Algorithmic Mathematics

COM373 Algorithmic Mathematics  Assignment (2nd Option) (Weight 20%) RSA Cryptography Note: Anyone taking the lecture can prefer this option (Yes, the previous grading policy has changed!). As you know, 1st option is participating in online lectures actively and answering questions anytime your name is picked from the list.  “RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers.” For more please visit RSA (cryptosystem) – Wikipedia 1. Find a working RSA implementation source code that can work with arbitrarily large integers, which means integers can have 1000 or more decimal digits. An open-source code that you can use is given here: GitHub – abdallahelattar/RSA-and-Big-Numbers-Implementation: RSA Encryption and Decryption using Public and Private keys including other operations. (This code works in Visual Studio (C++ empty project), but there is no clear explanation of functions used. Some large primes having more than 100 digits are provided in the Rea_Me file.) 2. Run the code and in a video, explain how the core algorithms in RSA are coded.  a. Explain general RSA algorithm b. Explain primality test algorithm c. Explain modular exponentiation algorithm Use Free screen recorder, video editor for Windows & macOS ( for video recording. The recording must show your face in the corner. 3. Find an alternative for the modular exponentiation algorithm. You can start from here: iscturkeyHaticeKübraGüner.pdf Code it as an alternative function. Compare the original algorithm in your original code with this one, based on running time in seconds, for numbers having more than 150 decimal digits. In your video explain your alternative algorithm. Give complexities for both algorithms and give running time results. Submission material.  1. Source Code. 2. Link for downloading the video (Video must be 30 minutes, at least. It must show your face. Otherwise your submission will not be valid.) 3. Report.

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