Download Residue Number Systems: Theory and Applications by P.V. Ananda Mohan PDF

By P.V. Ananda Mohan

This new and accelerated monograph improves upon Mohan's past ebook, Residue quantity structures (Springer, 2002) with a cutting-edge remedy of the subject. Replete with particular illustrations and precious examples, this ebook covers a number of leading edge subject matters akin to the middle functionality, the quotient functionality, new chinese language the rest theorems, and big integer operations. It additionally positive aspects many major purposes to functional conversation platforms and cryptography equivalent to FIR filters and elliptic curve cryptography.

Starting with a finished creation to the fundamentals and best as much as present examine traits that aren't but commonly allotted in different guides, this e-book might be of curiosity to either researchers and scholars alike.

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Additional info for Residue Number Systems: Theory and Applications

Sample text

The choice of sub-moduli m1 and m2 such that m1m2 > 2 m has been suggested. As an illustration, for m ¼ 19, m1 ¼ 6 and m2 ¼ 7 can be chosen. Considering multiplication of X ¼ 12 and Y ¼ 17, and base 2, for modulus m ¼ 19, the indices corresponding to X and Y can be seen to be 15 and 10 which in residue form are (3, 1) and (4, 3) corresponding to (m1, m2). Adding the indices corresponding to the product XY, we obtain the indices as (1, 4). Using CRT (which will be introduced later in Chapter 5), the decoded word corresponding to moduli {6, 7} can be shown to be 25 which mod 18 is 7.

The first technique follows the wellknown LowÀHigh lemma [21] based on the periodic property of modulus (2n + 1) discussed in Chapter 3. The LowÀHigh lemma states that ðABÞmodð2n þ 1Þ ¼ ððABÞmodðÁ2n Þ À ðABÞdivð2n ÞÞmodð2n þ 1Þ if ðABÞmodð2n Þ ! ðABÞdivð2n Þ Á ¼ ðABÞmodð2n Þ À ðABÞdivð2n Þ þ 2n þ 1 if ðABÞmodð2n Þ < ðABÞdivð2n Þ ð4:6Þ Note that when An ¼ 0, Bn ¼ 0, the result of multiplication is (AB) mod (2n + 1) ¼ (AL À AH). Thus, one’s complement of AH and 1 need to be added to AL. If carry is 1, the result is n LSBs.

YnÀi Þ þ xi ð0:::01:::111Þ ð4:10Þ and note that 0. 01. 111 indicates a number with (n À i) zeros and i ones. It can be seen that the MSBs of the circularly left-shifted words are one’s complemented and added. 9) are correction terms.

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