Hill Cipher
HILL CIPHER
TERM-PAPER
3/31/2013
LPU
vidit
Name: Vidit kumar Singh.
Reg no: 11009010
Roll no: B38.
Cap : 323.
Sub : Information Security and privacy.
INDEX
Introduction Workings Decryption Matrix Inverse Hill ciphers that encipher larger blocks Ciphertext Attack Known plaintext attack Security Key size Diffusion and Confusion Conclusion References
Hill Cipher
Introduction
Invented by Lester S. Hill in 1929, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Hill used matrices and matrix multiplication to mix up the plaintext.
To counter charges that his system was too complicated for day to day use, Hill constructed a cipher machine for his system using a series of geared wheels and chains. However, the machine never really sold. [1]
Hill's major contribution was the use of mathematics to design and analyse cryptosystems. It is important to note that the analysis of this algorithm requires a branch of mathematics known as number theory .Many elementary number theory text books deal with the theory behind the Hill cipher, with several talking about the cipher in detail (e.g. Elementary Number Theory and its applications, Rosen, 2000). It is advisable to get access to a book such as this, and to try to learn a bit if you want to understand this algorithm in depth. [2]
Each letter is represented by a number modulo 26. (Often the simple scheme A = 0, B = 1, ..., Z = 25 is used, but this is not an essential feature of the cipher.) To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, again modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n × n matrices (modulo 26). The cipher can, of course, be adapted to an alphabet
TERM-PAPER
3/31/2013
LPU
vidit
Name: Vidit kumar Singh.
Reg no: 11009010
Roll no: B38.
Cap : 323.
Sub : Information Security and privacy.
INDEX
Introduction Workings Decryption Matrix Inverse Hill ciphers that encipher larger blocks Ciphertext Attack Known plaintext attack Security Key size Diffusion and Confusion Conclusion References
Hill Cipher
Introduction
Invented by Lester S. Hill in 1929, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Hill used matrices and matrix multiplication to mix up the plaintext.
To counter charges that his system was too complicated for day to day use, Hill constructed a cipher machine for his system using a series of geared wheels and chains. However, the machine never really sold. [1]
Hill's major contribution was the use of mathematics to design and analyse cryptosystems. It is important to note that the analysis of this algorithm requires a branch of mathematics known as number theory .Many elementary number theory text books deal with the theory behind the Hill cipher, with several talking about the cipher in detail (e.g. Elementary Number Theory and its applications, Rosen, 2000). It is advisable to get access to a book such as this, and to try to learn a bit if you want to understand this algorithm in depth. [2]
Each letter is represented by a number modulo 26. (Often the simple scheme A = 0, B = 1, ..., Z = 25 is used, but this is not an essential feature of the cipher.) To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, again modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n × n matrices (modulo 26). The cipher can, of course, be adapted to an alphabet