Abstract:

The Ouroboros – a symbol of a serpent or dragon devouring its own tail and thereby forming a circle – have been used by a variety of ancient cultures around the world to depict eternity or renewal. The equivalent of the Ouroboros in the world of electronics is the Linear Feedback Shift Registers (LFSRs), where the output from a standard shift register is manipulated and fed back into its input for causing the function to endlessly cycle through a sequence of patterns.

LFSRs are simple to construct and useful for a wide range of applications, but are often neglected by designers. One of the more common forms of LFSR is formed from a simple shift register with feedback from two or more points (taps), in the register chain. The data input to the LFSR is generated by XOR-ing or XNOR-ing the tap bits; the remaining bits function as a standard shift register. The sequence of values generated by LFSRs is determined by its feedback function and tap selection.

LFSRs are used in encryption and decryption applications and cyclic redundancy check applications. The sequence of values generated by LFSRs can be used in the encryption (scrambling) and decryption (unscrambling) of data. A stream of data bits can be encrypted by XOR-ing them with the output from the LFSR. The stream of encrypted data bits in the receiver can be decrypted by XOR-ing them with the output of an identical LFSR. This is obviously a very trivial form of encryption, not very secure, but “cheap-and-cheerful” and may be useful in certain applications.

The paper describes MS EXCEL-based application implementing and graphically illustrating the processes of encryption and decryption of English texts using Fibonacci LFSRs. The processes of encryption and decryption of 3-symbol words in English are illustrated. Numerous examples obtained by the application developed are presented in the paper. The material is used in the educational process in the course “Telecommunication Security”, compulsory in the curriculum of the specialty “Internet and Mobile Communications” for Bachelors at the University of Ruse but it can be applied in other courses involving issues of cryptographic information protection. The application allows easily assimilation of the material studied by the students as the steps at each stage of encryption and decryption are tracked in details. Additionally, the application allows the teacher to automatically generate tasks for individual assignments to students, and assists the process of checking students’ solutions.

For better understanding the material studied by students, active learning methods are applied. An individual assignment is given to each student. The assignment includes:
1) determining the states of LFSR for a given initial state;
2) encrypting a given plaintext (3-symbol English text containing Latin letters, decimal digits, punctuation signs, arithmetic and logical operators and so on) using Fibonacci LFSR;
3) decrypting a given cipher-text using Fibonacci LFSR.

During the practical exercises, the students must solve the tasks of pre-prepared form published in the e-learning platform of the University of Ruse and submit to the teacher at the end of the classes.

The opportunity for extra work is given to the students:
1) decrypting a given cipher-text when the initial state of LFSR is not known;
2) implementing Fibonacci LFSR with D flip-flops and XOR gates and simulating its operation in Logisim;
3) implementation and testing on a laboratory board.

Keywords:

Encryption and decryption, English texts, MS Excel, Fibonacci LFSR.