N-state ripple adder scheme coding with corresponding N-state ripple adder scheme decoding

#This invention relates to the reversible coding of sequences of 2 or more binary or n-state symbols. More specifically it provides novel methods and apparatus for coding a first plurality of symbols with a second plurality of symbols using at least one reversible logic function and one non-reversible logic function.

#In general coding of plurality of symbols comprises using binary symbols, and combining symbols by using a binary reversible logic function, usually the XOR function. The other reversible binary logic function is the EQUAL function.

#The use of the XOR (also known as modulo-2 addition) is well known. This means that unauthorized users trying to read a coded digital message of binary symbols can make a reliable assumption that coding of the message uses the XOR function. This facilitates unauthorized decoding of a message. Messages using n-state symbols often are recoded into binary symbols. These messages are often coded by using again the XOR function, for instance by using additions over GF(n=2p), which can be expressed as a plurality of XOR functions.

#Various other objects, features and attendant advantages of the present invention will become fully appreciated as the same becomes better understood when considered in conjunction with the accompanying drawings, and wherein:

#FIG. 1 is a diagram of an n-state Fibonacci LFSR based scrambler in accordance with an aspect of the present invention;

#FIG. 2 is a diagram of an n-state Fibonacci LFSR based descrambler in accordance with an aspect of the present invention;

#Using the XOR function for coding binary and n-state symbols is well established and will not be explained herein. However one aspect of the XOR function should be highlighted and that is the aspect of being self-reversing. This means that combining two symbols A and B by a XOR will generate symbol C in accordance with A XOR B→C. The self reversing property allows determining for instance A when B and C are known in accordance with C XOR B→A.

#A, B and C may also be a plurality of binary symbols wherein the XOR is operated upon the individual bits as is known to someone of ordinary skills in the art of binary logic and coding. In general coding may consist of confusing an unauthorized user by using different transposition and substitution schemes. An authorized user familiar with the schemes may reverse the coder as a decoder and recover the original message. It is common to combine a message (for instance A) with a key (for instance B) which is only known to authorized users. A message C created from A XOR B can only be decoded if the key B is known.

#Clearly reversibility is an important aspect of coding. The terms coding and decoding are used herein. The methods of using transformation schemes for symbols are generally known as encipherment and specific methods are called ciphers. It is to be understood that coding herein means encipherment and that a code herein is a cipher.