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N. Takagi, "A Radix4 Modular Multiplication Hardware Algorithm for Modular Exponentiation," IEEE Transactions on Computers, vol. 41, no. 8, pp. 949956, August, 1992.  
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@article{ 10.1109/12.156537, author = {N. Takagi}, title = {A Radix4 Modular Multiplication Hardware Algorithm for Modular Exponentiation}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {8}, issn = {00189340}, year = {1992}, pages = {949956}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.156537}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A Radix4 Modular Multiplication Hardware Algorithm for Modular Exponentiation IS  8 SN  00189340 SP949 EP956 EPD  949956 A1  N. Takagi, PY  1992 KW  division subtraction; radix4 modular multiplication hardware algorithm; modular exponentiation; publickey cryptosystems; RSA cryptosystem; redundant representation; residue calculation; repeated multiplyadd; serialparallel modular multiplier; cellular array structure; bit slice; VLSI; cryptography; digital arithmetic. VL  41 JA  IEEE Transactions on Computers ER   
A fast radix4 modular multiplication hardware algorithm is proposed. It is efficient for modular exponentiation with a large modulus, used in publickey cryptosystems such as the RSA cryptosystem. The operands and the result of multiplication which are intermediate results in modular exponentiation are represented in a redundant representation. The computation proceeds in serialparallel fashion. Each subtraction for the division for residue calculation is embedded in the repeated multiplyadd. Each intermediate result is represented in a more redundant representation than that for the operands and the result, so that the number of the required addition/subtractions is reduced. All addition/subtraction are carried out without carry propagation. A serialparallel modular multiplier based on the algorithm has a regular cellular array structure with a bit slice feature and is suitable for VLSI implementation.
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