1장 암호 개론 ·································································································· 1

1.1 암호 시스템의 분류 / 3

1.2 용어 설명 / 5

1.3 암호의 수학적 표현 / 6

2장 고전 암호 ································································································ 11

2.1 스키테일 암호 / 11

2.2 카이사르 암호 / 13

2.3 아핀 암호 / 15

2.4 DES 암호 / 17

2.5 암호의 공격 / 20

3장 암호를 위한 기초 정수론 ······································································· 25

3.1 정수 기초 이론 / 26

3.2 소수판정법 / 29

3.3 확률적 소수판정법 / 34

3.4 페르마의 정리를 사용한 소수 판정 / 35

3.5 유사소수 / 37

3.6 카마이클 수 / 42

3.7 밀러-라빈 소수 판별법 / 43

3.8 폴라드(Pollard) 방법에 의한 인수분해 / 46

4장 암호를 위한 기초 현대대수 ··································································· 59

4.1 군의 기본 정리 / 59

4.2 환의 기본 정리 / 63

5장 공개키 암호시스템 ················································································· 66

5.1 공개키 암호시스템 / 66

5.2 RSA 공개키 암호시스템 / 72

5.3 빠른 지수법 / 76

5.4 RSA 암호시스템 실행 / 79

5.5 RSA의 안전성과 암호 공격 / 81

5.6 인증 / 85

5.7 비밀키 암호시스템과 공개키 암호시스템의 문제점 비교 / 87

6장 정수 성질과 메이플 프로그램 ································································ 91

6.1 정수의 기본 성질과 메이플 명령어 / 91

6.2 메이플 프로그램으로 정수 기초 이론 / 97

6.3 소수 판정 정리 / 102

6.4 인수분해 방법 / 106

6.5 소수성 판정법 / 109

6.6 메이플의 기본 명령어들 / 112

7장 정수방정식 풀이 ···················································································· 115

7.1 일차방정식 / 115

7.2 합동방정식 / 120

7.3 이차 합동방정식 / 124

8장 라빈 암호와 루카스 암호 ····································································· 138

8.1 라빈 암호 / 138

8.2 루카스 암호 / 151

8.3 루카스 수열 / 159

8.4 루카스 함수와 루카스 암호 / 162

8.5 새로운 공개키 암호시스템, LUC / 177

8.6 루카스 암호시스템의 대수적 발전 / 186

9장 디피-헬만, 엘가말, 메시-오무라 암호 ················································ 192

9.1 공개키 암호 / 192

9.2 디피-헬만의 키교환 / 193

9.3 엘가말 암호 방식 / 198

9.4 메시-오므라 암호 / 200

10장 영지식 증명과 동전 던지기 ································································· 203

10.1 영지식 증명 / 203

10.2 수학에서 영지식 증명의 사례 / 205

10.3 영지식 증명 프로토콜 / 209

10.4 영지식 게임 - 제곱근 게임 / 215

10.5 전화상의 동전던지기 / 218

11장 암호 공격 ····························································································· 230

11.1 암호 공격의 종류 / 231

11.2 RSA 암호의 공격 / 234

11.3 연분수 / 235

11.4 연분수와 RSA / 244

12장 여러 암호들 I - 행렬 암호와 힐 암호 ··············································· 259

12.1 행렬 암호 / 259

12.2 힐 암호 / 263

13장 여러 암호들 II - 배낭 암호와 통계 암호 ··········································· 275

13.1 배낭 암호 / 275

13.2 통계 암호 / 293

14장 타원곡선과 타원곡선 암호 ECC ························································· 309

14.1 실수 위에서의 타원곡선 / 310

14.2 실수 위에서 타원곡선 군 / 314

14.3 임의의 체   상에서의 타원곡선 / 319

14.4 유한체   에서의 타원곡선 군 / 321

14.5 타원곡선 암호시스템(공개키 암호, ECC 암호) / 327

14.6 타원곡선의 이산대수 문제 / 331

[부록 1] / 340

[부록 2] / 341

15장 부호 이론 ····························································································· 345

15.1 부호의 기본 이론 / 346

15.2 대수적 부호들 / 354

15.3 유한체   위에서 부호 / 366

16장 디지털 서명, 인증, 식별 ······································································ 376

16.1 서명 / 377

16.2 필기 서명과 디지털 서명의 차이점 / 379

16.3 디지털 서명 알고리즘 / 380

17장 정보 보호 ····························································································· 387

17.1 정보 사회에서의 정보 보호 / 387

17.2 정보 사회에서의 정보 보호학 / 389

17.3 정보 보안 / 391

17.4 보안과 해킹 / 394

17.5 바이러스와 악성코드 / 397

연습문제 정답 및 해설 / 401