Introduction:
Simple substitution cipher are generally easy to break in aciphertext –only attack using single –letter frequency distribution (cf.[3,6,7,11]) ,cipher based on shifted alphabets are usually easy to solve ,because each ciphertext letter is a constant distant from its corresponding plaintext letter .because simple substitution cipher use a single mapping from plaintext to ciphertext letter ,the single-letter frequency distribution of the plaintext letter is preserved in the ciphertext .homophonic substitutions conceal this distribution by defining multiple ciphertext elements for each plaintext letter .polyalphabetic substitution cipher conceal it by using multiple substitutions.the development of polyalphabetic cipher began with Leon Battista Alberti, in 1568 Alberti puplished a manuscript describing a cipher disk that defined multiple substitutions, most polyalphabetic ciphers are periodic substitution ciphers based on aperiod d,given d cipher alphabets c1,c2,……,cd let fi:p?ci be a mapping from the plaintext alphabets p to the ith cipher alphabet ci (1?i?d),For the special case d=1, the cipher is monoalphabetic and equivalent to simple substitution ,now for vigenere ,Beaufort ,Variant Beaufort and Hill ciphers(cf.[2,8,11]),
And in 1978,Pohlig and Hellman published an encryption scheme based on computing exponentials over a finite field,at about the same time ,Rivest,Shamir,and Adleman published a similar scheme,the encipher and decipher transformation are based on Euler s generalization of Fermat s Theorem ,which states that for every p relatively prime to k(n) ,(cf.[1,4,5,9,10,12]), for digital signature in classical and public key cryptography by using ?-?? and ??-?? laws, I use the laws ?-?? and ??-?? where
?-??=min(max(26-c,k),max(c,26-k))
??-??=min(max(26- ?-??,k),max(?-??,26-k))