The Use of Locally Invertible Convolutional Encoders for Encryption

Symmetric key crypto-systems use a single key to encrypt and decrypt data to create a secure communication over an insecure channel. Traditionally, this has been accomplished by creating a sequence of seemingly random numbers from the key and combining the sequence with the intended plaintext message. This method has been effective, with variations and iterations, for almost forty years.;This dissertation presents a new variation of symmetric cipher based on convolutional codes. The method creates a large amount of valid parity from random input into a very large convolutional encoder and combines the output with a modified plaintext message. The decoder removes the valid parity by using a syndrome former that acts as an annihilator for the valid parity while revealing the intended plaintext message. This method, called LInCC, leverages the property of local invertibility to create a usable instance of a convolutional encoder that combines a large memory value and/or a high rate to create a very complex encoder. With the increased memory and rates the number of valid encoder choices that act as keys for the system increases at an exponential rate. The system can be made more secure by increasing the amount of memory or increasing the choice of possible coding rates. The LInCC system is a new type of cipher. The LInCC cipher has the potential to provide more security than most current ciphers. The ability to increase the ciphers strength exponentially by increasing the memory linearly allows the system to become more secure. The best known brute force attack would require more than 2900 key attempts for a 113 byte key. On the other hand, LInCC uses a single fixed key for multiple ciphertexts. This may prevent certain modes of operation from being effective. It can also expand the ciphertext to more than double the size of the original plaintext message. This may impact the effectiveness of the cipher. However, we believe that in some situations, such as streaming or downloading protected video content, this overhead may be quite acceptable.