US6049815A  Method and apparatus for finite field multiplication  Google Patents
Method and apparatus for finite field multiplication Download PDFInfo
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 US6049815A US6049815A US08/997,673 US99767397A US6049815A US 6049815 A US6049815 A US 6049815A US 99767397 A US99767397 A US 99767397A US 6049815 A US6049815 A US 6049815A
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 239000000047 products Substances 0.000 claims abstract description 58
 230000001603 reducing Effects 0.000 claims abstract description 35
 238000006722 reduction reactions Methods 0.000 claims abstract description 16
 230000000295 complement Effects 0.000 claims description 3
 230000003247 decreasing Effects 0.000 claims description 3
 125000004122 cyclic group Chemical group 0.000 claims description 2
 239000012467 final product Substances 0.000 claims 6
 238000004590 computer program Methods 0.000 claims 3
 241001442055 Vipera berus Species 0.000 claims 1
 239000000543 intermediates Substances 0.000 description 7
 238000000034 methods Methods 0.000 description 7
 230000000694 effects Effects 0.000 description 5
 239000002585 bases Substances 0.000 description 2
 230000014509 gene expression Effects 0.000 description 2
 230000004048 modification Effects 0.000 description 2
 238000006011 modification reactions Methods 0.000 description 2
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 230000000875 corresponding Effects 0.000 description 1
 230000003111 delayed Effects 0.000 description 1
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 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRIC DIGITAL DATA PROCESSING
 G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
 G06F7/60—Methods or arrangements for performing computations using a digital nondenominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and nondenominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
 G06F7/72—Methods or arrangements for performing computations using a digital nondenominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and nondenominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
 G06F7/724—Finite field arithmetic
Abstract
Description
A=x.sup.7 +x.sup.5 +x.sup.3 +x.sup.2 +x.sup.1 +x.sup.0 (3)
f.sub.1 (x)=x.sup.4 +x.sup.3 +x.sup.2 +x.sup.1 +x.sup.0 (4)
f.sub.1 (x)=x.sup.n +x.sup.n1 + . . . x.sup.2 +x+1 (6)
f.sub.2 (x)=(x+1)f.sub.1 (x)=x.sup.n+1 +1 (7)
f.sub.1 (x)=x.sup.10 +x.sup.9 + . . . +x.sup.2 +x+1
b=x.sup.9 +x.sup.8 +x.sup.6 +x.sup.4 +x.sup.3 +x.sup.2 +x.sup.1 +1
b'=b+f.sub.1 =x.sup.10 +x.sup.7 +x.sup.5
O.sub.1 =0000, O.sub.0 =1011, e.sub.1 =0001, e.sub.0 =0110
O.sub.1 =00000000, O.sub.0 =10001010, e.sub.1 =00000001, e.sub.0 =00010100
TABLE__________________________________________________________________________2+ 113 293 473 676* 873 1110 1310 1533 17903 119 299 483 683 876* 1116* 1323 1539 17914* 130* 303 490+ 686 879 1118 1329 1541 18065 131 306 491 690 882* 1119 1331 1548* 18116 134 30 700* 891 1121 1338 1559 18189 135 316* 508* 708* 893 1122* 1341 1570* 182110* 138* 323 509 713 906* 1133 1346 1583 182911 146 326 515 719 911 1134 1349 1593 183512* 148* 329 519 723 923 1146 1353 1601 183814 155 330 522* 725 930 1154 1355 1618* 184518+ 158 338 530 726 933 1155 1359 1620* 185023 162* 346* 531 741 935 1166 1370 1626 185426 172* 348* 540* 743 938 1169 1372* 1636* 185928* 173 350 543 746 939 1170* 1380* 1649 1860*29 174 354 545 749 940* 1178 1394 1653 186330 178* 359 546* 755 946* 1185 1398 1659 1866+33 179 371 554 756* 950 1186* 1401 1661 1876*35 180* 372* 556* 761 953 1194 1409 1666* 188336* 183 375 558 765 965 1199 1418 1668* 188939 186 378+ 561 771 974 1211 1421 1673 189841 189 378* 562* 772* 975 1212* 1425 1679 1900*50 191 386 575 774 986 1218 1426* 1685 190151 194 388* 585 779 989 1223 1430 1692* 1906*52* 196* 393 586* 733 993 1228* 1439 1703 192353 209 398 593 785 998 1229 1443 1706 192558* 210+ 410 606 736* 1013 1233 1450* 1730 192660* 221 411 611 791 1014 1236* 1451 1732* 1930*65 226* 413 612* 796* 1018* 1238 1452* 1733 193166* 230 414 614 803 1019 1251 1454 1734 193869 231 418* 615 809 1026 1258* 1463 1740* 1948*74 233 419 618+ 810 1031 1265 1469 1745 195381 239 420* 629 818 1034 1269 1478 1746* 195582* 243 426 638 820* 1041 1271 1481 1749 195883 245 429 639 826* 1043 1274 1482* 1755 195986 251 431 641 828* 1049 1275 1492* 1758 196189 254 438 645 831 1055 1276* 1498* 1763 196590 261 441 650 833 1060* 1278 1499 1766 1972*95 268* 442* 651 834 1065 1282* 1505 1769 197398 270 443 652* 846 1070 1289 1509 1773 1978*99 273 453 653 852* 1090* 1290* 1511 1778 1983100*278 460* 658* 858* 1103 1295 1518 1779 1986*105 281 466* 659 866 1106 1300* 1522* 1785 1994106*292* 470 660* 870 1108* 1306* 1530* 1786* 1996*__________________________________________________________________________ ≅2000 for which the field F.sub.2 = has an ONB.
Claims (18)
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GBGB9627069.9A GB9627069D0 (en)  19961230  19961230  A method and apparatus for finite field multiplication 
GB9627069  19961230 
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US6049815A true US6049815A (en)  20000411 
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US08/997,673 Expired  Lifetime US6049815A (en)  19961230  19971224  Method and apparatus for finite field multiplication 
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US (1)  US6049815A (en) 
CA (1)  CA2225899A1 (en) 
DE (1)  DE19758079A1 (en) 
FR (1)  FR2757969A1 (en) 
GB (2)  GB9627069D0 (en) 
Cited By (49)
Publication number  Priority date  Publication date  Assignee  Title 

US6230179B1 (en) *  19970418  20010508  Motorola, Inc.  Finite field multiplier with intrinsic modular reduction 
WO2001033335A1 (en) *  19991028  20010510  Philip Druck  Selfstabilizing, portable and efficient computer arithmetic using mappings of d scale points 
US6279023B1 (en) *  19971229  20010821  Maxtor Corporation  System for computing the multiplicative inverse of an element of a Galois field without using tables 
US6286022B1 (en) *  19971118  20010904  Rsa Security Inc.  Efficient finite field basis conversion involving a dual basis 
WO2001076132A1 (en) *  20000331  20011011  The State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon S Tate University  Scalable and unified multiplication methods and apparatus 
US6321247B1 (en) *  19981228  20011120  Compaq Computer Corporation  System and method for multiplication modulo (2N+1) 
US6343305B1 (en) *  19990914  20020129  The State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University  Methods and apparatus for multiplication in a galois field GF (2m), encoders and decoders using same 
US6366940B1 (en) *  19980302  20020402  Matsushita Electric Industrial Co., Ltd.  Highspeed modular multiplication apparatus achieved in small circuit 
US6389442B1 (en)  19971230  20020514  Rsa Security Inc.  Efficient finite field multiplication in normal basis 
US20020062330A1 (en) *  20000919  20020523  Christof Paar  Method for efficient computation of odd characteristic extension fields 
US20030068037A1 (en) *  20011010  20030410  Stmicroelectronics S.R.I.  Circuit for the inner or scalar product computation in galois fields 
US20030093450A1 (en) *  20011009  20030515  International Business Machines Corporation  Blockserial finite field multipliers 
US20030110196A1 (en) *  20011130  20030612  Yosef Stein  Galois field multiply/ multiplyadd/multiply accumulate 
US20030115234A1 (en) *  20011218  20030619  Yosef Stein  Reconfigurable input Galois field linear transformer system 
EP1324188A2 (en) *  20011229  20030702  Philips Intellectual Property & Standards GmbH  Method for multiplying two Galois field factors and multiplier for carrying out the method 
US20030123654A1 (en) *  20011231  20030703  Lambert Robert J.  Method and apparatus for performing finite field calculations 
US20030133568A1 (en) *  20011218  20030717  Yosef Stein  Programmable data encryption engine for advanced encryption standard algorithm 
US20030135530A1 (en) *  20010920  20030717  Stmicroelectronics, Inc.  Flexible galois field multiplier 
US20030140212A1 (en) *  20020121  20030724  Yosef Stein  Single instruction multiple data array cell 
US20030140213A1 (en) *  20020121  20030724  Yosef Stein  Center focused single instruction multiple data (SIMD) array system 
US20030206628A1 (en) *  20020501  20031106  Sun Microsystems, Inc.  Generic modular multiplier using partial reduction 
US6671709B2 (en) *  19981218  20031230  Motorola, Inc.  Multiplier cell and method of computing 
US20040039767A1 (en) *  20020821  20040226  International Business Machines Corporation  Check sum generation for modular reduction 
US6721771B1 (en) *  20000828  20040413  Sun Microsystems, Inc.  Method for efficient modular polynomial division in finite fields f(2{circumflex over ( )}m) 
US20040078409A1 (en) *  20021009  20040422  Yosef Stein  Compact Galois field multiplier engine 
US6766345B2 (en)  20011130  20040720  Analog Devices, Inc.  Galois field multiplier system 
US6772184B2 (en) *  20000828  20040803  Sun Microsystems, Inc.  Method for efficient modular division over prime integer fields 
US20040267855A1 (en) *  20030630  20041230  Sun Microsystems, Inc.  Method and apparatus for implementing processor instructions for accelerating publickey cryptography 
US6865661B2 (en)  20020121  20050308  Analog Devices, Inc.  Reconfigurable single instruction multiple data array 
US20050058285A1 (en) *  20030917  20050317  Yosef Stein  Advanced encryption standard (AES) engine with real time Sbox generation 
US20050086278A1 (en) *  20031016  20050421  Samsung Electronics Co., Ltd.  Method and apparatus for performing multiplication in finite field GF(2n) 
US20050105723A1 (en) *  20031118  20050519  Vincent Dupaquis  Randomized modular reduction method and hardware therefor 
US6963644B1 (en) *  19990407  20051108  Matsushita Electric Industrial Co., Ltd.  Multiword arithmetic device for faster computation of cryptosystem calculations 
US20060123325A1 (en) *  20041122  20060608  James Wilson  Condensed galois field computing system 
US7277540B1 (en) *  19990120  20071002  Kabushiki Kaisha Toshiba  Arithmetic method and apparatus and crypto processing apparatus for performing multiple types of cryptography 
US7283628B2 (en)  20011130  20071016  Analog Devices, Inc.  Programmable data encryption engine 
US20080109501A1 (en) *  20061106  20080508  Atmel Corporation  Modular multiplication method with precomputation using one known operand 
US20090157788A1 (en) *  20071031  20090618  Research In Motion Limited  Modular squaring in binary field arithmetic 
US20090234866A1 (en) *  20080317  20090917  Paul Caprioli  Floating Point Unit and Cryptographic Unit Having a Shared Multiplier Tree 
US7650374B1 (en)  20040302  20100119  Sun Microsystems, Inc.  Hybrid multiprecision multiplication 
US20100023572A1 (en) *  20050512  20100128  Vincent Dupaquis  Randomized modular polynomial reduction method and hardware therefor 
US7895253B2 (en)  20011130  20110222  Analog Devices, Inc.  Compound Galois field engine and Galois field divider and square root engine and method 
US20110087895A1 (en) *  20091008  20110414  Olson Christopher H  Apparatus and method for local operand bypassing for cryptographic instructions 
US20140208079A1 (en) *  20130123  20140724  International Business Machines Corporation  Vector galois field multiply sum and accumulate instruction 
US9436467B2 (en)  20130123  20160906  International Business Machines Corporation  Vector floating point test data class immediate instruction 
US9471311B2 (en)  20130123  20161018  International Business Machines Corporation  Vector checksum instruction 
US9715385B2 (en)  20130123  20170725  International Business Machines Corporation  Vector exception code 
US9740482B2 (en)  20130123  20170822  International Business Machines Corporation  Vector generate mask instruction 
US9823924B2 (en)  20130123  20171121  International Business Machines Corporation  Vector element rotate and insert under mask instruction 
Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

US4162480A (en) *  19770128  19790724  Cyclotomics, Inc.  Galois field computer 
US4165444A (en) *  19761211  19790821  National Research Development Corporation  Apparatus for electronic encypherment of digital data 
GB2176325A (en) *  19861216  19861217  Cryptech Systems Inc  Finite field multiplication 
US4797921A (en) *  19841113  19890110  Hitachi, Ltd.  System for enciphering or deciphering data 
US5313530A (en) *  19910305  19940517  Canon Kabushiki Kaisha  Calculating apparatus and method of encrypting/decrypting communication data by using the same 
US5642367A (en) *  19940207  19970624  Mitsubishi Semiconductor America, Inc.  Finite field polynomial processing module for error control coding 
Family Cites Families (2)
Publication number  Priority date  Publication date  Assignee  Title 

SE466822B (en) *  19900615  19920406  Mastrovito Edoardo  DEVICE FOR MULTIPLICATION OF TWO ELEMENTS IN A GALOIC BODY 
WO1996004602A1 (en) *  19940729  19960215  Certicom Corp.  Elliptic curve encryption systems 

1996
 19961230 GB GBGB9627069.9A patent/GB9627069D0/en active Pending

1997
 19971224 US US08/997,673 patent/US6049815A/en not_active Expired  Lifetime
 19971229 CA CA002225899A patent/CA2225899A1/en not_active Abandoned
 19971230 DE DE19758079A patent/DE19758079A1/en not_active Withdrawn
 19971230 FR FR9716666A patent/FR2757969A1/en active Pending
 19971230 GB GB9727494A patent/GB2323457A/en not_active Withdrawn
Patent Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

US4165444A (en) *  19761211  19790821  National Research Development Corporation  Apparatus for electronic encypherment of digital data 
US4162480A (en) *  19770128  19790724  Cyclotomics, Inc.  Galois field computer 
US4797921A (en) *  19841113  19890110  Hitachi, Ltd.  System for enciphering or deciphering data 
GB2176325A (en) *  19861216  19861217  Cryptech Systems Inc  Finite field multiplication 
US5313530A (en) *  19910305  19940517  Canon Kabushiki Kaisha  Calculating apparatus and method of encrypting/decrypting communication data by using the same 
US5642367A (en) *  19940207  19970624  Mitsubishi Semiconductor America, Inc.  Finite field polynomial processing module for error control coding 
Cited By (96)
Publication number  Priority date  Publication date  Assignee  Title 

US7424504B2 (en)  19970418  20080909  Certicom Corp.  Arithmetic processor for accomodating different field sizes 
US6230179B1 (en) *  19970418  20010508  Motorola, Inc.  Finite field multiplier with intrinsic modular reduction 
US6286022B1 (en) *  19971118  20010904  Rsa Security Inc.  Efficient finite field basis conversion involving a dual basis 
US6279023B1 (en) *  19971229  20010821  Maxtor Corporation  System for computing the multiplicative inverse of an element of a Galois field without using tables 
US6389442B1 (en)  19971230  20020514  Rsa Security Inc.  Efficient finite field multiplication in normal basis 
US6366940B1 (en) *  19980302  20020402  Matsushita Electric Industrial Co., Ltd.  Highspeed modular multiplication apparatus achieved in small circuit 
US6671709B2 (en) *  19981218  20031230  Motorola, Inc.  Multiplier cell and method of computing 
US6321247B1 (en) *  19981228  20011120  Compaq Computer Corporation  System and method for multiplication modulo (2N+1) 
US7277540B1 (en) *  19990120  20071002  Kabushiki Kaisha Toshiba  Arithmetic method and apparatus and crypto processing apparatus for performing multiple types of cryptography 
US6963644B1 (en) *  19990407  20051108  Matsushita Electric Industrial Co., Ltd.  Multiword arithmetic device for faster computation of cryptosystem calculations 
US6343305B1 (en) *  19990914  20020129  The State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University  Methods and apparatus for multiplication in a galois field GF (2m), encoders and decoders using same 
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US7240204B1 (en)  20000331  20070703  State Of Oregon Acting By And Through The State Board Of Higher Education On Behalf Of Oregon State University  Scalable and unified multiplication methods and apparatus 
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US20090077144A1 (en) *  20011231  20090319  Lambert Robert J  Method and apparatus for performing finite field calculations 
US8666062B2 (en)  20011231  20140304  Certicom Corp.  Method and apparatus for performing finite field calculations 
US20030123654A1 (en) *  20011231  20030703  Lambert Robert J.  Method and apparatus for performing finite field calculations 
US7372960B2 (en) *  20011231  20080513  Certicom Corp.  Method and apparatus for performing finite field calculations 
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US9804840B2 (en) *  20130123  20171031  International Business Machines Corporation  Vector Galois Field Multiply Sum and Accumulate instruction 
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US10338918B2 (en)  20130123  20190702  International Business Machines Corporation  Vector Galois Field Multiply Sum and Accumulate instruction 
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FR2757969A1 (en)  19980703 
GB9627069D0 (en)  19970219 
CA2225899A1 (en)  19980630 
GB9727494D0 (en)  19980225 
GB2323457A (en)  19980923 
DE19758079A1 (en)  19980709 
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