Realization of RSA algorithm for generating large prime number by Miller_rabin algorithm

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ImportMath fromFunctoolsImportReduce#used to combine characters fromOsImportUrandom#system-Random charactersImportBinascii#conversion between binary and ASCII#===========================================defmod_1 (x,n):" "modulo negative 1 algorithm: Calculates the value of x2= x^-1 (mod n), r = gcd (A, B) = ia + JB, x and n are mutual primes" "x0=x y0=N X1=0 Y1= 1X2= 1y2=0 whilen! =0:q= x//n (x, N)= (n, x%N) (x1, x2)= ((x2-(Q *x1), x1) (y1, y2)= ((y2-(Q *y1)), y1)ifX2 <0:x2+=y0ifY2 <0:y2+=x0returnX2#===========================================defFast_mod (a,p,m):" "Fast modulus exponential algorithm: calculates the value of (a ^ p)% m and can be replaced with POW ()" "a,p,m=Int (a), int (p), int (m)if(p = =0):return1R= a%m K= 1 while(P > 1):                if((P & 1)! =0): K= (k * r)%m R= (R * r)%m P>>= 1return(R * k)%m#===========================================defrandint (n):" "Random is a pseudo-random number that requires a higher security number to be generated, so use Os.urandom () or systmerandom module, generate N-byte random number (8 bits per byte), return 16 binary to 10 binary integer return" "Randomdata=urandom (n)returnInt (binascii.hexlify (randomdata), 16)    #===========================================defprimality_testing_1 (n):" "test One, a small prime test, with a small prime number within 100 to detect random numbers x, can be a large probability of elimination is not prime, #创建有25个素数的元组" "Sushubiao= (2,3,5,7,11,13,17,19,23,29,31,37,41                   ,43,47,53,59,61,67,71,73,79,83,89,97)         forYinchSushubiao:ifn%y==0:returnFalsereturnTrue#===========================================defprimality_testing_2 (n, k):" "Test Two, K-detection of n using the Miller_rabin algorithm" "        ifN < 2:                returnFalse D= N-1R=0 while  not(D & 1): R+ = 1D>>= 1 for_inchRange (k): a= Randint (120)#Random numberx =Pow (A, D, N)ifx = = 1orx = = N-1:                        Continue                 for_inchRange (r-1): x= POW (x, 2, N)ifx = = 1:                        returnFalseifx = = N-1:                         Break        Else:                returnFalsereturnTrue#===========================================defGetprime (byte): whiletrue:n=randint (Byte)ifprimality_testing_1 (n):ifPrimality_testing_2 (N, 10) :                                Pass                        Else:Continue                Else:Continue                 returnN#===========================================defRSA (): P=getprime (128)#Large integer of 1024bitQ=getprime (128)         whileP==Q:#avoid the same p/q valueQ=getprime (128) n=p*q#N-Value DisclosureOrla= (p-1) * (q-1)#Euler functionse=524289" "E's choice: The binary representation of e should contain as little as 1. E take e=524289, the second binary is 10000000000000000001, only two 1, fast encryption speed and large numbers" "D=mod_1 (E,orla)Print('the public key is ({0},{1}); \ n the private key is ({2},{3})'. Format (n,e,n,d)) message=input ('Please enter any content that needs to be encrypted:')        #receive data from standard input and output streams, digitize and decryptMessage=list (map (ord,message))Print('Ciphertext digitization:', message) ciphertext=[]         forXinchmessage:ciphertext.append (POW (x,e,n))Print('Ciphertext Encryption:', ciphertext) message=[]         whileTrue:message.append (int (Input ('Enter the redaction group \ n (enter 0 at the end):')))                ifmessage[-1]==0:delMessage[-1]                         Breakplaintext=[]         forXinchmessage:plaintext.append (POW (x,d,n))Print('PlainText decryption:', plaintext) plaintext=list (map (chr,plaintext))Print('plaintext word Fu Hua:', plaintext)Print('plaintext=', Reduce (Lambdax,y:x+y), plaintext))#===================================================RSA ()

Realization of RSA algorithm for generating large prime number by Miller_rabin algorithm