Write some Software

Implement the Euclid algorithm in java . Your need to use a package for large number operations:

1. It finds the greatest common divisor between two numbers. int gcd(int a, int b)// it returns gcd(a,b).

2. It computes the inverse element:

int inverse(int a, int m)// it returns b such that ab=1(mod m). Print out your source code and provide sufficient your test results.

4. Implement with java the first randomized algorithm in the slides for checking prime numbers. Use a packing for large number operations. Print out your source code and provide sufficient your test results. You need to test prime numbers of 100 digits. Run your program on numbers less than 1000. What is the probability to give the wrong answer?

Implement the RSA with java. You need to use a package for large number operations:

1. It should be able to find a public key given a private key

2. It has an efficient way to compute the exponential function.

3. It can select large two prime numbers

4. It can do both encryption and decryption.

You need to use the modules in problems 3 and 4 . Print out your source code and provide sufficient your test results.

Java

Project ID: #11839414

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