Tancia Boone |
SCHOOL: The University of Mississippi
MAJOR: Mathematics/Math Ed MENTOR: Dr. Prezmo Kranz EXPECTED GRADUATION DATE: May 2003 ORGANIZATIONS & HONORS:
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ABSTRACT
Mathematical Principles of RSA Cryptography
| Cryptography is considered an art or science of secret messaging. It is a scientific method with usage of mathematical functions to encode and decode message. All messages have to be converted into a form that is only understood by the intended recipient. The two elements that make up a cryptosystem are encryption and decryption. Encryption is the process that plain text is converted to, to make the coded message (cipher text). Decryption is the process of the cipher text being converted back into original formation by the intended audience. In the world today, the usage of this coding process includes ATM machines for electrical transfers, protects tapping in cell phone calling, encodes and decodes data entry while using the Internet, etc. However, the only secure form of cryptography known today is RSA (named for the three inventers-Ronald Rivest, Adi Shamir and Leonard Adleman) Cryptography. The purpose of this system is to create a one-way function system; a system that computes a function easily but makes inverting almost impossible. Suppose p and q are large prime numbers (numbers that are divisible by 1 and itself) containing 500 digits each. The results n=pq is a 1000 digit composite number. On a typical computer the multiplication takes under a second to compute. The variables p and q are considered private keys. The person decoding the message should know the private keys, whereas the general public knows the public key, which is n. Instead of given the primes, p and q, one is given the product n. From the number assigned to n, the two prime factors are to be founded. Using trail division to factor n would take 10500: 109 seconds or centuries to factor. The illustration above shows the basic structure of RSA Cryptography. |