The modulus of RSA has been enlarged over the years in order to thwart improved attacks. As one would assume, public-key algorithms become slower as the modulus length increases. We study the relation between modulus length and performance in this problem. The performance of RSA, and of almost any other public-key algorithm, is dependent on how fast modulo exponentiation with large numbers can be performed.1. Assume that one modulo multiplication or squaring with k-bit numbers takes c · k2 clock cycles, where c is a constant. How much slower is RSA encryption/decryption with 1024 bits compared to RSA with 512 bits on average? Only consider the encryption/decryption itself with an exponent of full length and the square-and-multiply algorithm.

2. In practice, the Karatsuba algorithm, which has an asymptotical complexity that is proportional to klog2 3, is often used for long number multiplication in cryptography. Assume that this more advanced technique requires clock cycles for multiplication or squaring where c’ is a constant. What is the ratio between RSA encryption with 1024 bit and RSA with 512 bit if the Karatsuba algorithm is used in both cases? Again, assume that full-length exponents are being used.

Create a class hand in its own module. one object of class hand represents a hand of cards and so one object stores a number of card objects. for this assignment you will submit three separate modules, one with the definition of class card, one with the definition of class hand and one with the main application that thoroughly tests class hand.class hand must contain the following four methods: 1) , numcardsinhand) takes an integer as parameter and initializes a hand object with numcardsinhand card objects inside it. these card objects are generated randomly. for simplicity, assume an infinite number of decks of cards.2) bjvalue(self) returns the blackjack value for the whole hand of cards3) ) returns a string containing all the cards in the hand4) hitme(self) adds one randomly generated card to the handcreate a main program in its own module that thoroughly tests class hand. you will have three modules/files to upload to your etudes assignment submission: card.py, hand.py and the module that contains your main program.two alternatives for extra credit - you cannot get credit for both! (+1 point): after you have thoroughly tested the class hand and all of its methods, add code to your main program that stores one hand object as a pickle file and reads it back into a new hand object. you are only eligible for this extra credit if class hand has all four of the methods above working.or(+2 points): after you have thoroughly tested the class hand and all of its methods, add code to your main program that stores one hand object as a text file on the disk and reads it back into a new hand object. you are only eligible for this extra credit if class hand has all four of the methods above working.notes: -start by making any and all modifications suggested by my comments to your previous submission of class card from assignment #6 "a robust card object"-once your class card is tested and working well, you will not make any further modifications to it for the purposes of class hand.-you can keep the test code for class card intact. if it is indented inside an if __name__ == "__main__", then it will not be executed when your main program's module imports it.-to save time, write and test one method for class hand at a time.-under no circumstances are you to attempt the extra credit until you are completely finished with writing and testing all the methods in class hand.