RSA Algorithm report

RSA Algorithm report

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  RSA CODE REPORT ABSTRACT Thisreport to document the RSA code and how it works from encrypting certain message to how to decrypt it using general and private keys which will be generated in the given code. mohamed el saidy – 201400711 Under supervision: Dr: Asharaf said Eng: Mohamed Zidan Discrete Math project
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  RSA(Rivest-Shamir-Adleman) Code Report Abstract Thisreport to document the RSA code and how it works from encrypting certain message to how to decrypt it using general and private keys which will be generated in the given code. The sequence of the report will be as following (theory, RSA Algorithm, Matlap implementation, GUI implementation, Challenges then recommendations). Theory Firstly, RSA is a cryptosystem for public-key encryption, and is widely used for securing sensitive data, particularly when being sent over an insecure network such as the Internet. RSA was first described in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman of the Massachusetts Institute of Technology. Public-key cryptography, also known as asymmetric cryptography, uses two different but mathematically linked keys, one public and one private. The public key can be shared with everyone, whereas the private key must be kept secret. In RSA cryptography, both the public and the private keys can encrypt a message; the opposite key from the one used to encrypt a message is used to decrypt it. This attribute is one reason why RSA has become the most widely used asymmetric algorithm: It provides a method of assuring the confidentiality, integrity, authenticity and non-reputability of electronic communications and data storage. RSA derives its security from the difficulty of factoring large integers that are the product of two large prime numbers. Multiplying these two numbers is easy, but determining the original prime numbers from the total - factoring - is considered infeasible due to the time it would take even using today’s super computers. RSA Algorithm The public and the private key-generation algorithm is the most complex part of RSA cryptography. Two large prime numbers, p and q, are generated. A modulus n is calculated by multiplying p and q. This number is used by both the public and private keys and provides the link between them. The public key consists of the modulus n, and a public exponent, e as it's a prime number that is not too large. The e figure doesn’t have to be a secretly selected prime number as the public key is shared with everyone. The private key consists of the modulus n and the private exponent d, which is calculated using the Extended Euclidean algorithm to find the multiplicative inverse with respect to the totient of n.
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  Matlap implementation primegen.m The firstfunction which will be used to generate the two large prime numbers. Egen.m This function to generate the e exponent number in which (gcdf), implemented, is used to assert that e is coprime with m=(p-1)*(q-1). Figure (1) prime generator function Figure (2) e exponent generator function
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  This is theimplementation code for the gcdf.m function. dgenf.m This is the function which is used to generate d which is used with n to decrypt the massage. Figure (3) GCD function Figure (4) d exponent generator function
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  encrypt.m This function isused to convert certain massage to the ciphered text(encrypted), using e and n=p*q through this equation: Me mod n = C (M: stand for massage and C: for ciphered text) decrypt.m This function is used to the Ciphered text to the original massage, using d and n=p*q through this equation: Cd mod n = M (M: stand for massage and C: for ciphered text) Figure (5) encryption function Figure (6) decryption function
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  GUI implementation The wholeimplemented functions have been used to create this simple GUI in Figure (7). Figure (7) RSA GUI
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  Challenges • Matlab haslimited number of digits to store which in case of large numbers (ex..11 digits) truncate the number which causes error in the process. Recommendation • Using language other than Matlab(ex.. C++) to create the project. References http://searchsecurity.techtarget.com/definition/RSA