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Hill Cipher & Vigenere CipherKriptografi - Week 4

Aisyatul Karima, 2012

Standar Kompetensi Pada akhir semester, mahasiswa menguasai pengetahuan, pengertian,

& pemahaman tentang teknik-teknik kriptografi. Selain itu mahasiswadiharapkan mampu mengimplementasikan salah satu teknik kriptografiuntuk mengamankan informasi yang akan dikirimkan melalui jaringan.

Menganalisa perbedaan metode Hill cipher dengan metode kriptografisebelumnya

Menguasai teknik enkripsi hill cipher Menguasai teknik dekripsi hill cipher Menyelesaikan soal teknik hill cipher Menguasai teknik vigenere cipher Menyelesaikan soal teknik vigenere cipher

Kompetensi Dasar

Contents

1

Hill Cipher Method2

Hill Cipher Decryption Technique

3

Introduction

4

Hill Cipher Encryption Technique

References

6

7

Conclusion

5 Vigenere Cipher

Introduction

Hill Cipher is one of symmetrical keycryptography algorithm. Hill Cipher uses matrix m x m as a key to

encryption and decryption process. The basic theory that used on Hill Cipher are

matrix multiplication and matrix inverse.

Introduction

Matrix : Matrix is the structure of element scalar on

rows and columns The length matrix A consist of m rows and n

column (m x n) is : The a ij are called matrix element on rows-i and column-j

Introduction

If m = n, then the matrix called square matrix. The matrix that have element aij where i = j = 1

and the another element is 0 called identitasmatrix (I). A metrix B called invers from matrix A if

AB = I. B usually wrote on A-1.

10

Introduction

Arithmatic operation matrix : Summation

• Summation on 2 matrix ; if it has the same length.

• Summation using add each element matrix that has the same position.

Introduction Multiplication

• Two matrix can be multiply if amount of 1st matrix column has the same with amount of the 2nd matrix rows.

Multiplication using scalar matrix• For k is scalar, then multiplication matrix A with k is multiply

every element matrix with k.

Hill Cipher Method

Another interesting multiletter cipher is the Hillcipher It is developed by the mathematician Lester Hill

in 1929 Hill Cipher is one of the implementation

arithmetic modulo on cryptography. Hill Cipher uses square matrix as the key to

encryption and decryption process.

Hill Cipher Method

This technique was made to create theciphertext that unbreakable using analysisfrequency technique. Hill Cipher do not replace the same letter on

plaintext with the another letter on ciphertextbecause uses matrix multiplication on encryptionand decryption process.

Hill Cipher Method Although uses matrix multiplication, Hill

Cipher also uses invers matrix technique. The key on Hill Cipher is matrix n x n with n is

length of letter block. Matrix K which is as key must be an invertible

matrix, which is has inverse K-1

The inverse K-1 of a matrix K is defined by theequation K K-1 = K-1 K = I

Hill Cipher Encryption

Encryption process on Hill Cipher works eachplaintext block. The length of block must same with the length of

Key matrix. The encryption algorithm takes m successive

plaintext letters and substitutes for them mciphertext letters.

Hill Cipher Encryption

The substitution is determined by m linearequations in which each character is assigned anumerical value (a = 1, b = 2 ... z = 0).

Hill Cipher Encryption

Regarding mathematic, encryption process onHill Cipher describe as follow :

C = K . P (equation 1) C = Ciphertext K = Key P = Plaintext

For example, plaintext P:P = STRIKE NOW

Define the ciphertext using matrix key P = ……………………… ??

Hill Cipher Encryption

Plaintext will be encrypted using Hill Cipher techniquewith Key K is a 2x2 matrix.

Because length of Key matrix is 2, so the plaintext splitinto block that each length block is 2 character.

Because the last character don’t have a pair, so giventhe same pair character that is W.

Plaintext become STRIKENOWW.

Hill Cipher Encryption

The 1st block from plaintext P is :

This block plaintext will be encrypted using KeyK as follow :

Hill Cipher Encryption The result produce the number doesn’t

correspondence with the letter, so uses themodulo 26 we can find the answer.

The character that correspondence with 7 and20 are G and T. so Sbecome G and T become T. After finished the encryption process for all block

plaintext, so the ciphertext is… ???

Hill Cipher Decryption The decryption process same with the

encryption process. Although, the key matrixmust be inverse. Regarding mathematic, decryption process

requires using the inverse of the matrix K. The equation can be reduced from the equation

(1)

The equation of decryption process :

Hill Cipher Decryption

Using this key :

Ecryption process starting by find the matrixinvers K Define the inverse using row operation method or

determinan method. After calculation, matrix K-1 that is invers from matrix

K, are :K-1 = ……… ???K.K-1 = ……… ???

Hill Cipher Decryption Result :

Ciphertext C = GTNKGKDUSK, will be decrypted usingdecryption key K-1 with the equation.

Decryption process works each block like encryptionprocess.

At first, replace the letters on ciphertext become thenumerical sequence.

C = 7 20 14 11 7 11 4 21 19 11

Hill Cipher Decryption

1st block decryption process :

2nd block decryption process :

After finished decryption process, the plaintextare …. ???

Hill Cipher Decryption 1st block decryption process :

2nd block decryption process :

The result :

P = 19 20 18 9 11 5 14 15 23P = STRIKENOW

Kriptografi Klasik

Vigenere Chiper Angka

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

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Kunci : CIPHER ( 2,8,15,7,4,17),

K A R I M A10 0 17 8 12 0

2 8 15 7 4 1712 8 32 15 16 17

K A R I M A

Conclusion

Hill Cipher is the classic cryptography algorithmwhich is unbreakable. The key matrix must be a invertible matrix.

Greater the key matrix, stronger the security. Hill Cipher strong on ciphertext-only attack but

weak if attack using knownplaintext attack.

Referensi

Munir, Rinaldi, Diktat Kuliah IF5054 Kriptografi,Program Studi Teknik Informatika, SekolahTeknik Elektro dan Informatika, 2006. Forouzan, Behrouz, Cryptography and Network

Security, McGraw-Hill, 2006. H. Anton, C. Rorres, Elementary Linear Algebra,

John Wiley & Sons, 2000 Munir, Rinaldi, Diktat Kuliah IF2153 Matematika

Diskrit, Program Studi Teknik Informatika,Sekolah Teknik Elektro dan Informatika, 2006.

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