A course in number theory and cryptography
A course in number theory and cryptography
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Cryptography and Secure Communications
Cryptography and Secure Communications
Fundamentals of Computer Security
Fundamentals of Computer Security
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Finding the multiplicative inverse of an element in Galois Field(p), GF(p) for small values of p such as 5 or 7 is no problem. One can find the multiplicative inverse by constructing multiplication tables and establish the desired value directly. The look-up table procedure, when implemented through software, is fast and handy, and is employed in the design of S-boxes of the Rijndael encryption algorithm used in advanced encryption standard (AES). However, a second choice, if execution time is not the consideration, is the use of extended Euclid's algorithm. The two methods of finding multiplicative inverse in GF(2^8) presented in many books are discussed in this paper. An effort is made to present the working of these methods in a detailed manner which is not found in any text. A comparison of these methods vis-a-vis time, transistor count and complexity is also made. Section 1 contains a brief introduction to the topic, Section 2 reviews multiplication in polynomial arithmetic. Multiplicative inverses in GF(2^8) are taken up in Sections 3, and 4 concludes the paper.