To build the program please run the following command

$ g++ BigInt.cpp RSA.cpp hm6.cpp -o hm6

To Execute the program $./hm6

<<<<<<< HEAD Observations: 1. -We found that all the non prime numbers above 30,000 were unsuccessful in running RSA.

if we select a number n=p x q where p,q are both prime, we will have selected a number we can factor but, if it is large enough, no one else can factor. The reason for this is because, using known factorization algorithms for arbitrary integers, the running time of such algorithms depends on the relative size of the second largest prime factor of the input. This means that given the public exponent e only you can determine the private exponent d.

-Challenge response scheme worked on the 16 bit random numbers which were generated.

571c990358d959646cff8cf9677b14233f3b5e8e

Sample run hm6 : ( we have used time delay so that the same random number is not generated by the generator)

Shrirangs-MacBook-Pro:HM6 shrirang$ ./hm6

1)------------------Encryption and Decryption using RSA---------------------- a) 10 instances of RSA routine(argument-less) encryption-decryption

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

Message: 0x0A99 986D Encrypted: 0x0002 A3F5 3034 Decrypted: 0x0A99 986D

b) 5 RSA instances(1 prime number(>30,000) as argument) encryption-decryption

Message: 0x257F 009A Encrypted: 0xF48D 7388 Decrypted: 0x257F 009A

Message: 0x03C9 BB64 Encrypted: 0xB8D5 C8F0 Decrypted: 0x03C9 BB64

Message: 0x03C9 BB64 Encrypted: 0xB2F2 402B Decrypted: 0x03C9 BB64

Message: 0x1ACE EEFD Encrypted: 0x8A16 07C6 Decrypted: 0x1ACE EEFD

Message: 0x1ACE EEFD Encrypted: 0xC598 5C3E Decrypted: 0x1ACE EEFD

c) 5 RSA instances(2 prime numbers(>30,000) as arguments) encryption-decryption

Message: 0x60C2 54AB Encrypted: 0x1DA8 E6A4 Decrypted: 0x60C2 54AB

Message: 0x60C2 54AB Encrypted: 0x1338 A2CB Decrypted: 0x60C2 54AB

Message: 0x60C2 9652 Encrypted: 0x60AE 1F00 Decrypted: 0x60C2 9652

Message: 0x60C2 D7F9 Encrypted: 0x6003 8944 Decrypted: 0x60C2 D7F9

Message: 0x60C2 D7F9 Encrypted: 0x410D 8C3D Decrypted: 0x60C2 D7F9

d) 5 RSA instances(2 non prime numbers(>30,000) as arguments) encryption-decryption

Message: 0x60C3 19A0 Encrypted: 0x514C 6880 Decrypted: 0x0765 4AB0

Message: 0x60C3 19A0 Encrypted: 0x1DD0 FD40 Decrypted: 0x3186 3100

Message: 0x60C3 19A0 Encrypted: 0x1DD0 FD40 Decrypted: 0x3186 3100

Message: 0x60C3 19A0 Encrypted: 0x10C9 CA78 Decrypted: 0x2BB8 C728

Message: 0x60C3 19A0 Encrypted: 0x3C2C D968 Decrypted: 0x339F E7BC

Message: 0x60C3 19A0 Encrypted: 0x2B32 8800 Decrypted: 0x3530 0C00

Message: 0x60C3 19A0 Encrypted: 0x3C2C D968 Decrypted: 0x339F E7BC

Message: 0x60C3 19A0 Encrypted: 0x10C9 CA78 Decrypted: 0x2BB8 C728

Message: 0x60C3 5B47 Encrypted: 0x106C A157 Decrypted: 0x2197 BB97

Message: 0x60C3 5B47 Encrypted: 0x106C A157 Decrypted: 0x2197 BB97

2)--------------------Challenge response scheme-------------------- Plain Text:0x5EFA FBBC Decrypted Text:0x5EFA FBBC Challenge response scheme is Successful

3)------------------Blind signature--------------------- message: 0x2FA5 245B signature: 0x0001 0B3D DF46 decrypted: 0x2FA5 245B

Blind signature: Blind signature Successful