스템의 분류 • 시대별 분류: • 고전 암호시스템:19세기이전 • 근대 암호시스템:1,2차 대전 • 현대암호화 시스템:1950년이후 • 평문의 암호화 단위분류: • 블록 암호시스템 • 스트림 암호시스템 • 암호화 형식에 의한 분류: • 비밀키(대칭형) 암호시스템:비밀키 • 공개키(비대칭형) 암호시스템:공개키와 비공개키 Prof. Jk LEE/security

  13. 키 생성 알고리즘 비밀키 기밀성과 무결성이 보장되는 채널 Original plaintext plaintext ciphertext decryption encryption 평문 길이 최소 단위:한 개 단위의 비트나 문자 스트림 암호: stream cipher 암호화의 속도가 빠르다 비트가 독립적인 관계로 각각의 비트를 암호의 개별적인 개체로 취급이 가능 오류의 영향이 적다 암호키에 대한 엄격한 동기화 요구 Synchronization! 키 생성 알고리즘이 중요! Prof. Jk LEE/security

  14. 비밀키 기밀성과 무결성이 보장되는 채널 Bolck ciphertext Original plaintext plaintext decryption encryption 평문의 길이가 한개이상 블록 암호:Block cipher DES,RSA등 스트림 암호와 대칭성 암호화,블럭화에 대한 처리 시간이 요구 오류시 다른 비트등에 영향 Prof. Jk LEE/security

  15. 암호화,복호화 키가 동일 관용암호시스템:conventional cryptosystem or 대칭형암호시스템:symmetric cryptosystem Ex) DES 송수신자간에 대칭키(비밀 키) 공유 Prof. Jk LEE/security

  16. 암호화,복호화 키가 다를 경우 공개키암호시스템:Public-key cryptosystem or 비대칭형암호시스템:Asymmetric cryptosystem Ex) 디지털 서명,개인신분확인등에 활용 송신자: 공개키, 수신자: 개인키 Prof. Jk LEE/security

  17. Representation of Characters • Letter/code A 0 B 1 C 2 D 3 E 4 F 5 G 6 H 7 I 8 J 9 K 10 L11 M12 N13 O14 P15 Q16 R17 S18 T19 U20 V21 W22 X23 Y24 Z25 • A + 3 =D or K -1 = J :modular arithmetic Prof. Jk LEE/security

  18. Monoalphabetic ciphers • The Caesar cipher: Ci =E(pi) =pi +3 Plaintext: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Ciphert.: D E F G H I J K L M N O P Q R s T U V W X Y Z A B C Ex) TREATY IMPOSSIBLE WUHDWB LPSRVVLEOH Prof. Jk LEE/security

  19. Example L FDPH L VDZ L FRQTXHUHG L  I ?? I  I+3 I CAME I SAW I CONQUERED Prof. Jk LEE/security

  20. C: L GR QRW OLNH BUXWXV F(m) = (m+?) mod 26 P: I DO NOT LIKE BRUTUS Prof. Jk LEE/security

  21. Advantage/disadvantage of the Caesar cipher • Quite simple cipher • obvious pattern is major weakness 암호화: C = Ek(m) = (m + k) mode 26 복호화: m = Dk(c) = (c - k) mode 26 Prof. Jk LEE/security

  22. Frequency distributions Ex) UZQSOVUOHXMOPVGPOPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWTMXUZUHSX EPTEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ Prof. Jk LEE/security

  23. Frequency distributions • Cipher’s frequency: P 13.13 Z 11.67 S 8.33 U 8.33 O 7.50 M 6.67 H 5.83 D 5.00 E 5.00 V 4.17 X 4.17 F 3.33 W 3.33 Q 2.50 T 2.50 A 1.67 B 1.67 G 1.67 Y 1.67 I 0.83 J 0.83 C 0 K 0 L 0 N 0 R 0 Prof. Jk LEE/security

  24. Frequencies of English letters E 12.75 T 9.25 R 8.50 N 7.75 I 7.75 O 7.50 A 7.25 S 6.00 D 4.25 L 3.75 H 3.50 C 3.50 F 3.00 U 3.00 M 2.75 P 2.75 Y 2.25 G 2.00 W 1.50 V1.50 B 1.25 K 0.50 X 0.50 Q 0.50 J 0.25 Z 0.25 Prof. Jk LEE/security

  25. P:e, Z:t • {S,U,O,M,H} {r,n,I,o,a,s} • {A,B,G,Y,I,J} {w,v,b,k,x,q,j,z} • digraph:2 문자 빈도: “th” • ZW 3times occurs: Z:t,W:h • “ZWP” the : trigraph Prof. Jk LEE/security

  26. UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ t a e e t e a t h a t e e a a VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWTMXUZUHSX e t t a t h a e e e a e t h t a EPTEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ e e e t a t e t h e et Prof. Jk LEE/security

  27. “ it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow” Prof. Jk LEE/security

  28. Other monoalphabetic substitutions • Permutation: number of 1 to 10 • p1 = 1,3,5,7,9,10,8,6,4,2 • p2 = 10,9,8,7,6,5,4,3,2,1 • ex) p1(3) = 5 or p2(7) = 4 Prof. Jk LEE/security

  29. Let a1,a2,…,ak be a set of the plaintext alphabet, p is a permutation of 1,2,..,k in a monoalphabetic substitution each ci is ap(pi). Ex) p(l) = 25 - l then A : z, B:y and Z: a • ABCDEFGHIJKLMNOPQRSTUVWXYZ • ke y • a bc d fg hi j l m no pq r s t u v wxz Prof. Jk LEE/security

  30. ABCDEFGHIJKLMNOPQRSTUVWXYZ • sp ec t a u l r • bd f g h i j kmn oq v wxyz • :spectacular • ex) ABCDEFGHIJKLMNOPQRSTUVWXYZ • a dg j • permutation: p(l) = (3* l) mod 26 • p(K) = (3* 10) mod 26 =30-26=4=e Prof. Jk LEE/security

  31. Cryptanalysis of monoalphabetic ciphers • Brute-force:가능한 모든 키를 시도 • Probable-word attack:추정단어공격 • ex) 계좌 화일의 전송 --> 파일 머릿부분에 키워드의 존재 원시코드--> 표준화 된 위치에 키 문장 • 암호알고리즘의 특성: • 절대 안정성 • 계산상 안정성:정보가치초과,유효기간초과 Prof. Jk LEE/security

  32. steganography • 문자 마킹(character marking) • 보이지 않는 잉크(invisible ink) • 핀 구멍(Pin punctures) • 타자수정리본(tpewriter correction ribbon) Prof. Jk LEE/security

  33. Polyalphabetic substitution ciphers • If T --> a, or T --> b and X --> a or X --> b: • T:high frequency X:low frequency E1(T) = a, E2(T) = b while E1 (X)= b and E2(X)= a • combine two distributions: • odd positions • even positions Prof. Jk LEE/security

  34. Two encryption algorithms • Odd positions: A B C D E F G H I J K L M N O P Q R a d g j m o s v y b e h k n q t w z S T U V W X Y Z c f i l o r u x : p(l) = (3* l) mod 26 Prof. Jk LEE/security

  35. Even positions: A B C D E F G H I J K L M N O P Q R n s x c h m r w bg l q v a f k p u S T U V W X Y Z z e j o t y d i : p(l) = ((5* l)+ 13) mod 26 Prof. Jk LEE/security

  36. example • TREATY IMPOSSIBLE • TREAT YIMPO SSIBL E encryption • fumnf dyvtv czysh h Prof. Jk LEE/security

  37. Vigenere tableaux • “but soft what light through yonder window breaks” juliet : key words • julie tjuli etjul ietju lietj uliet julie tjuli • BUTSO FTWHA TLIGH TTHRO UGHYO NDERW INDOW BREAK En • KOEAS YCQSI ….. Prof. Jk LEE/security

  38. Cryptanalysis of polyalphabetic substitution • Kasiski method for repeated patterns: use repetions in the ciphertext to give cluses to the dryptanalyst of the period P : TOBEO RNOTT OBE K: NOWNO WNOWN OWN C: GCXRC NACPG CXR Prof. Jk LEE/security

  39. Index of coincidence(IC): introduced in 1920 by W. Friedman measures the variation in the frequencies of the letters in a cipheretext Prof. Jk LEE/security

  40. example • Dcrypt using vigenere ciper: TSMVM MPPCW CZUGX HPECP RFAUE IOBQW PPIMS FXIPC TSQPK SZNUL OPACR DDPKT SLVFW ELTKR GHIZS FNIDF ARMUE NOSKR GDIPH WSGVL EDMCM SMWKP IYOJS TLVFA HPBJI RAQIW HLDGA IYOU Prof. Jk LEE/security

  41. Ic =0.04066 : (åP(ai)) • split the ciper text into 5 ection gettings: a->6 g->5 I->6 q->3 v->4 b->2 h->5 m->8 r->6 w->6 c->6 I->10 n->3 s->10 x->2 d->6 j->2 o->5 t->5 y->2 e->5 k->5 p->l3 u->5 z->3 f->6 Prof. Jk LEE/security

  42. We split the cipher text into five sections getting: • TMCHRIPFTSODSEGFANGWESITHRHI from text positions 51, l = 0, I, ...,27. • SPZPFOPXSZPDLLHNRODSDMYLPALY from text positions 51+1, l " 0,1,...,27. • MPHEABIIQNAPVTIIMSIGMWOVBQDO from text positions 51+2, l = 0,1,...,27. • VCGCUQMPPUCKFKZDUKPVCKJFJIGU from text positions 51+3, l = 0,1,..., 27. • MWXPEWSCKLRTWRSFERHLMPSAIWA from text positions 51+4, l = 0,1,..., 27. • 5i=0.04233 5i+1=0.06614 5i+2=0.05026 • 5I+3=0.06614 5I+4=0.04843 Prof. Jk LEE/security

  43. The second section is: SPZPFOPXSZPDLLHNRODSDMYLPALY P-> E, Q-> F: HEOEUDEMHOESAAWCGDSHSBNAEPAN • The fourth section is: VCGCUQMPPUCKFKZDUKPVCKJFJIGU U->A,V-> B: BIMIAWSVVAIQLQFJAQVBIQPLFOMA Prof. Jk LEE/security

  44. C-> A or K-> A. Trying these gives respectively: TAEASOKNNSAIDIXBSINTAIHDHGES CGCEGCFFECAFAJDEAFFCADFDCGE • Of these two the first looks the most promising so we look at what we have for our five sections as rows: • ………………………………………………... HEOEUDEMHOESAAWCGDSHSBNAEPAN ………………………………………………... TAEASOKNNSAIDIXBSINTAIHDHGES ………………………………………………... Prof. Jk LEE/security

  45. M -> E, N-> F,... in the third row giving: TMCHRIPFTSODSEGFANGWES ITHRHI HEOEUDEMHOESAAWCGDSHSBNAEPAN E H M WSTAAIFSHN L A AE K A YEOGN T IVG TAEASOKNNSAIDIXBS INTAIHDHGES • Hence we decide that the plaintext is: THE TIME HAS COME THE WALRUS SAID TO SPEAK OF MANY THINGS OF SHOES AND SHIPS AND SEALING WAX OF CABBAGES AND KINGS AND WHY THE SEA IS BOLLING HOT AND WHETHER PIGS HAVE WINGS Prof. Jk LEE/security

  46. EXAMPLE • “STAR WARS” I KNOW ONLY THATI KNOW NOTHING H UINF NIAP OCSO H UINF INOCHIT Prof. Jk LEE/security

  47. VERNAM CIPHER • VERNAMCIPHER • 21417130122 8157 417 • 76 48 16 82 44 03 58 II 60 05 48 8 • Plaintext VERNAMCIPHE R Numeric Equivalent 21 4 17 13 0 12 2 8 15 7 4 17 + Random Number 76 48 16 82 44 3 58 II 60 5 48 88 =Sum 97 52 33 95 44 15 60 19 75 12 52 105 = mod 26 19 0 7 17 18 15 8 19 23 12 0 1 Ciphertext : tahrsp itxma Prof. Jk LEE/security

  48. LONG SEQUENCE FROM BOOKS • “What of thinking? I am,Iexist,that is certain” • Machine cannot think iamie xistt hatis cert MACHI NESCA NNOTT HINK Prof. Jk LEE/security

  49. USED BY VIGENERE TABLE: • Machines cannot think • uaopm kmkvt unhbl jmed Prof. Jk LEE/security

  50. High-frequency letters: • A,E,O,T : 40% and N,I: 25% a e I n o t A a e I n o t E e l m r s x I I m r w x c N n r w b c h O o s x c d l T t x b g h m Prof. Jk LEE/security