Soft public key Cipher

Received, 2019 Encryption in general is the process of keeping up the secrecy of data (both fixed and versatile) utilizing programs that can Convert and make an interpretation of that data into codes so that whenever got to by unapproved people doesn't They can comprehend anything since what appears to them is a blend of images, numbers and unlimited characters, the file is encrypted And decryption by password, which must be known to both parties (sender and receiver) This is called With symmetric encryption, Decryption means decryption. The quality and viability of encryption rely upon two key factors: the algorithm, and the key length evaluated by Bit, the higher the bit, the greater the security and difficulty of decrypting. The concept of soft set was studied and applied on the public key cryptography like simple Knapsack and Trapdoor Knapsack ciphers. Significant results were presented that was the measure of the evaluate encryption using the SNR and PSNR. Keyword:


Introduction
Moldtsov introduced in 1999 new mathematics to deal with the uncertainty concept of soft set Since this concept make the link between the set with the parameters of the set does not affect the current methods and be free of difficulties Since this theory has multiple applications has been previously proved by Moldtsov [1].Maji,p.k [2], from the theoretical side of soft sets, defined and studied many operations.Knapsack problem depending on the difficulty of solving that uses for either secrecy or authenticity, but not both the simple. Trapdoor Knapsack method depending on the Knapsack problem [3,4]. The signal to noise ratio (SNR) is an appropriate yardstick that uses in the characterization of the physical layer performance. A high SNR at the receiver allows an accurate synchronization. Various modulation formats applies to exploit the high SNR available at receiver for decoding and This scale Peak signal-to-noise ratio (PSNR) is used which represents the light accuracy between the ratio of the maximum value of the signal potential forces with the power of noise sabotage [5][6][7][8][9][10].

Definition
Let E be a set of parameters defined on the initial universal set I, called the pair (F, S) and defined on the set I by the soft set where F: SP (I) is an mapping and P (I) represents the set of power for I as well SE [1].

Example
Suppose the following: I is a diplomatic men under consideration E Represents a set of parameters and each parameter indicates either a word or a sentence E={tall ,average length ,small ,black hair ,blonde hair ,fat man ,graceful man ,weak man ,black eyes ,blue eyes ,white skin ,black skin} In order to define the soft set (F,S) in this case describes the attributes of the human, consider six men in the universe set I ,given by I={H 1 ,H 2 ,….,H 6 } ,and let S={a 1 ,a 2 ,….,a 8 } such that a 1 , a 2 ,….., a 7 and a 8 stand for the parameters: tall, small, black hair, blonde hair, black eyes , blue eyes, white skin and thin respectively. Suppose that :F(a 1 ) ={H 3

Trapdoor Knapsack
Merkle and Hellman convert it to a Trapdoor Knapsack [4], which hard to solve -choose A=(a 1 ,a 2 ,….a n ) , a i  -choose U2a n  -choose W so that gcd(U,W)=1 -compute W -1 = W (u)-1 mod U -compute E A =W*A mod U Where E A is public-key,A and W -1 are secrete to encipher is : C=E A *M To decipher : C'=w -1 *C mod U you have A and C' solve linearly form C'=A*M

Measurement (SNR and PSNR)
In this section we will explain the measurement of SNR and PSNR shown in the following

Conclusions
We calculated during the calculation of the SNR and in contrast to his PSNR that the ratios of the difference between the two methods are different where in the simple Knapsack cipher that the difference was more than 3 which is a reasonable rate and is a method is noticeable compared with the soft Trapdoor Knapsack which gave very good ratios more than 27 and therefore more reliable in Encryption method which gives more security and all this can be seen in the previous table .