Abstract:
Disclosed is a method for implementing precomputation of a large number in an embedded system. A modulo module, a modulo adding module, and a Montgomery modular multiplier are invoked according to a data format of a modulus length and a value of each data bit of a binary number corresponding to the modulus length, to perform an iterative operation, so that a precomputation result of a large number can be obtained when the modulus length is an arbitrary value, thereby improving the data processing speed.

Description:
This application claims priority to Chinese Patent Application No. 201310132081.6, entitled ‘METHOD FOR REALIZING PRECOMPUTATION FOR LARGE NUMBER IN AN EMBEDDED SYSTEM’, filed on Apr. 16, 2013 with State Intellectual Property Office of PRC, which is incorporated herein by reference in its entirety. 
     FIELD 
     The present disclosure relates to field of information security, more particularly, to a method for realizing pre-computation for a large number in an embedded system. 
     BACKGROUND 
     With popularity of network application, network security is becoming more and more important, thus many products for network security come out. Network security products relate to many aspects, such as information privacy and vulnerability defense, which usually use large numbers computation to ensure confidentiality of data. 
     In the conventional technology, during a process of a large number computation based on Montgomery Modulo Multiplication, pre-computed value can be obtained via subtraction and shifting, but processing speed is tardy. 
     SUMMARY 
     The present disclosure provides a method for realizing pre-computation for a large number in an embedded system, which solves the problem that the processing speed is tardy during the process of the large number computation. 
     An embodiment of the present disclosure provides a method for realizing pre-computation for a large number in an embedded system, including: 
     SA1, including: reading data in a first register, and writing the data which is read into a first random access memory; reading data in a second register, and writing the data which is read into a second random access memory; where the first register is configured to store a first data, the second register is configured to store a second data, the second data is a power with 2 as its base number and a third data as its exponent, the third data is an integer; 
     SA2, including: invoking a module for modulo to perform an operation on the data in the first random access memory and the data in the second random access memory, and writing a result which is obtained from the operation into a third register and a fourth register respectively; where the module for modulo is configured to perform modulo operation with the data in the second random access memory mod the data in the first access memory; 
     SA3, including: reading data in the third register, and writing the data which is read into a third random access memory and a fourth random access memory respectively; reading data in the first register, and writing the data which is read into a fifth random access memory; 
     SA4, including: invoking an modulo addition module to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and updating the data in the third register with a result which is obtained from the operation; where the modulo addition module is configured to perform modulo addition operation with the data in the third random access memory plus the data in the fourth random access memory to obtain a sum, and the sum mod the data in the fifth random access memory; 
     SA5, including: reading data at the least significant bit in a sixth register according to data in a fifth register, and making the data which is read as data at current bit, where an initial value of the data in the fifth register is a preset value, the sixth register is configured to store the third data; 
     SA6, including: determining a value of the data at the current bit, executing step SA7 if the value of the data at the current bit is 0; executing step SA10 if the value of the data at the current bit is 1; 
     SA7, including: reading data in the third register, and writing the data which is read into a sixth random access memory and a seventh random access memory respectively; reading data in the first register, and writing the data which is read into an eighth random access memory; 
     SA8, including: invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the third register with a result which is obtained from the modulo multiplication; where the Montgomery modulo multiplier is configured to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory as a first input parameter, a second input parameter and a third input parameter respectively; 
     SA9, including: updating data in the fifth register, and according to the updated data in the fifth register, reading data which is one-bit higher than the data at the current bit from the sixth register, and making the data which is read as updated data at the current bit, and returning to step SA6; 
     SA10, including: reading data in the fourth register, and updating the data in the sixth random access memory with the read data; reading data in the third register, and updating the data in the seventh random access memory with the read data; reading data in the first register, and updating the data in the eighth random access memory with the read data; 
     SA11, including: invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the fourth register with a result which is obtained from the modulo multiplication; 
     SA12, including: determining whether data at the current bit is data at the most significant bit in the sixth register, executing step SA13 if the data at the current bit is the data at the most significant bit in the sixth register; returning to step SA7 if the data at the current bit is not the data at the most significant bit in the sixth register; and 
     SA13, including: outputting the data in the fourth register. 
     An embodiment of the present disclosure provides another method for realizing pre-computation for a large number in an embedded system, including: 
     SB1, including: reading data in a first register, and writing the data which is read into a first random access memory; reading data in a second register, and writing the data which is read into a second random access memory; where the first register is configured to store a first data, the second register is configured to store a second data, the second data is a power with 2 as its base number and a third data as its exponent, the third data is an integer; 
     SB2, including: invoking a module for modulo to perform an operation on the data in the first random access memory and the data in the second random access memory, and writing a result which is obtained from the operation into a third register and a fourth register respectively; where the module for modulo is configured to perform modulo operation with the data in the second random access memory mod the data in the first access memory; 
     SB3, including: reading data in the third register, and writing the data which is read into a third random access memory and a fourth random access memory respectively; reading data in the first register, and writing the data which is read into a fifth random access memory; 
     SB4, including: invoking an modulo addition module to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and updating the data in the third register with a result which is obtained from the operation; where the modulo addition module is configured to perform modulo addition operation with the data in the third random access memory plus the data in the fourth random access memory to obtain a sum, and the sum mod the data in the fifth random access memory; 
     SB5, including: reading data in the fourth register, and writing the data which is read into a sixth random access memory and a seventh random access memory respectively; reading data in the first register, and writing the data which is read into a eighth random access memory; invoking the Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the fourth register with a result which is obtained from the modulo multiplication; where the Montgomery modulo multiplier is configured to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory as a first input parameter, a second input parameter and a third input parameter respectively; 
     reading data at the most significant bit from a sixth register according to data in a fifth register, and making the read data as data at current bit, where an initial value of the data in the fifth register is a preset value, the sixth register is configured to store the third data; 
     SB6, including: determining a value of the data at the current bit, executing step SB9 if the value is 0; executing step SB7 if the value is 1; 
     SB7, including: reading data in the fourth register, updating the data in the sixth random access memory with the data which is read; reading data in the third register, and updating the data in the seventh random access memory with the data which is read; reading data in the first register, and updating the data in the eighth random access memory with the data which is read; 
     SB8, including: invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the fourth register with a result which is obtained from the modulo multiplication, and executing step SB9; 
     SB9, including: determining whether the data at the current bit is the data at the least significant bit in the sixth register, executing step SB11 if the data at the current bit is the data at the least significant bit in the sixth register; executing step SB10 if the data at the current bit is not the data at the least significant bit in the sixth register; 
     SB10, including: reading data in the fourth register, and updating the data in the sixth random access memory and the data in the seventh random access memory with the data which is read respectively; reading data in the first register, updating the data in the eighth random access memory with the data which is read; invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random memory and the data in the eighth random access memory, and updating the data in the fourth random access memory with a result which is obtained from the modulo multiplication; where the Montgomery modulo multiplier is configured to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory as a first input parameter, a second input parameter and a third input parameter respectively; 
     updating the data in the fifth register, and in accordance with the updated data in the fifth register, reading the data which is one bit lower than the data at the current bit from the sixth register, and making the read data as updated data at the current bit, and returning to step SB6; 
     SB11, including: outputting the data in the fourth register. 
     An embodiment of the present disclosure provides another method for realizing pre-computation for a large number in an embedded system, including: 
     SC1, including: reading data in a first register, and writing the data which is read into a first random access memory; reading data in a second register, and writing the data which is read into a second random access memory; 
     SC2, including: invoking a module for modulo to perform an operation on the data in the first random access memory and the data in the second random access memory, and writing a result which is obtained from the operation into a third register and a fourth register respectively; where the module for modulo is configured to perform modulo operation with the data in the second random access memory mod the data in the first access memory; 
     SC3, including: reading data in the third register, and writing the data which is read into a third random access memory and a fourth random access memory respectively; reading data in the first register, and writing the data which is read in to a fifth random access memory; 
     SC4, including: invoking a modulo addition module to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and updating the data in the third register with a result which is obtained from the operation; where the modulo addition module is configured to perform modulo addition operation with the data in the third random access memory plus the data in the fourth random access memory to obtain a sum, and the sum mod the data in the fifth random access memory; 
     SC5, including: reading the data in the third register, writing the data which is read into a sixth random access memory and a seventh random access memory respectively; reading the data in the first register, and writing the data which is read into an eighth random access memory; 
     SC6, including: invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the third register with a result which is obtained from the modulo multiplication; where the Montgomery modulo multiplier is configured to perform modulo multiplication with the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory as a first input parameter, a second input parameter and a third input parameter respectively; 
     SC7, including: updating data in a fifth register, and determining whether the data in the fifth register is equal to a length of data in a sixth register, executing step SC8 if the data in the fifth register is equal to the length of the data in the sixth register; returning to step SC5 if the data in the fifth register is not equal to the length of the data in the sixth register; and 
     SC8, including: outputting the data in the third register. 
     An embodiment of the present disclosure provides another method for realizing pre-computation for a large number in an embedded system, including: 
     SD1, including: reading data in a first register, and writing the data which is read into a first random access memory; reading data in a second register, and writing the data which is read into a second random access memory; 
     SD2, including: invoking a module for modulo to perform an operation on the data in the first random access memory and the data in the second random access memory, and writing a result which is obtained from the operation into a third register and a fourth register respectively; where the module for modulo is configured to perform modulo operation with the data in the second random access memory mod the data in the first access memory; 
     SD3, including: reading data in the third register, and writing the data which is read into a third random access memory and a fourth random access memory respectively; reading data in the first register, and writing the data which is read into a fifth random access memory; 
     SD4, including: invoking an modulo addition module to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and updating the data in the third register with a result which is obtained form the operation; where the modulo addition module is configured to perform modulo addition operation with the data in the third random access memory plus the data in the fourth random access memory to obtain a sum, and the sum mod the data in the fifth random access memory; 
     SD5, including: reading the data in the third register, and writing the data which is read into a sixth random access memory and a seventh random access memory respectively; reading the data in the first register, and writing the data which is read into an eighth random access memory; 
     SD6, including: invoking a Montgomery modulo multiplier to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and updating the data in the third register with a result which is obtained form the modulo multiplication; where the Montgomery modulo multiplier is configured to perform modulo multiplication with the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory as a first input parameter, a second input parameter and a third input parameter respectively; 
     SD7, including: determining whether data in a fifth register is equal to a length of data in a sixth register, executing step SD9 if the data in the fifth register is equal to the length of the data in the sixth register; executing step SD8 if the data in the fifth register is not equal to the length of the data in the sixth register; 
     SD8, including: updating the data in the fifth register, and returning to step SD5; and 
     SD9, including: outputting the data in the third register. 
     Technical solutions according to embodiments of the present disclosure may improve processing speed of data by using Montgomery modulo multiplier to perform iterative operation on data and to get pre-computation result. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a flowchart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 1 of the present disclosure; 
         FIG. 2  is a flowchart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 2 of the present disclosure; 
         FIG. 3  is a flow chart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 3 of the present disclosure; and 
         FIG. 4  is a flow chart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 4 of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure is further described with the embodiments and the drawings below to make the technical solutions of the present disclosure more clearly. Nevertheless, the following embodiments are just a few of embodiments of the disclosure. Any other embodiments made by those skilled in the art on the basis of embodiments of the disclosure without creative work fall in the protective scope of the disclosure. 
     An embodiment provides a method for data processing based on Montgomery modulo multiplication, during the procedure of data processing, CPU (Central Processing Unit) may invoke a module for modulo, an addition module and a Montgomery modulo multiplier. The module for modulo is configured to perform modulo operation, in which data in a second random access memory mod data in a first random access memory. The modulo addition module is configured to perform modulo addition operation on data in a third random access memory, data in a fourth random access memory and data in a fifth random access memory, which is the data in the third access memory plus the data in the fourth random access memory makes a sum, and then the sum mod the data in the fifth random access memory. The Montgomery modulo multiplier is configured to perform modulo multiplication on data in a sixth random access memory, data in a seventh random access memory and data in an eighth random access memory which are regarded as a first input parameter, a second input parameter and a third input parameter respectively. 
     In the embodiment, a first register is configured to store a first data N, a second register is configured to store a second data R=2 n , n is an integer, a third register, a fourth register and a fifth register are configured to store intermediate data during the data processing, a sixth register is configured to store a third data which is a length n. 
       FIG. 1  illustrates a flowchart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 1 of the disclosure, including step  101  to step  114 . 
     In step  101 , data in a first register is read, and the read data is written into a first random access memory; data in a second register is read, and the data which is read is written into a second random access memory. 
     In step  102 , a module for modulo is invoked to perform an operation on the data in the first random access memory and the data in the second random access memory, and a result which is obtained from the operation is written into a third register and a fourth register respectively. 
     In the embodiment, after the module for modulo is invoked to perform the operation, data in the third register is recorded as W, data in the fourth register is recorded as S, and S is equal to W and equal to R mod N. For instance, N is 
     0xD99E413375024660171E3AB08CA00A3E1AA4985BEAAF8AC09F892DA9C61 915945C7B4D72849EC1CD747586AB780D0B171FD8C27A5688A2E085AF6C506 87AE3E0997238134D7DA34B96B8B7C0C993B4F1DF3FF6D46826460E13B0E8F AFA0BD59B2843627A4B8B253C5873FA87720D28DC3021A1898CF7DE8B4BC7 525086CBFFE7CD1176663EC8EE958D59C94D60010E2F6063D5108049931454D 00985B478064C2607DEB977D973C7750A19B2BC65DA102DD0A371, and 
     R is 
     0x1000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000. 
     A value of W and a value of S both are 
     0x2661BECC8AFDB99FE8E1C54F735FF5C1E55B67A41550753F6076D25639E6E A6BA384B28D7B613E328B8A795487F2F4E8E0273D85A9775D1F7A5093AF978 51C1F668DC7ECB2825CB46947483F366C4B0E20C0092B97D9B9F1EC4F170505 F42A64D7BC9D85B474DAC3A78CO5788DF2D723CFDE5E7673082174B438AD AF7934001832EE8999C137116A72A636B29FFEF1D09F9C2AEF7FB66CEBAB2F F67A4B87F9B3D9F8214688268C388AF5E64D439A25EFD22F5C8F. 
     In step  103 , the data in the third register is read, and the read data is written into a third random access memory and a fourth random access memory respectively; reading the data in the first register, and the read data is written into a fifth random access memory. 
     In step  104 , the modulo addition module is invoked to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and a result which is obtained from the operation is written into the third register. 
     In the embodiment, after the modulo addition module is invoked to perform the operation, the result (R mod N)+(R mod N) mod N=2R mod N may be obtained, the data W in the third register may be updated with 2R mod N. For instance, after being updated, the value of W in the third register is 
     0x4CC37D9915FB733FD1C38A9EE6BFEB83AB6CF482AA0EA7EC0EDA4AC7 3CDD4D74709651AF6C27C651714F2A90FE5E9D1C04E7B0B52EEBA3EF4A127 5F2F0A383ECD1B8FD96504B968D28E907E6CD8961C418012572FB373E3D89E 2E0A0BE854C9AF793B0B68E9B5874F180AF11BE5AE479FBCBCECE61042E96 8715B5EF268003065DD1333826E22D4E54C6D653FFDE3A13F3855DEFF6CD9D 7565FECF4970FF367B3F0428D104D187115EBCC9A87344BDFA45EB91E. 
     In step  105 , data in a fifth register is initialized. 
     Preferably, in the embodiment, the data in the fifth register may be set as 1. 
     In step  106 , in accordance with the data in the fifth register, data at the corresponding bit in a sixth register is read. 
     A position where the data is to be read in the sixth register is determined according to the value of the data in the fifth register, and the data at the corresponding bit in the sixth register is read according to the position. 
     Preferably, in the embodiment, an order of the bits of the data which may need to be read in the sixth register may be obtained according to the data in the fifth register, and data of 1 bit is read from the sixth register in accordance with the order of the bits. The order of the bits is a serial number of position of the data at each bit in the sixth register; for instance, when data, in the sixth register, is n, and n=n k *2 k +n k-1 *2 k-1 + . . . +n i *2 i + . . . +n 1 *2 1 +n 0 *2 0  (n i =1 or 0), the data is (n k n k-1  . . . n i  . . . n 1 n 0 ) 2  in a case that being converted into the binary system, the bit orders of n k , n k-1 , n i , n 1  and n 0  is k, k−1, i, 1 and 0 respectively. In the case that the data in the fifth register is 1, according to the data in the fifth register, the data which is read at the corresponding bit is data n 0  at the least significant bit. In the case that the data in the fifth register is k+1, according to it, the data which is read at the corresponding bit is data n k  at the most significant bit. 
     In the embodiment, in the case that the value of data n in the sixth register may be 1440, whose binary format is (101 1010 0000) 2 , after initialization, in the case that the data in the fifth register is 1, the data which is first read is 0 at least significant bit. 
     In step  107 , whether a value of data which is latest read from the sixth register is 0 is determined, step  108  is executed if the value of the data which is latest read from the sixth register is 0; step  111  is executed if the value of data which is latest read from the sixth register is not 0. 
     In step  108 , the data in the third register is read, and the data which is read is written into a sixth random access memory and a seventh random access memory respectively; the data in the first register is read, and the data is written into an eighth random access memory. 
     In step  109 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and then the data in the third register is updated with a result of the modulo multiplication. 
     In the embodiment, the data W in the third register, the data W in the third register and the data N in the first register are respectively set as three input parameters of the Montgomery modulo multiplier, and modulo multiplication is performed on them to obtain MontMul (W, W, N)=W*W*R −1  mod N, the data W in the third register is updated with W*W*R −1  mod N. 
     For instance, in the case that the data which is read is n 0 , data W in the third register is updated with 
     0x9986FB322BF6E67FA387153DCD7FD707956D9E905541D4FD81DB4958E79B A9AE8E12CA35ED84F8CA2E29E5521FCBD3A3809CF616A5DD747DE9424EBE 5E14707D9A371FB2CA0972D1A51D20FCD9B12C38830024AE5F66E7C7B13C5 C1417D0A9935EF27616D1D36B0E9E3015E237CB5C8F3F7979D9CC2085D2D0E 2B6BDE4D00060CBBA266704DC45A9CA98DACA7FFBC7427E70ABBDFED9B 3AEACBFD9E92E1FE6CF67E0851A209A30E22BD799350E6897BF48BD723C. 
     In the case that the data which is read is n 1 , data W in the third register is updated with 
     0xB2DF6A61C5D70D3E5FDFDF961CBF47A2206D49897FA83E74C85ACA10123 C7B917F548DF2ACD65F8DCFBC87F18F15385FC2C25365EA648C3699AA6258 A75BFA3535F80EA48D2A84AF67031471D39D46FE4D80A510AD4F13029D8F9 E5A6B2AFB172B431366B03761C1C7D86279FB1320849DA2A45416925A34ABF C365685A801B394C5ACCF95DF397C0FAFD88F3FED00AB38FB04D6FAD3A89 2095F54994F8F8EA5537256F592B5DBF9C54A316EC0D6AADCC754820E. 
     In the case that the data which is read is n 2 , data W in the third register is updated with 
     0x20ED567F6C534104D174FE6AA7D3F4FAAC78DBED0F99DB846BB54F62148 1A08F4305F05A1156216E11D0A863D8A9F5CF8E23562841587E02D0BDA57527 8210EB94B4114DE347001FC8CFF252FD543F9C81CAC8418AFFA172D8FE10E8 0015D891A8C536352D65380BFFA26EBEE686F51B68751145408F5637E6A43751 82241C73E277C9C82DBF7A28CD6E50061EC2524BAA9E7B99297E11184764CD CACEE0987748BF1FEE1552DE7B631FC8D87C3E9AFA21AFD423. 
     In the case that the data which is read is n 3 , data W in the third register is updated with 
     0x9FD8D1C8F4EA928E0681B472F4337574846D4F6AC3CCEBD406F29AE119E7 5B3D4BA2DB11A690A99287366664D8062A1F69294A188035D57CE59B6137FF D3183DED1CFB05C659E29070870C5F6852C09AA7499E0389F30CC2110E52BE F816DCA0CB3597062E90850A81378ECB99010AB950134AD5A28B2F3964A119 8E21D4777A073235006DA6BE9A72FC24A2822A30A24FA9F8B673254342CDEC 60F616C787FB19F4DE8D88974BC7C04907F4477C9BBAE2DBE03A. 
     In the case that the data which is read is n 4 , data W in the third register is updated with 
     0x19B89EFA54C8B5C69A2B02086FAE826F65194FDCD7132643A1FCA3CB3269 7FECB16086B2E50C13A98AE7A929E577FEDEDCCF0FE21C89A6A954D2B7F4 C41815A71B6168B097BC8CE38236A6C267F3F5E3EC3FE92ADFD0FECBA2BD 8EA8674C81948812864F6242BBE6EE4857F4EC340420B6E44FA5A61C6789C351 C7B16393CD8B5F5EB78CBB8B4D56AF4BD2A3AA2CF706E458024A386020D8 49D7870656AAEF0D9AAEA154EC42C08B0AB00426739C7C94DE0CA196. 
     In the case that the data which is read is n 5 , data W in the third register is updated with 
     0x737AD2CCAEA97D279F22DE4C575118ECBF39F9E41F1BDA8C740677C14A8 FBAA19CBB5DA2125FB13BBD3815EB7DA6D6454A4716A0E71BF59F578DE15 9809F82EF52AA42DD0452155DF6AE438506C7C7B0C28921EA7CE4EB5BD6C8 8362FF45F9DF3999B591A03AEC9B305B0753E40AC3928973836BF12119DA294 FF815EAF2F8ACFB2B436AFA9BED27EF69C68AB81A059BC7BD678A82BCD2 CEF9DFF577CC8F33E1B9822B8E3F0D5804A225A44B1EE53CB6EEF93848. 
     In the case that the data which is read is n 6 , data W in the third register is updated with 
     0xD33D4904E41AC66FB543E22D002A68946486D522E59CCD6C1C59A81ED619 FA6D095A98DDC04A47B42576D3C91DA81498F59B59CBB1753C7603979261A3 3A7208167F0F1CEA375139E8DD99D04F2423E4A6EE10F39AE347A0AEB54446 25AD2574545E236EEA5174DEBF82EFF3DC5405971FC1212EC726E49B2BE7CE 6AF543ACD508872EA4DC5B38A2C2742E4AA80A7A9D63B190D39B3C095753 D1EBE8725A9B711437D93B585539FB3948163775F8C15EAD65C935. 
     In the case that the data which is read is n 7 , data W in the third register is updated with 
     0x1AD2EA8F41E8E7D6C06D04317F406C438950CF08918357FFB4BA6C1437274 0E319D5FB082ECDD03D741FF45168AA01EA8112D1F1BE57EDE660D1DD510 D1B1E9F4C4355D690F864BC2644247AD1E254EF85C106ED14FAC18327BB8D D7441D0FB68D5F1B0E761988D72C87843803896D0B76A5EB674C9D4384BDA7 6861713AE8962AD204631EC1ABA0843F66E49E6D2EFE5DBA80A95DF371990 BF14A86DC5AD5F67125B9696DF601E04DE091214B5F82F5B47457EF. 
     In the case that the data which is read is n 8 , data W in the third register is updated with 
     0x4AF096BF06BE71B157C1B12A7A39EC6FD9DDBBC4E8B8C5FA317562B31D FB0FED8C71B4D37D5F9F000FCC0BFDD49CBA1591D619F615098ED7D578866 2AEEA2443CE8F3ABD8B766E928D9CF9F0D0E94AA0B7D179DFF1715AA215B 400150F331BA33514DF597D677D8490E0E0C73219E0907600EB08A876A0F49A AB3B14E2F728C54192A8480B216EC1BCE54B5DADFC1581AC04FCB87ABFFD B1E854511242AB801366BFE0C01C5639878D658BDE44CC6237DB4330BD. 
     In the case that the data which is read is n 9 , data W in the third register is updated with 
     0x956CB88B112F1DCB30309A00C50A3098B51AABC48B94E89DDF0F8582DCB 07371D7194494E08EA453A528616950ABB1B65176956399E6FBC74BD334812D 9DA3D3B5B229BCD643307D7E52DADC3E64C61874EB307BD62CB6A77E4AA 893A2FCF9A64759D9B88E6E676511AC5101F1F358231652B00D78AA05AA0AF B71F161AA89CF0DEAE77CCD412441620B35E3D3D3728CAA84368ACDF3353 8BE766BAFA60F6CD40C867FB024363D1489B87D604936EEB7D44034F5. 
     In the case that the data which is read is n 10 , data W in the third register is updated with 
     0xCDE0AC6F912257FF9A51B338A27E951CBE0A5B3A790CA56E2488CED7ED CA526900012803FCC3A6EBF9819D5490F2438DC50DB41B48B19C2DE714895E 8853334269ED374748BB9EE99B81FB6A7CC97B64BD1CDB14AA48C1677BB46 D7C06770FA8608E0D74984DE085CE5CF0ADDB3EE4271D8E93D9949D553E34 456CA8A9E41DA95744EB840A81498E081193048734C370CDECECBE976FE7A9 622B40E805A7881184C2F7FE85357CA13FB01C2EB1A7159ED229CC99. 
     In step  110 , updating the data in the fifth register, and returning to step  106 . 
     A result obtained by the data in the fifth register plus a preset step which may be 1 is made as updated data in the fifth register. 
     In step  111 , the data in a fourth register is read, and the data in the sixth random access memory is updated with the data which is read; the data in the third register is read, and the data in the seventh random access memory is updated with the data which is read; the data in the first register is read, and the data in the eighth random access memory is updated with the data which is read. 
     In step  112 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the fourth random access memory is updated with a result which is obtained from the modulo multiplication. 
     In the embodiment, data S in the fourth register, data W in the third register and data N in the first register are respectively set as three input parameters of the Montgomery modulo multiplier, and modulo multiplication is performed on the data to obtain MontMul (S, W, N)=S*W*R −1  mod N, and after the result is stored into the fourth register, data S in the fourth register is updated with S*W*R −1  mod N. 
     In the case that the data which is read is n 5 , a value of which is 1, data in the fourth register is updated with 
     0x19B89EFA54C8B5C69A2B02086FAE826F65194FDCD7132643A1FCA3CB3269 7FECB16086B2E50C13A98AE7A929E577FEDEDCCF0FE21C89A6A954D2B7F4 C41815A71B6168B097BC8CE38236A6C267F3F5E3EC3FE92ADFD0FECBA2BD 8EA8674C81948812864F6242BBE6EE4857F4EC340420B6E44FA5A61C6789C351 C7B16393CD8B5F5EB78CBB8B4D56AF4BD2A3AA2CF706E458024A386020D8 49D7870656AAEF0D9AAEA154EC42C08B0AB00426739C7C94DE0CA196. 
     In the case that the data which is read is n 7 , a value of which is 1, data in the fourth register is updated with 
     0xCDA46337DD938E5CBBE5BD34A433D49223AEDC489354AEA5961317A372 FF02A2DE00FC155C91FD4629CECF48ABA3E6B5FB6E47D192931C41F5D2257 9A187F99061FBA714BE6C8BF44B6E2F4DA3F9D549B7CD638227182DE2D3094 05178EC7DD8DE2C05EAD5F073636C11A56FD0A7E6FC77847B4090EF0F13EE 529A47CB9003EC4D96796ABAB10F9E9EE64D02EF6B8ED46DB07E0C32A6D3 98DB4126A61A592E7DDE02215134E7AE35902F525D3A96C5B45CEDEAA4. 
     In the case that the data which is read is n 8 , a value of which 1, data in the fourth register is updated with 
     0xBCA266809D0887DFDD16887E3D061AFD601DED198DE11BA3196241D5C64 7615002B30D1FA2AC61D8EE8A2493ABD4D0D8C48D6255F7CC043070E385A4 DA0D1A0EC746A9BA501D403162D185AD4A69C619B60B217060A9B23F41296 DF95852A4373DD5D71D7FCCF7DD9E3F26432F41CF6CA2D726EF5B49C63FF5 7D535C58BB42D87BB258E6804FF5730CF3D71276305A0630359656CB5DA6E5 A095A45F00F724B6B181C37A9830E456947B3AC5F249D4D723D6E34D. 
     In the case that the data which is read is n 10 , a value of which is 1, data in the fourth register is updated with 
     0xB83C9F28C1E3054ABC74607F8D0E9BF7749570117F35B79B891169D963F693 E928F26FC3422F7EB469E4360872C2C1122A27EA331D8EA13B559CF48F5F605 73FDCAAAA8F83103CD6A5FF4E6AB3B6F6A4C2C073CEBC2E12EEC89CF8FB 0CD4EF713C354FE5C3D7E60E5D2DA4D7C82D181B4B1DEF3DE585A616398C ACE990EBDAF23C441DD72D89D1A295163B6337F5AFB59FA35E77FA7EDF39 1F257220D0D5BB61395D26826690AD1297D714B5D114A2CBD0A814E7. 
     In step  113 , whether the data which is latest read in the sixth register is the data at most significant bit in the sixth register is determined, step  114  is executed if the data which is latest read in the sixth register is the data at most significant bit in the sixth register; step  108  is returned to if the data which is latest read in the sixth register is not the data at most significant bit in the sixth register. 
     It&#39;s may determined that whether a value of the data in the fifth register is equal to a length of the data in the sixth register, the data which is read is the data at most significant bit in the sixth register if the value of the data in the fifth register is equal to the length of the data in the sixth register; the data is not the data at most significant bit in the sixth register if the value of the data in the fifth register is not equal to the length of the data in the sixth register. 
     In step  114 , the data in the fourth register is output. 
     In the embodiment, the output result is 
     0xB83C9F28C1E3054ABC74607F8D0E9BF7749570117F35B79B891169D963F693 E928F26FC3422F7EB469E4360872C2C1122A27EA331D8EA13B559CF48F5F605 73FDCAAAA8F83103CD6A5FF4E6AB3B6F6A4C2C073CEBC2E12EEC89CF8FB 0CD4EF713C354FE5C3D7E60E5D2DA4D7C82D181B4B1DEF3DE585A616398C ACE990EBDAF23C441DD72D89D1A295163B6337F5AFB59FA35E77FA7EDF39 1F257220D0D5BB61395D26826690AD1297D714B5D114A2CBD0A814E7. 
     In the case that the length is any value, by applying the technical solution of the disclosure, the result of pre-computation for a large number may be obtained via performing iterative operation by the Montgomery modulo multiplier according to the value at each bit of binary numbers which is corresponding to length, thereby the speed of data processing is improved. 
     It&#39;s important to note that in other embodiments of the disclosure, the data in the fifth register may be initialized as any value beside 1, and the value is corresponding to the position of the data at the least significant bit in the sixth register; when being updated, the data in the fifth register may be increased any value beside 1, and then the data in the sixth register is read in accordance with the updated data in the fifth register, the read data in the sixth register is one-bit higher than the data in the sixth register which is read according to the data in the fifth register before updated, in that case, the objective of the disclosure can also be realized. 
       FIG. 2  illustrates a flowchart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 2 of the disclosure, in this embodiment, the length, stored in the sixth register, is n which is equal to 2 k , and the method for realizing pre-computation for a large number includes step  201  to step  210 . 
     In step  201 , data in a first register is read, and the data which is read is written into a first random access memory; data in a second register is read, and the data which is read is written into a second random access memory. 
     In step  202 , the module for modulo is invoked to perform an operation on the data in the first random access memory and the data in the second random access memory, and the result which is obtained from the operation is written into a third register. 
     In the embodiment, after invoking module for modulo to perform the operation, the data in the third register is recorded as W which is equal to R mod N. 
     In step  203 , data in the third register is read, and the data which is read is written into a third random access memory and a fourth random access memory respectively; reading data in the first register, and the data which is read is written into a fifth random access memory. 
     In step  204 , a modulo addition module is invoked to perform an operation on the data in the third random access memory, the data in the fourth random access memory and data in the fifth random access memory, and a result which is obtained from the operation is written into the third register. 
     In the embodiment, after the modulo addition module is invoked to perform the operation, the result (R mod N)+(R mod N) mod N=2R mod N may be obtained, the data W in the third register may be updated with 2R mod N. 
     In step  205 , data in the fifth register is initialized. 
     Preferably, in the embodiment, the data in the fifth register may be set as 0. 
     In step  206 , the data in the third register is read, and the data which is read is written into the sixth random access memory and the seventh random access memory respectively; the data in the first register is read, and the data which is read is written into an eighth random access memory. 
     In step  207 , a Montgomery modulo multiplier is invoked to perform an operation on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the third register is updated with a result which is obtained from the operation. 
     In the embodiment, data W in the third register, data W in the third register and data N in the first register are set as three input parameters of Montgomery modulo multiplier, and the modulo multiplication are performed on the data to obtain MontMul (W, W, N)=W*W*R −1  mod N, the result which is get from modulo multiplication is stored into the third register, data W in the third register is updated with W*W*R −1  mod N. 
     In step  208 , the data in the fifth register is updated. 
     Specifically, the data in the fifth register is increased by 1, and the result which is obtained is made as the updated data in the fifth register. 
     In step  209 , whether a value of the data in the fifth register is equal to a length of data in the sixth register is determined, step  210  is executed if value of the data in the fifth register is equal to the length of the data in the sixth register; step  206  is returned to if value of the data in the fifth register is not equal to the length of the data in the sixth register. 
     In step  210 , the data in the third register is output. 
     In the case that the length is 2 k , by applying the technical solution of the disclosure, the result from pre-computation for a large number may be obtained via performing iterative operation by the Montgomery modulo multiplier, thereby the speed of data processing is improved. 
     It&#39;s important to note that in other embodiments of the disclosure, the data in the fifth register may also be initialized as 1, and after step  206  to step  207  are executed, step  209  is executed, which is determining whether the value of the data in the fifth register is equal to the length of the data in the sixth register is determined, the data in the third register is output if the value of the data in the fifth register is equal to the length of the data in the sixth register; the data in the fifth register is increased 1, and the result is made as the updated data in the fifth register if the value of the data in the fifth register is not equal to the length of the data in the sixth register, and step  206  to step  207  are executed, and then step  209  is executed, circulating successively, the objective of the disclosure may also be realized. 
       FIG. 3  shows a flowchart of a method for realizing pre-computation for a large number according to embodiment 3 of the disclosure, including step  301  to step  316 . 
     In step  301 , data in a first register is read, and the data which is read is written into a first random access memory; data in a second register is read, and the data which is read is written into a second random access memory. 
     In step  302 , a module for modulo is invoked to perform an operation on the data in the first random access memory and the data in the second random access memory, and a result which is obtained from the operation is written into a third register and a fourth register respectively. 
     In the embodiment, after invoking the module for modulo to perform operation, the data in the third register is recorded as W, the data in the fourth register is recorded as S, and S equal to W and equal to R mod N. 
     In step  303 , the data in the third register is read, and the data which is read is written into a third random access memory and a fourth random access memory respectively; the data in the first register is read, and the read data is written into a fifth random access memory. 
     In step  304 , after an modulo addition module is invoked to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and a result which is obtained from the operation is written into the third register. 
     In the embodiment, after the modulo addition module is invoked to perform the operation, the result (R mod N)+(R mod N) mod N=2R mod N may be obtained, the data W in the third register may be updated with 2R mod N. 
     In step  305 , data in a fifth register is initialized. 
     Preferably, in the embodiment, the data in the fifth register may be set as 0. 
     In step  306 , in accordance with the data in the fifth register, the data at the corresponding bit in a sixth register is read. 
     In accordance with value of the data in the fifth register, a position where the data is to be read in the sixth register is determined, and corresponding data in the sixth register is read according to the position. 
     Preferably, in the embodiment, making the data in the fifth register as orders of data which need to be read in the sixth register, and reading the data of one-bit in the sixth register, wherein, the order is a serial number of data of each bit in the sixth register. 
     For instance, in the case that the data, in the sixth register, is n, and n=n k *2 k +n k-1 *2 k-1 + . . . +n i *2 i + . . . +n 1 *2 1 +n 0 *2 0  (n i =1 or 0), the data is (n k n k-1  . . . n i  . . . n 1 n 0 ) 2  in a case that being converted into the binary system, the bit orders of n k , n k-1 , n i , n 1  and n 0  is k, k−1, i, 1 and 0 respectively. In the case that the data in the fifth register is 0, the data which is read at the corresponding bit according to the data in the fifth register is n 0  at the least significant bit. In the case that the data in the fifth register is k, the data which is read at the corresponding bit is n k  at the most significant bit. 
     In step  307 , whether a value of the latest read data in the sixth register is 0 is determined, step  310  is executed if the value of the latest read data in the sixth register is 0, step  308  is executed if the value of the latest read data in the sixth register is not 0. 
     In step  308 , the data in the third register is written into the fourth register. 
     In step  309 , whether the latest read data in the sixth register is the data at most significant bit in the sixth register is determined, step  316  is executed if the latest read data in the sixth register is the data at most significant bit in the sixth register; step  310  is executed if the latest read data in the sixth register is not the data at most significant bit in the sixth register. 
     In step  310 , the data in the fifth register is updated, and according to the updated data, data at the corresponding bit in the sixth register is read. 
     Specifically, the data in the fifth register is increased by 1, and the result is made as the updated data in the fifth register. 
     In step  311 , the data in the third register is read, and the data which is read is written into a sixth random access memory and a seventh random access memory respectively; the data in the first register is read, and the data which is read is written into an eighth random access memory. 
     In step  312 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the third register is updated with a result which is obtained from the modulo multiplication. 
     In the embodiment, data W in the third register, data W in the third register and data N in the first register are respectively set as three input parameters of the Montgomery modulo multiplier, modulo multiplication is performed on the data to obtain MontMul(W, W, N)=W*W*R −1  mod N, and storing the result in the third register, and then data W in the third register is updated with W*W*R −1  mod N. 
     In step  313 , whether the value of the latest read data in the sixth register is 0 is determined, step  310  is returned to if the value of the latest read data in the sixth register is 0, step  314  is executed if the value of the latest read data in the sixth register is not 0. 
     In step  314 , the data in the fourth register is read, and the data which is read is written into the sixth random access memory; the data in the third register is read, and the data in the seventh random access memory is updated according to the read data; the data in the first register is read, and the data in the eighth random access memory is updated according to the read data. 
     In step  315 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the fourth register is updated with a result which is obtained from the modulo multiplication, and step  309  is returned to. 
     In the embodiment, data S in the fourth register, data W in the third register and data N in the first register are respectively set as three input parameters of the Montgomery modulo multiplier, modulo multiplication is performed on the data to obtain MontMul (S, W, N)=S*W*R −1  mod N, the result is stored into the fourth register, and data S in the fourth register is updated with S*W*R −1  mod N. 
     In step  316 , the data in the fourth register is output. 
     In the case that the length is any value, by applying the technical solution of the disclosure, the result from large numbers pre-computation may be obtained via performing iterative operation by the Montgomery modulo multiplier according to the value at each bit of binary numbers which is corresponding to length, thereby the speed of data processing is improved. 
     It&#39;s important to note that in other embodiments of the disclosure, the data in the fifth register can be initialized as any value beside 0, and the value is corresponding to the position of the data at the least significant bit in the sixth register; when being updated, the data in the fifth register may be increased by any value beside 1, and then the data in the sixth register is read in accordance with the updated data in the fifth register, the read data in the sixth register is one-bit higher than the data in the sixth register which is read according to the data in the fifth register before updated, in that case, the objective of the disclosure may also be realized. 
       FIG. 4  illustrates a flowchart of a method for realizing pre-computation for a large number in an embedded system according to embodiment 4 of the disclosure, including step  401  to step  214 . 
     In step  401 , data in a first register is read, and the data which is read is written into a first random access memory; data in a second register is read, and the data which is read is written into a second random access memory. 
     In step  402 , the module for modulo is invoked to perform an operation on the data in the first random access memory and the data in the second random access memory, and a result which is obtained from the operation is written into a third register and a fourth register respectively. 
     In the embodiment, after the module for modulo is invoked to perform the operation, the data in the third register is set as W, the data in the fourth register is set as S, and S is equal to W and is equal to R mod N. For instance: 
     N is 
     0xD99E413375024660171E3AB08CA00A3E1AA4985BEAAF8AC09F892DA9C61 915945C7B4D72849EC1CD747586AB780D0B171FD8C27A5688A2E085AF6C506 87AE3E0997238134D7DA34B96B8B7C0C993B4F1DF3FF6D46826460E13B0E8F AFA0BD59B2843627A4B8B253C5873FA87720D28DC3021A1898CF7DE8B4BC7 525086CBFFE7CD1176663EC8EE958D59C94D60010E2F6063D5108049931454D 00985B478064C2607DEB977D973C7750A19B2BC65DA102DD0A371; 
     R is 
     0x1000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000, and 
     the value of W which is equal to S is 
     0x2661BECC8AFDB99FE8E1C54F735FF5C1E55B67A41550753F6076D25639E6E A6BA384B28D7B613E328B8A795487F2F4E8E0273D85A9775D1F7A5093AF978 51C1F668DC7ECB2825CB46947483F366C4B0E20C0092B97D9B9F1EC4F170505 F42A64D7BC9D85B474DAC3A78CO5788DF2D723CFDE5E7673082174B438AD AF7934001832EE8999C137116A72A636B29FFEF1D09F9C2AEF7FB66CEBAB2F F67A4B87F9B3D9F8214688268C388AF5E64D439A25EFD22F5C8F. 
     In step  403 , reading the data in the third register, and writing the data which is read into a third random access memory and a fourth random access memory respectively; reading the data in the first register, and writing the data which is read into a fifth random access memory. 
     In step  404 , invoking a modulo addition module to perform an operation on the data in the third random access memory, the data in the fourth random access memory and the data in the fifth random access memory, and writing a result which is obtained from the operation into the third register. 
     In the embodiment, the modulo addition module is invoked to perform the operation to get the result (R mod N)+(R mod N) mod N=2R mod N, and data W in the third register is updated with 2R mod N. 
     In the embodiment, the value of updated data W in the third register is 
     0x4CC37D9915FB733FD1C38A9EE6BFEB83CAB6CF482AA0EA7EC0EDA4AC7 3CDD4D74709651AF6C27C651714F2A90FE5E9D1C04E7B0B52EEBA3EF4A127 5F2F0A383ECD1B8FD96504B968D28E907E6CD8961C418012572FB373E3D89E 2E0A0BE854C9AF793B0B68E9B5874F180AF11BE5AE479FBCBCECE61042E96 8715B5EF268003065DD1333826E22D4E54C6D653FFDE3A13F3855DEFF6CD9D 7565FECF4970FF367B3F0428D104D187115EBCC9A87344BDFA45EB91E. 
     In step  405 , the data in a fifth register is initialized. 
     Preferably, in the embodiment, the data in the fifth register can be set equal to the length of the data in a sixth register. 
     In step  406 , in accordance with the data in the fifth register, the data at a corresponding bit in the sixth register is read. 
     The position where the data is to be read in the sixth register is determined according to the value of the data in the fifth register, and the data at the corresponding bit in the sixth register is read according the position. Preferably, in the embodiment, order of the bits of the data which need to be read in the sixth register may be obtained according to the data in the fifth register, and the data of 1 bit may be read from the sixth register in accordance with the order of the bits which is serial number of the position of the data at each bit in the sixth register. 
     For instance, in the case that the data, in the sixth register, is n, and n=n k *2 k +n k-1 *2 k-1 + . . . +n i *2 i + . . . +n 1 *2 1 +n 0 *2 0  (n i =1 or 0), the data is (n k n k-1  . . . n i  . . . n 1 n 0 ) 2  in a case that being converted into the binary system, where, the bit orders of n k , n k-1 , n i , n 1  and n 0  is k, k−1, i, 1 and 0 respectively. In the case that the data in the fifth register is 1, the data which is read at the corresponding bit according to the data in the fifth register is n 0  at the least significant bit, In the case that the data in the fifth register is k+1, the data which is read at the corresponding bit is n k  at the most significant bit. 
     In the embodiment, in the case that the value of the data n in the sixth register is 1440, and its binary format is (101 1010 0000) 2 , after being initialized, the data in the fifth register is 11, and the data which is firstly read is 1. 
     In step  407 , the data in the fourth register is read, the data which is read is written into a sixth random access memory and a seventh random access memory respectively; the data in the first register is read, and the data which is read is written into an eighth random access memory. 
     In step  408 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the fourth register is updated with a result which is obtained from the modulo multiplication. 
     In the embodiment, data S in the fourth register, data S in the fourth register and data N in the first register are set as three input parameters of the Montgomery modulo multiplier, and modulo multiplication is performed on the data to obtain a result MontMul (S, S, N)=S*S*R −1  mod N, the result is stored into the fourth register, and then the data S in the fourth register may be updated with S*S*R −1  mod N. 
     For instance, in the case that the data which is read is n 10 , the updated data in the fourth register is 
     0x2661BECC8AFDB99FE8E1C54F735FF5C1E55B67A41550753F6076D25639E6E A6BA384B28D7B613E328B8A795487F2F4E8E0273D85A9775D1F7A5093AF978 51C1F668DC7ECB2825CB46947483F366C4B0E20C0092B97D9B9F1EC4F170505 F42A64D7BC9D85B474DAC3A78CO5788DF2D723CFDE5E7673082174B438AD AF7934001832EE8999C137116A72A636B29FFEF1D09F9C2AEF7FB66CEBAB2F F67A4B87F9B3D9F8214688268C388AF5E64D439A25EFD22F5C8F. 
     In the case that the data which is read is n 9 , the updated data S in the fourth register is 
     0x9986FB322BF6E67FA387153DCD7FD707956D9E905541D4FD81DB4958E79B A9AE8E12CA35ED84F8CA2E29E5521FCBD3A3809CF616A5DD747DE9424EBE 5E14707D9A371FB2CA0972D1A51D20FCD9B12C38830024AE5F66E7C7B13C5 C1417D0A9935EF27616D1D36B0E9E3015E237CB5C8F3F7979D9CC2085D2D0E 2B6BDE4D00060CBBA266704DC45A9CA98DACA7FFBC7427E70ABBDFED9B 3AEACBFD9E92E1FE6CF67E0851A209A30E22BD799350E6897BF48BD723C. 
     In the case that the data which is read is n 8 , the updated data S in the fourth register is 
     0xB2DF6A61C5D70D3E5FDFDF961CBF47A2206D49897FA83E74C85ACA10123 C7B917F548DF2ACD65F8DCFBC87F18F15385FC2C25365EA648C3699AA6258 A75BFA3535F80EA48D2A84AF67031471D39D46FE4D80A510AD4F13029D8F9 E5A6B2AFB172B431366B03761C1C7D86279FB1320849DA2A45416925A34ABF C365685A801B394C5ACCF95DF397C0FAFD88F3FED00AB38FB04D6FAD3A89 2095F54994F8F8EA5537256F592B5DBF9C54A316EC0D6AADCC754820E. 
     In the case that the data which is read is n 7 , the updated data S in the fourth register is 
     0x83B559FDB14D041345D3F9AA9F4FD3EAB1E36FB43E676E11AED53D88520 6823D0C17C168455885B84742A18F62A7D73E388D58A10561F80B42F695D49E 0843AE52D045378D1C007F233FC94BF550FE72072B21062BFE85CB63F843A00 0576246A314D8D4B594E02FFE89BAFB9A1BD46DA1D44515023D58DF9A90D D46089071CF89DF2720B6FDE8A335B940187B09492EAA79EE64A5F844611D93 372B3B8261DD22FC7FB8554B79ED8C7F2361F0FA6BE886BF508C. 
     In the case that the data which is read is n 6 , the updated data S in the fourth register is 
     0x022679CABF39B7DD61E056533B7B7BBA371BE1D0DD007BA47277561B1B3 BD915EE138C634B04CFE96C05DFBAF7257E9B7186D1AA2A5F7800DBA36B3 CC636393F1B4675E65C67A93B75D95B751291EE41D5A92FE35DBC53EED619E 9AA1D8AF0B66906AD17C5956C8C1098B4084FD82DE72EA60D27C149F2C63E AE46BFB5A9E2F326588355E2CBD927CB8D336BEA5A8DE1382A0F953BCECF F7E8E67DF98FD8D6CB81C5BF5524E6B051956745414873E5C04DAA0CC1. 
     In the case that the data which is read is n 5 , the updated data S in the fourth register is 
     0x1ABC6003530F5BF6FAF99131099398E735CDBFA97E81E5F22AE25E2C1091F E972F4CC10E0514303E4C6002288744F614BB2E727D0016A4D06BD6843BF903 9D13FA9904FD47457D3A7530BE02241C2579E9A404682790478E9E720BF409B9 6F2908FEC6ED58AC08CD4A39A6AF9F60CB234564F25341D7DCD9D7A375FA 6328E3B63674F26A00F258357F69A4594D719CB34365D05376F3722D1F1E64A1 7C04F1B30334381D94E9CB91B929D14D9739074A2BA45E5C. 
     In the case that the data which is read is n 4 , the updated data S in the fourth register is 
     0x8A7128F0EF38233D76C6D8AFBA66D0C2473B5F689344E19E7DEA9CEB7DC BAC9B5C7BDB9075052C77595E892754BD98B6E437FC212FF564D33A51F9522 30B997C066C0165712821EC0CD43B3063D4D331293B80E37D9FE28D447D29D 510C40417796EEBF09DCE40240969D87E9B29608CE9479B72F989D02884CF0B 54D2861DD96FC66FB6C52974CAB7288CB5CF927BDD4A70C5AA27F3E1BB2B F491D6C3C67FEF1C2F5716539F569535F1E601A4C90ED5E3D38EA5. 
     In the case that the data which is read is n 3 , the updated data S in the fourth register is 
     0x531BC239F295E4934C5AF1EF888563C5F0DA69A5B3F228983F89EDC6E3426 D11944D372E299D28020DD9B0F0E613A3E90821CD5D81D1C8A21B6915F0A02 74A73DCAB3E080D16581C3ACA2D604EAF0A347348D29B40B756A8196CFBB A737F2F2C1C7CE95D75C8AE953DBCB0FEAC60E7A71857074D41C4BBFC0F5 528115CAAB9877292A206A97553F0AC735212B83858203754DF69D1042C07C8 88D30CBA570898D37F0C0565ADF0C7E16C9EA6411774CBCB39FDCA. 
     In the case that the data which is read is n 2 , the updated data S in the fourth register is 
     0x0871B99B9478368B4A9AD8631C3E72E08A91D37611FD998D0517BF8757E0E 5DA896A8AB60E53B8814CA9F38FE671FBC903059E4E37450546CAF563F65A7 B644FDA8A206C8944157534F62E8D6AA548B138069FCD7389569C4D721BD7B 9395A3379E0D41709DF4ED1BA93B8F2461B57D530959E69CE9B8591EF27CF0 D5BA1BD1F8D446C8685F1DE91649351CFB0CEEC751E76F59A1E8CE702D4DF D9E20A8A263C7F36F4985A1BC08236CAF0CCFE95893670D5D406. 
     In the case that the data which is read is n 1 , the updated data S in the fourth register is 
     0x07010678BB199C55EA69B55807E60458299B2374A9137F6E61DE2749010B02 232A67B08843C0F24CF146863C8457D7AF3508301D6A74686D402C8E4F4E99D D4C63FD9BF70CE8773E0919B98891080EB666B21621792BD0D02356A816CD6 BCEE83F15C2AE86B08A081C35C3D6F14631BD80A061BC212B398BC0CE83A6 A2F202B0898C2564AA9AF159E236F787B8747D31A82C5979E69534CF0BAF78 F9A99A1AF99D82BC6922BF77D87F4C0E55E3793A2CC29E0C14. 
     In the case that the data which is read is n 0 , the updated data S in the fourth register is 
     0xB83C9F28C1E3054ABC74607F8D0E9BF7749570117F35B79B891169D963F693 E928F26FC3422F7EB469E4360872C2C1122A27EA331D8EA13B559CF48F5F605 73FDCAAAA8F83103CD6A5FF4E6AB3B6F6A4C2C073CEBC2E12EEC89CF8FB 0CD4EF713C354FE5C3D7E60E5D2DA4D7C82D181B4B1DEF3DE585A616398C ACE990EBDAF23C441DD72D89D1A295163B6337F5AFB59FA35E77FA7EDF39 1F257220D0D5BB61395D26826690AD1297D714B5D114A2CBD0A814E7. 
     In step  409 , whether a value of the data which is latest read in the sixth register is 0 is determined, step  412  is executed if the value of the data which is latest read in the sixth register is 0, step  410  is executed if the value of the data which is latest read in the sixth register is not 0. 
     In step  410 , the data in the fourth register is read, and the data in the sixth random access memory is updated according to the data which is read; reading the data in the third register, and the data in the seventh random access memory is updated according to the data which is read; the data in the first register is read, and the data in the eighth random access memory is updated according to the data which is read. 
     In step  411 , the Montgomery modulo multiplier is invoked to perform modulo multiplication on the data in the sixth random access memory, the data in the seventh random access memory and the data in the eighth random access memory, and the data in the fourth register is updated with a result which is obtained from the modulo multiplication. 
     In the embodiment, data S in the fourth register, data W in the third register and data N in the first register are respectively set as three input parameters of the Montgomery modulo multiplier, modulo multiplication is performed on the data to obtain the result MontMul (S, W, N)=S*W*R −1  mod N, and the result is stored into the fourth register, and then data S in the fourth register is updated with S*W*R −1  mod N. 
     In the case that the data which is read is N 10  whose value is 1, the updated data S in the fourth register is 
     0x4CC37D9915FB733FD1C38A9EE6BFEB83CAB6CF482AA0EA7EC0EDA4AC7 3CDD4D74709651AF6C27C651714F2A90FE5E9D1C04E7B0B52EEBA3EF4A127 5F2F0A383ECD1B8FD96504B968D28E907E6CD8961C418012572FB373E3D89E 2E0A0BE854C9AF793B0B68E9B5874F180AF11BE5AE479FBCBCECE61042E96 8715B5EF268003065DD1333826E22D4E54C6D653FFDE3A13F3855DEFF6CD9D 7565FECF4970FF367B3F0428D104D187115EBCC9A87344BDFA45EB91E. 
     In the case that the data which is read is n 8  whose value is 1, the updated data S in the fourth register is 
     0x8C20939016ABD41CA8A1847BACDE85062635FAB714A0F228F12C66765E5F E18EA22DCE72D50DFD4E2B038937A61D65A865ABE4517E40758CADA55860 E63D1089D27DE535CCD76613374D7122DDA6D90ABBC1534CF277DFF7276E5 3B9DC4A20932E42C45314E39E47373CCA6C8419182D0B23A71EA02CD5DE0C 311A5C8484037F5C79E338ECF584629205E7D11FD8F3271192349D755DBE0FB DEE9FACEAA716FE80DCCF31AD92442C158A492AC5477BA960D860AB. 
     In the case that the data which is read is n 7  whose value is 1, the updated data S in the fourth register is 
     0x2DCC72C7ED97C1C67489B8A4B1FF9D974922470C921F5162BE214D66DDF3 EEE5BBB4355E061249A31A0FBC734D42A3655141EEC7B43B4D36003DBF58D 395A37C0C2E525BCCBA5DB2AFC6DAD7210E47F22F164B37EFD6C588B43F9 E4506A2EEF21DE64F2F1F9E9B23A49F7B6FC22A7FFF1386E8A07782D333E95 A683B8A54E3B746ACD7DB2F32E2B0DE18B6E39611842DF49007B8CBA6F5A DE65664D0C28CBD6E1FF120B732BD8013A3F42D11258EFDC0DFADFDA7. 
     In the case that the data which is read is n 5  whose value is 1, the updated data S in the fourth register is 
     0x3578C006A61EB7EDF5F322621327310E6B9B7F52FD03CBE455C4BC582123F D2E5E99839C0A28607C98C004510E89EC29765CE4FA002D49A0D7AD0877F20 73A27F53209FA8E8AFA74EA617C0448384AF3D34808D04F208F1D3CE417E813 72DE5211FD8DDAB158119A94734D5F3EC196468AC9E4A683AFB9B3AF46EBF 4C651C76C6CE9E4D401E4B06AFED348B29AE3396686CBA0A6EDE6E45A3E3 CC942F809E3660668703B29D397237253A29B2E720E945748BCB8. 
     It&#39;s important to note that after step  411  is executed, step  412  is executed. 
     In step  412 , whether the data which is latest read in the sixth register is the data at the least significant bit in the sixth register is determined, step  414  is executed if the data which is latest read in the sixth register is the data at the least significant bit in the sixth register; step  413  is executed if the data which is latest read in the sixth register is not the data at the least significant bit in the sixth register. 
     In step  413 , the data in the fifth register is updated, and step  407  is returned to. 
     Specifically, the data in the fifth register may be decreased by 1, and then making the result as updated data in the fifth register. 
     In step  414 , the data in the fourth register is output. 
     In the case that the length is any value, by applying the technical solution of the disclosure, the result from large numbers pre-computation may be obtained via performing iterative operation by the Montgomery modulo multiplier according to the value at each bit of binary numbers which is corresponding to length, thereby the speed of data processing is improved. 
     It&#39;s important to note that in other embodiments of the disclosure, the data in the fifth register can be initialized as any value beside the length of the data in the sixth register, and the value is corresponding to the position of the data at the most significant bit in the sixth register; when being updated, the data in the fifth register may be decreased by any value beside 1, and then reading the data in the sixth register in accordance with the updated data in the fifth register, the read data in the sixth register is one-bit lower than the data in the sixth register which is read according to the data in the fifth register before being updated, and in that case, the objective of the disclosure may also be realized. 
     Steps described in the method according to embodiments of the disclosure can be implemented by hardware, software module executed by CPU, or combination of hardware and software module. The software module can be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically-programmable ROM, electrically-erasable programmable ROM, register, rigid disk, removable disc, CD-ROM, or other memory mediums which is known to all technicians in the technical field. 
     While all above are preferred embodiments of the present disclosure, protective scope of the disclosure is not limited to hereof, variations and changes which can be made by those skilled in the art easily fall in scope of the disclosure. It is intended that the following claims defined the scope of the disclosure and that method and structures within the scope of these claims and their equivalents be covered thereby.