A montgomery modular multiplication calculation method suitable for embedded systems
An embedded system and calculation method technology, which is applied in the direction of calculation using non-numerical representation, calculation using residual algorithm, calculation, etc., can solve problems such as inability to use, improve implementation efficiency, and reduce the number of memory accesses Effect
Active Publication Date: 2020-04-14
INST OF ACOUSTICS CHINESE ACAD OF SCI +1
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The method using fewer registers (5) requires more memory access operations, while the method using more registers (n+4) requires fewer memory access operations, but often because the number of registers required exceeds the available processor number of registers and cannot be used
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[0046] The method of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.
[0047] A kind of Montgomery modular multiplication calculation method applicable to embedded systems, said method comprising:
[0048] Step 1) If the large number N is an m-bit prime number, and the word length of the processor is W bits, then the word size of N is A, B are two N residual classes, namely 0nW , n 0 '=-n 0 -1 mod r, n 0 is the lowest bit of N; select d, d is the word size of the inner loop (using operand scanning); then the size of the outer loop (using product scanning) is It is the smallest integer operation greater than or equal to it;
[0049] Step 2) Calculate the modular multiplication result C of A and B, the calculation process is:
[0050] 1) C=A*B;
[0051] 2) M=C*n 0 'mod R;
[0052] 3) C=(C+M*N) / R.;
[0053] Such as image 3 As shown, A and B represent 2 m-bit multi-precision int...
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The invention discloses a Montgomery modular-multiplication calculation method suitable for an embedded system. The Montgomery modular-multiplication calculation method comprises the steps that multi-precision multiplication and Montgomery reduction are performed; for the two parts of multi-precision multiplication and Montgomery reduction, a mixed scanning mode is adopted for calculation, an operand scanning mode is adopted for internal cycle, and a product scanning mode is adopted for external cycle. A coarseness integration mode is adopted between the two parts of multi-precision multiplication and Montgomery reduction, namely the two parts are calculated alternatively. By adopting the Montgomery modular-multiplication calculation method, the internal storage access quantity in the embedded system can be decreased, and the Montgomery modular-multiplication algorithm achieving efficiency can be improved.
Description
technical field [0001] The invention relates to the field of public key cryptosystems, in particular to a Montgomery modular multiplication calculation method suitable for embedded systems. Background technique [0002] In 1985, P.L. Montgomery proposed the Montgomery modular multiplication algorithm, which is the most widely used modular multiplication algorithm. The basic idea is to replace time-consuming inversion and division operations with simple and time-saving addition and shift operations. For calculating the modular multiplication P=A*B mod N (A, B, N are n-bit binary integers and 0<A, B<N), the algorithm first selects an integer R that is mutually prime with N (generally R = 2 n ), convert the multiplication operation modulo N into the multiplication operation modulo R. Below we define the Montgomery product: MonPro(A,B)=A*B*R -1 mod N. [0003] For the calculation structure of Montgomery's modular multiplication algorithm, see figure 1 As shown, it is...
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IPC IPC(8): G06F7/72
CPCG06F7/722
Inventor 曾学文李杨叶晓舟
Owner INST OF ACOUSTICS CHINESE ACAD OF SCI