N-state ripple adder scheme coding with corresponding N-state ripple adder scheme decoding
View Patent ↗Methods and apparatus for implementing an n-state ripple-adder scheme coder with n≧2 using an n-state reversible switching function and a non-reversible n-state switching function acting upon a first and a second word of at least 2 n-state symbols are disclosed. Corresponding decoding methods and apparatus are also disclosed. A resulting codeword may be a codeword which can be decoded by using the identical or different n-state switching functions in a corresponding ripple adder scheme decoder. Feistel networks and LFSRs apply the coding and decoding. Systems using the coding and decoding methods may be communication, storage and/or financial systems.
1. An apparatus for enciphering a plurality of n-state symbols with n>2, each n-state symbol assuming one of n states, comprising:
a first device with an input to receive a signal representing a first n-state symbol in the plurality of n-state symbols, the plurality of n-state symbols being processed as a block cipher, and an output for generating a signal representing a transformed first n-state symbol;
a second device with a first input, a second input and an output, the first input enabled to receive a signal representing a second n-state symbol in the plurality of n-state symbols, the second input enabled to receive the signal representing the transformed n-state symbol and the output generating a signal representing an n-state symbol that is generated in accordance with a first reversible n by n n-state truth table, and wherein:
the first reversible n by n n-state truth table is characterized by combining an addition over an n-state Finite Field GF(n) and one or more multiplications over the n-state Finite Field GF(n) not only being a multiplication 1.
2. The apparatus as claimed in claim 1 , wherein the first reversible n by n n-state truth table cannot characterized by exclusively using an addition over an n-state Finite Field GF(n) and a multiplication over the n-state Finite Field GF(n).
3. The apparatus as claimed in claim 1 , wherein the first device has a second input enabled to receive a signal representing a key.
4. The apparatus as claimed in claim 1 , wherein the first n-state symbol has been generated in a first path of a previous enciphering round and the second n-state symbol has been generated in a second path of a previous enciphering round.
5. The apparatus as claimed in claim 1 , further comprising a corresponding deciphering apparatus for recovering the first n-state symbol from an enciphered n-state symbol.
6. The apparatus as claimed in claim 1 , wherein the second device implements a reversible n-state ripple adder coder.
7. The apparatus as claimed in claim 1 , wherein the apparatus includes a Feistel network.
8. The apparatus as claimed in claim 1 , wherein the first n by n reversible n-state truth table is replaced by an implementation of a second n by n reversible n-state truth table after processing the second n-state symbol.
9. The apparatus as claimed in claim 1 , wherein an n-state symbol is represented by one or more binary signals.
10. The apparatus as claimed in claim 1 , wherein the transformed first n-state symbol is generated in a non-reversible manner.
11. A system for enciphering a plurality of n-state symbols including a first n-state symbol and a second n-state symbol with n>2, each n-state symbol assuming one of n states, comprising:
a processor with a memory, the memory enabled to store instructions, the processor retrieving the instructions from the memory and executing the instruction on one or more signals representing the plurality of n-state symbols wherein the plurality of n-state symbols is being processed as part of a block cipher, to perform the steps of:
transforming a signal representing the first n-state symbol in the plurality of n-state symbols into a signal representing a transformed first n-state symbol; and
processing a signal representing the second n-state symbol and the signal representing the transformed first n-state symbol to generate a signal representing an enciphered n-state symbol in accordance with a first reversible n by n truth table that cannot be characterized by exclusively using an addition over an n-state Finite Field and a multiplication over the n-state Finite Field.
12. The system as claimed in claim 11 , wherein the transformed first n-state symbol is generated by applying a key.
13. The system as claimed in claim 11 , wherein the first n-state symbol is generated in a first path of a previous enciphering round and the second n-state symbol is generated in a second path of a previous enciphering round.
14. The system as claimed in claim 11 , further comprising a deciphering apparatus for recovering the first n-state symbol from an enciphered n-state symbol.
15. The system as claimed in claim 11 , wherein the system includes a Feistel network.
16. The system as claimed in claim 11 , wherein the first reversible n by n n-state truth table is replaced by an implementation of a second reversible n by n n-state truth table after processing the second n-state symbol.
17. The system as claimed in claim 11 , wherein an n-state symbol is represented by one or more binary signals.
18. The system as claimed in claim 11 , wherein the system is part of a financial system.
19. A method for enciphering a plurality of n-state symbols with n>2, each n-state symbol being represented by a signal, comprising:
processing a plurality of signals representing the n-state symbols as a block cipher by a processor, including the steps of:
transforming a signal representing the first n-state symbol in the plurality of n-state symbols, into a signal representing a transformed first n-state symbol; and
processing a signal representing the second n-state symbol and the signal representing the transformed first n-state signal by the processor to generate a signal representing an enciphered n-state symbol in accordance with a first reversible n by n truth table that cannot be characterized by exclusively using an addition over an n-state Finite Field GF(n) and a multiplication over the n-state Finite Field GF(n).
20. The method as claimed in claim 19 , further comprising a method for deciphering the enciphered n-state symbol.