10-01-2011, 02:59 PM
By
SANGEETA PATEL
And
PARTHA PRITTAM NAYAK
ABSTRACT
Security can only be as strong as the weakest link. In this world of cryptography, it is now well established, that the weakest link lies in the implementation of cryptographic algorithms. This project deals with RSA algorithm implementation with and without Chinese Remainder Theorem and also using Variable Radix number System. In practice, RSA public exponents are chosen to be small which makes encryption and signature verification reasonably fast. Private exponents however should never be small for obvious security reasons. This makes decryption slow. One way to speed things up is to split things up, calculate modulo p and modulo q using Chinese Remainder Theorem. For smart cards which usually have limited computing power, this is a very important and useful technique. This project aims at implementing RSA algorithm using Chinese Remainder Theorem as well as to devise a modification using which it would be still harder to decrypt a given encrypted message by employing a Variable radix system in order to encrypt the given message at the first place.
INTRODUCTION
Cryptography, defined as the science and study of secret writing concerns the ways in which communications and data can be encoded to prevent disclosure of their contents through eavesdropping or message interception, using codes, ciphers and other methods, so that only certain people can see the real message.
Security often requires that data be kept safe from unauthorized access. And the best line of defence is physical security (placing the machine to be protected behind physical walls). However, physical security is not always an option, due to cost and/or efficiency considerations. Instead, most computers are interconnected with each other openly, thereby exposing them and the communication channels that they use. With regards to confidentiality, cryptography is used to encrypt data residing on storage devices or travelling through communication channels to ensure that any illegal access is not successful. Also, cryptography is used to secure the process of authenticating different parties attempting any function on the system. Since a party wishing be granted a certain functionality on the system must present something that proves that they indeed who they say they are. That something is sometimes known as credentials and additional measures must be taken to ensure that these credentials are only used by their rightful owner. The most classic and obvious credential are passwords. Passwords are encrypted to protect against illegal usage.
Authorization is a layer built on top of authentication in the sense that the party is authenticated by presenting the credentials required (passwords, smart cards ... etc.). After the credentials are accepted the authorization process is started to ensure that the requesting party has the permissions to perform the functions needed.
Data integrity and Non-Repudiation are achieved by means of digital signature, a method that includes performing cryptography among other things.
Cryptography can essentially be classified into two types, the symmetric and asymmetric type. With a secret or symmetric key algorithm, the key is a shared secret between two communicating parties. Encryption and decryption both use the same key. The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES) are examples of symmetric key algorithms.
With a public key (PKA) or asymmetric key algorithm, a pair of keys is used. One of the keys, the private key, is kept secret and not shared with anyone. The other key, the public key, is not secret and can be shared with anyone. When data is encrypted by one of the keys, it can only be decrypted and recovered by using the other key. The two keys are mathematically related, but it is virtually impossible to derive the private key from the public key. The RSA algorithm is an example of a public key algorithm.
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