CS ASSIGNMENT 代写 : Secret Sharing Scheme For Image Encryption

With a ever increasing growth of multimedia applications, security is an important issue in communication and storage of images, and encryption is one of the way to ensure security. Image encryption has applications in internet communication, multimedia systems, medical imaging, telemedicine and military communications. In modern times, cryptography is considered to be a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering [1].

Many encryption schemes have been analyzed as possible solution systems. The basic ideas can be classified into three major types: position permutation [2]&[3], value transformation [4]&[5] and the combined form [6]. The Novel crypto system [7] uses randomly generated self invertible matrix as an encryption key for each block encryption. The resulting image from the algorithm is scrambled using a random matrix which is used as another secret key. This increases the secrecy of data. This method encompasses less computational complexity during decryption, as self invertible matrix [ 8 ] is used as key.

In the present paper an innovative technique for image encryption is proposed based on the random generation of polynomial. The new algorithm provides image encryption at two levels and hence security against the image is achieved at low computational overhead.

II. .Secret Sharing

Any method of dividing a secret into multiple (that is "n") participants is secret sharing. Each person receives a piece of the secret and the secret can be recovered by combining some or all of the shares. The secret is in the form of polynomial of degree "t-1", where "t "is the number of keys needed to get the secret (i.e., threshold value). The polynomial is expressed mathematically as follows.

F(x) = (1)

Where ai is a coefficient.

A. Secret process

A (t,n) threshold secret sharing scheme [1,2] is a cryptographic primitive used to distribute a secret "s" to "n" participants in such a way that a set of "t" or more participants can recover the secret "s" and a set of (t-1) or fewer participants cannot recover the secret "s".

The secret to be shared consists in text data , but also images can be considered. The first scheme to share images was due to Naor and Shamir [3] and it is called visual cryptography. It is based on visual threshold schemes t of n.

In this method, the coefficients a0, a1, …,a t-1 are randomly generated .The polynomial with the coefficients a0,a1, ….,a t-1 of degree (t-1) is represented as follows.

F(x) = a0 + a1 x + …..+ at-1 x t-1. (2)

Let the registered participant be "n" and let t < n, where t is a threshold value. Each participant has their own identity value IDi ( i = 1 to n ) . The function value of the polynomial for the input of participant's ID value is performed. Each function value is given to the corresponding participant. The function value for ID1 is share1; the function value for ID2 is share2 and so on. The sender sends share1 to the participant for ID1, share2 for ID2 and so on. The process is clear from the following flowchart.

Participant

For ID 1

Share

1

F(id1)

F(id1)

Share

2

Participant

for ID 2

F(id2)

. . .

Send to∙ . . ∙ .

. . . .

Participant

for ID n

Share

n

F(idn) ∙ ∙

Fig.1. Secret process flow chart

B. Polynomial generation

The first level of encryption is based on polynomial generation. The polynomial used in this level is generated at random and is of degree (t-1), where t is a threshold value. This could be expressed as follows.

F(x) = (3)

Where ai ia randomly generated coefficients.

III. Encryption Techniques

This technique is based on the following mathematical theorem.