USRE40530E1 - Public key cryptographic apparatus and method - Google Patents
Public key cryptographic apparatus and method Download PDFInfo
- Publication number
- USRE40530E1 USRE40530E1 US09/694,416 US69441600A USRE40530E US RE40530 E1 USRE40530 E1 US RE40530E1 US 69441600 A US69441600 A US 69441600A US RE40530 E USRE40530 E US RE40530E
- Authority
- US
- United States
- Prior art keywords
- message
- prime numbers
- mod
- distinct random
- ciphertext
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Lifetime
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q20/00—Payment architectures, schemes or protocols
- G06Q20/38—Payment protocols; Details thereof
- G06Q20/382—Payment protocols; Details thereof insuring higher security of transaction
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
- H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/08—Randomization, e.g. dummy operations or using noise
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/12—Details relating to cryptographic hardware or logic circuitry
- H04L2209/125—Parallelization or pipelining, e.g. for accelerating processing of cryptographic operations
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/56—Financial cryptography, e.g. electronic payment or e-cash
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Theoretical Computer Science (AREA)
- Computing Systems (AREA)
- Computer Security & Cryptography (AREA)
- Accounting & Taxation (AREA)
- Finance (AREA)
- Signal Processing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Strategic Management (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Storage Device Security (AREA)
- Computer And Data Communications (AREA)
- Mobile Radio Communication Systems (AREA)
Abstract
Description
n=p·q (1)
where p and q are different prime numbers, and e is a number relatively prime to (p−1) and (q−1); that is, e is relatively prime to (p−1) or (q−1) if e has no factors in common with either of them. Importantly, the sender has access to n and e, but not to p and q. The message M is a number representative of a message to be transmitted wherein
0≦M<n−1. (2)
The sender enciphers M to create ciphertext C by computing the exponential
C=Me(mod n) C≡Me(mod n). (3)
M=Cd(mod n) M≡Cd(mod n) (4)
e(mod(lcm((p−1), (q−1)))) (5)
so that
e·d=1(mod(lcm((p−1), (q−1)))) e·d≡1(mod(lcm((p−1 ), (q−1 )))) (6)
where lcm((p−1), (q−1)) is the least common multiple of numbers p−1 and q−1. Most commercial implementations of RSA employ a different, although equivalent, relationship for obtaining d:
d=e−1mod(p−1) (q−1) d≡e−1 mod((p−1 )·(q−1 )). (7)
This alternate relationship simplifies computer processing.
C=Me(mod(n)) C≡Me(mod n).
M=Cd(mod(n)) M≡Cd(mod n).
d=e−1mod ((p1−1) (p2−1)) . . . (pk−1)) d≡e−1 mod((p 1 −1 )·(p 2 −1 )· . . . ·(p k −1 )), or equivalently
d≡e −1 mod(lcm((p 1 −1 ), (p 2 −1 ), . . . (p k −1 )))
C=Memod n C≡Me(mod n).
M=Cdmod n M≡Cd(mod n)
where n and d are those values identified above.
M s ≡M d(mod n).
M≡Ms e(mod n).
M=Cd(mod n) M≡Cd(mod n)
is used to develop the decryption sub-tasks:
M1=C1 d
M2=C2 d
M3=C3 d
where
C1=Cmod p1; C1 ≡C(mod p 1);
C2=Cmod p2; C2 ≡C(mod p 2);
C3=Cmod p3; C3 ≡C(mod p 3);
d1=dmod (p1−1) d1 ≡d(mod(p 1 −1 ));
d2=dmod (p2−1) d2 ≡d(mod(p 2 −1 )); and
d3=dmod (p3−1) d3 ≡d(mod(p 3 −1 )).
Yi=Yi−1+[(Mi−Yi−1) (wi −1mod pi)mod pi]·wimod n Yi ≡Y i−1+((M 1 −Y i−1)(w i −1(mod p i)))mod p i))·w i(mod n)
where
i≧2 2≦i≦k
where k is the number of prime factors of n, and
Encryption is performed in much the same manner as that used to obtain the plaintext M, provided (as noted above) the factors of n are available. Thus, the relationship
C=Me(mod n) C≡Me(mod n),
can be broken down into the three sub-tasks,
C1=M1 e1mod p1 C1 ≡M 1 e
C2=M2 e2mod p2 C2 ≡M 2 e
C3=M3 e3mod p3 C3 ≡M 3 e
where
M1=M(mod p1) M1 ≡M (mod p 1),
M2=M(mod p2) M2 ≡M (mod p 2),
M3=M(mod p3) M3 ≡M (mod p 3),
e1=emod (p1−1) e1 ≡e (mod(p 1 −1 )),
e2=emod (p2−1) e2 ≡e(mod(p 2 −1 ), and
e3=emod (p3−1) e3 ≡e(mod(p 3 −1 )).
k is the number (3 or more) of distinct primes chosen to develop the product n.
M=M1(w1 −1mod p1) w1mod/n+M2(w2 −1mod p2) w2mod n+M3(w3 −1mod p3) w3mod n
M=M1 −1(w 1 −1(mod p 1))·w 1(mod n)+M 2(w 2 −1(mod p 2))·w 2(mod n)+M 3(w 3 −1(mod p 3))·w 3(mod n)
where
w1=p2p3, w2=p1p3, and w3=p1p2.
0≦M≦N−1 0≦M≦n−1.
Claims (56)
0≦M≦n−1
C≡M e(mod n)
C=Me(mod n)
M=Cd(mod n)M≡Cd(mod n).
ni=Pi,1·pi,2·, . . . , ·pi,kni =p i,1 ·p i,2 · . . . ·p i,k
ei(mod(lcm((pi,1−1), (pi,2−1), . . . , (pi,k−1)))),;
CA≡MA ″eB(mod nB.)Cx ≡M x ″ey(mod n y); and
n=p 1 ·p 2 · . . . ·p k ,
n=p1·p2·. . . ·pk
C≡Me(mod n), and
M′≡Cd(mod n)
e(mod(lcm((p1−1), (p2−1), . . . , (pk−1))));
nA=pA,1·pA,2·. . . ·PA,k
lcm(pA,1−1, pA,2−1, . . . , pA,k−1), and
eA(mod(lcm((pA,1−1), (pA,2−1), . . . , (pA,k−1)))),; and
0≦MB≦nA −1, and
CB=MB eA(mod nA)CB ≡M B e
MB′=CB d
nB=pB,1·pB,2·. . . ·pB,k,
lcm(pB,1−1, pB,2−1, . . . , pB,k−1), and
eB(mod(lcm((pB,1), (pB,2−1), . . . , (pB,k−1)))),
0≦MA eB(mod nB),0≦MA ≦n B −1, and
CA=MA eB(mod nB)CA ≡M A e
MA′≡CA dB(mod nB)MA ′≡C A d
0≦M≦n−1,
C≡aeMe+ae−1Me−1+. . . +ao(mod n)
0≦Mi≦ni−1,
ni=pii,1·pi,2·. . . pi,k n i =p i,1 ·p i,2 ·. . . ·p i,k
ei(mod(lcm((pi,1−1), (pi,2−1), . . . , (pi,k−1))));
MAS≡MA dA(mod nA)M1S ≡M 1 d
MA≡MAS eA(mod nA)Mi ≡M 1S e
0≦M i ≦n i −1
ni=pi,1·pi,2·. . . ·pi,k
ei(mod(lcm((pi,1−1), (pi,2−1), . . . , (pi,k−1)))),
CA=MA″Eb(mod nB)C1 ≡M 1″e
MA″≡CA Db(mod nB)M1 ″≡C 1 d
0≦M≦n−1
C≡aeMe+ae−1Me−1+. . . +ao(mod n)
C≡Me(mod n)
M≡C d(mod n),
C≡M e(mod n),
C≡M e(mod n),
M′≡C′ d(mod n);
C≡M e(mod n),
M′≡C′d(mod n),
M≡C d(mod n);
M S ≡M d(mod n),
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US09/694,416 USRE40530E1 (en) | 1996-12-09 | 2000-10-20 | Public key cryptographic apparatus and method |
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US3327196P | 1996-12-09 | 1996-12-09 | |
US08/784,453 US5848159A (en) | 1996-12-09 | 1997-01-16 | Public key cryptographic apparatus and method |
US09/694,416 USRE40530E1 (en) | 1996-12-09 | 2000-10-20 | Public key cryptographic apparatus and method |
Related Parent Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US08/784,453 Reissue US5848159A (en) | 1996-12-09 | 1997-01-16 | Public key cryptographic apparatus and method |
Publications (1)
Publication Number | Publication Date |
---|---|
USRE40530E1 true USRE40530E1 (en) | 2008-10-07 |
Family
ID=26709486
Family Applications (3)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US08/784,453 Ceased US5848159A (en) | 1996-12-09 | 1997-01-16 | Public key cryptographic apparatus and method |
US09/328,726 Expired - Fee Related US7231040B1 (en) | 1996-12-09 | 1998-10-26 | Multiprime RSA public key cryptosystem |
US09/694,416 Expired - Lifetime USRE40530E1 (en) | 1996-12-09 | 2000-10-20 | Public key cryptographic apparatus and method |
Family Applications Before (2)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US08/784,453 Ceased US5848159A (en) | 1996-12-09 | 1997-01-16 | Public key cryptographic apparatus and method |
US09/328,726 Expired - Fee Related US7231040B1 (en) | 1996-12-09 | 1998-10-26 | Multiprime RSA public key cryptosystem |
Country Status (6)
Country | Link |
---|---|
US (3) | US5848159A (en) |
EP (1) | EP0950302B1 (en) |
JP (1) | JP2001510583A (en) |
AU (1) | AU5689398A (en) |
IL (1) | IL130239A (en) |
WO (1) | WO1998026536A1 (en) |
Families Citing this family (75)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5848159A (en) * | 1996-12-09 | 1998-12-08 | Tandem Computers, Incorporated | Public key cryptographic apparatus and method |
JPH1185507A (en) * | 1997-09-05 | 1999-03-30 | Mitsubishi Electric Corp | Central processor and microcomputer system |
US7587044B2 (en) | 1998-01-02 | 2009-09-08 | Cryptography Research, Inc. | Differential power analysis method and apparatus |
ATE429748T1 (en) | 1998-01-02 | 2009-05-15 | Cryptography Res Inc | LEAK RESISTANT CRYPTOGRAPHIC METHOD AND APPARATUS |
CA2267721C (en) * | 1998-03-26 | 2002-07-30 | Nippon Telegraph And Telephone Corporation | Scheme for fast realization of encryption, decryption and authentication |
CA2333095C (en) | 1998-06-03 | 2005-05-10 | Cryptography Research, Inc. | Improved des and other cryptographic processes with leak minimization for smartcards and other cryptosystems |
ATE360866T1 (en) | 1998-07-02 | 2007-05-15 | Cryptography Res Inc | LEAK-RESISTANT UPDATING OF AN INDEXED CRYPTOGRAPHIC KEY |
US6337910B1 (en) * | 1998-09-09 | 2002-01-08 | Koninklijke Philips Electronics N.V. (Kpenv) | Method and apparatus for generating one time pads simultaneously in separate encryption/decryption systems |
US6363152B1 (en) * | 1998-09-09 | 2002-03-26 | Koninklijke Philips Electronics N.V. (Kpenv) | Hybrid one time pad encryption and decryption apparatus with methods for encrypting and decrypting data |
US6640303B1 (en) | 2000-04-28 | 2003-10-28 | Ky Quy Vu | System and method for encryption using transparent keys |
US20020087884A1 (en) * | 2000-06-12 | 2002-07-04 | Hovav Shacham | Method and apparatus for enhancing network security protection server performance |
US20020039420A1 (en) * | 2000-06-12 | 2002-04-04 | Hovav Shacham | Method and apparatus for batched network security protection server performance |
JP4683442B2 (en) * | 2000-07-13 | 2011-05-18 | 富士通フロンテック株式会社 | Processing apparatus and integrated circuit |
US6959091B1 (en) | 2000-07-28 | 2005-10-25 | Atmel Corporation | Cryptography private key storage and recovery method and apparatus |
US7137143B2 (en) | 2000-08-07 | 2006-11-14 | Ingrian Systems Inc. | Method and system for caching secure web content |
US20040015725A1 (en) * | 2000-08-07 | 2004-01-22 | Dan Boneh | Client-side inspection and processing of secure content |
US20020041683A1 (en) * | 2000-09-29 | 2002-04-11 | Hopkins Dale W. | Method for selecting optimal number of prime factors of a modulus for use in a cryptographic system |
FI111491B (en) * | 2000-11-28 | 2003-07-31 | Setec Oy | Generating a key pair |
US7757278B2 (en) * | 2001-01-04 | 2010-07-13 | Safenet, Inc. | Method and apparatus for transparent encryption |
US7016494B2 (en) * | 2001-03-26 | 2006-03-21 | Hewlett-Packard Development Company, L.P. | Multiple cryptographic key precompute and store |
KR100406754B1 (en) * | 2001-04-11 | 2003-11-21 | 한국정보보호진흥원 | Forward-secure commercial key escrow system and escrowing method thereof |
US7017064B2 (en) * | 2001-05-09 | 2006-03-21 | Mosaid Technologies, Inc. | Calculating apparatus having a plurality of stages |
DE10124139A1 (en) * | 2001-05-17 | 2002-11-21 | Philips Corp Intellectual Pty | Method for securing data transfer between a CPU and ROM memory, used in a chip card or similar, has an additional individual encryption code so that if a first code is known the memory remains secure |
US20030161472A1 (en) * | 2002-02-27 | 2003-08-28 | Tong Chi Hung | Server-assisted public-key cryptographic method |
FR2841411B1 (en) * | 2002-06-19 | 2004-10-29 | Gemplus Card Int | ELECTRONIC KEY GENERATION METHOD FOR PUBLIC KEY CRYTOGRAPHY AND SECURE PORTABLE OBJECT IMPLEMENTING THE METHOD |
KR100474526B1 (en) * | 2002-07-19 | 2005-03-10 | 매그나칩 반도체 유한회사 | Control system with protective ability for external program code |
AU2003262857A1 (en) * | 2002-08-24 | 2004-03-11 | Ingrian Networks, Inc. | Selective feature activation |
US7451326B2 (en) * | 2002-08-26 | 2008-11-11 | Mosaid Technologies, Inc. | Method and apparatus for processing arbitrary key bit length encryption operations with similar efficiencies |
US7386705B2 (en) | 2002-08-27 | 2008-06-10 | Mosaid Technologies Inc. | Method for allocating processor resources and system for encrypting data |
KR100453230B1 (en) * | 2002-11-08 | 2004-10-15 | 한국전자통신연구원 | Hyperelliptic curve crtpto processor hardware apparatus |
US20060149962A1 (en) * | 2003-07-11 | 2006-07-06 | Ingrian Networks, Inc. | Network attached encryption |
US8037102B2 (en) | 2004-02-09 | 2011-10-11 | Robert T. and Virginia T. Jenkins | Manipulating sets of hierarchical data |
US8442219B2 (en) * | 2004-03-31 | 2013-05-14 | Jesse Lipson | Public key cryptographic methods and systems |
US7519835B2 (en) * | 2004-05-20 | 2009-04-14 | Safenet, Inc. | Encrypted table indexes and searching encrypted tables |
US9646107B2 (en) | 2004-05-28 | 2017-05-09 | Robert T. and Virginia T. Jenkins as Trustee of the Jenkins Family Trust | Method and/or system for simplifying tree expressions such as for query reduction |
US7620632B2 (en) | 2004-06-30 | 2009-11-17 | Skyler Technology, Inc. | Method and/or system for performing tree matching |
US7882147B2 (en) * | 2004-06-30 | 2011-02-01 | Robert T. and Virginia T. Jenkins | File location naming hierarchy |
US7711955B1 (en) | 2004-09-13 | 2010-05-04 | Oracle America, Inc. | Apparatus and method for cryptographic key expansion |
US7620821B1 (en) * | 2004-09-13 | 2009-11-17 | Sun Microsystems, Inc. | Processor including general-purpose and cryptographic functionality in which cryptographic operations are visible to user-specified software |
US7801923B2 (en) | 2004-10-29 | 2010-09-21 | Robert T. and Virginia T. Jenkins as Trustees of the Jenkins Family Trust | Method and/or system for tagging trees |
US7627591B2 (en) | 2004-10-29 | 2009-12-01 | Skyler Technology, Inc. | Method and/or system for manipulating tree expressions |
US7636727B2 (en) | 2004-12-06 | 2009-12-22 | Skyler Technology, Inc. | Enumeration of trees from finite number of nodes |
US7630995B2 (en) * | 2004-11-30 | 2009-12-08 | Skyler Technology, Inc. | Method and/or system for transmitting and/or receiving data |
US8316059B1 (en) | 2004-12-30 | 2012-11-20 | Robert T. and Virginia T. Jenkins | Enumeration of rooted partial subtrees |
US8615530B1 (en) | 2005-01-31 | 2013-12-24 | Robert T. and Virginia T. Jenkins as Trustees for the Jenkins Family Trust | Method and/or system for tree transformation |
US7681177B2 (en) * | 2005-02-28 | 2010-03-16 | Skyler Technology, Inc. | Method and/or system for transforming between trees and strings |
US8356040B2 (en) | 2005-03-31 | 2013-01-15 | Robert T. and Virginia T. Jenkins | Method and/or system for transforming between trees and arrays |
US7899821B1 (en) | 2005-04-29 | 2011-03-01 | Karl Schiffmann | Manipulation and/or analysis of hierarchical data |
US20070079386A1 (en) * | 2005-09-26 | 2007-04-05 | Brian Metzger | Transparent encryption using secure encryption device |
US20070079140A1 (en) * | 2005-09-26 | 2007-04-05 | Brian Metzger | Data migration |
US7618214B2 (en) * | 2006-02-03 | 2009-11-17 | Maritime International, Inc. | Containment boom guide system and method |
US8386768B2 (en) * | 2006-02-08 | 2013-02-26 | Safenet, Inc. | High performance data encryption server and method for transparently encrypting/decrypting data |
US7958091B2 (en) | 2006-02-16 | 2011-06-07 | Ingrian Networks, Inc. | Method for fast bulk loading data into a database while bypassing exit routines |
US8670564B1 (en) * | 2006-08-14 | 2014-03-11 | Key Holdings, LLC | Data encryption system and method |
US8379865B2 (en) * | 2006-10-27 | 2013-02-19 | Safenet, Inc. | Multikey support for multiple office system |
US7917747B2 (en) * | 2007-03-22 | 2011-03-29 | Igt | Multi-party encryption systems and methods |
US20090132804A1 (en) * | 2007-11-21 | 2009-05-21 | Prabir Paul | Secured live software migration |
US10678709B2 (en) | 2013-07-15 | 2020-06-09 | Infineon Technologies Ag | Apparatus and method for memory address encryption |
US10176121B2 (en) * | 2013-07-15 | 2019-01-08 | Infineon Technologies Ag | Apparatus and method for memory address encryption |
US9949115B2 (en) | 2014-06-10 | 2018-04-17 | Qualcomm Incorporated | Common modulus RSA key pairs for signature generation and encryption/decryption |
US20150363333A1 (en) * | 2014-06-16 | 2015-12-17 | Texas Instruments Incorporated | High performance autonomous hardware engine for inline cryptographic processing |
US11809610B2 (en) * | 2014-06-16 | 2023-11-07 | Texas Instruments Incorporated | Hardware protection of inline cryptographic processor |
US10044695B1 (en) | 2014-09-02 | 2018-08-07 | Amazon Technologies, Inc. | Application instances authenticated by secure measurements |
US9246690B1 (en) | 2014-09-03 | 2016-01-26 | Amazon Technologies, Inc. | Secure execution environment services |
US9491111B1 (en) | 2014-09-03 | 2016-11-08 | Amazon Technologies, Inc. | Securing service control on third party hardware |
US9754116B1 (en) | 2014-09-03 | 2017-09-05 | Amazon Technologies, Inc. | Web services in secure execution environments |
US9442752B1 (en) | 2014-09-03 | 2016-09-13 | Amazon Technologies, Inc. | Virtual secure execution environments |
US10061915B1 (en) | 2014-09-03 | 2018-08-28 | Amazon Technologies, Inc. | Posture assessment in a secure execution environment |
US10079681B1 (en) | 2014-09-03 | 2018-09-18 | Amazon Technologies, Inc. | Securing service layer on third party hardware |
US9577829B1 (en) | 2014-09-03 | 2017-02-21 | Amazon Technologies, Inc. | Multi-party computation services |
US9584517B1 (en) | 2014-09-03 | 2017-02-28 | Amazon Technologies, Inc. | Transforms within secure execution environments |
KR101754796B1 (en) * | 2014-09-17 | 2017-07-07 | 전남대학교 산학협력단 | Apparatus And method for Controlling Secure Authentication Using Prime Number Feature |
US10333696B2 (en) | 2015-01-12 | 2019-06-25 | X-Prime, Inc. | Systems and methods for implementing an efficient, scalable homomorphic transformation of encrypted data with minimal data expansion and improved processing efficiency |
US10205598B2 (en) | 2015-05-03 | 2019-02-12 | Ronald Francis Sulpizio, JR. | Temporal key generation and PKI gateway |
FR3088452B1 (en) * | 2018-11-08 | 2023-01-06 | Idemia France | METHOD FOR VERIFYING THE INTEGRITY OF A PAIR OF CRYPTOGRAPHIC KEYS AND CRYPTOGRAPHIC DEVICE |
Citations (15)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4200770A (en) * | 1977-09-06 | 1980-04-29 | Stanford University | Cryptographic apparatus and method |
US4218582A (en) * | 1977-10-06 | 1980-08-19 | The Board Of Trustees Of The Leland Stanford Junior University | Public key cryptographic apparatus and method |
US4351982A (en) | 1980-12-15 | 1982-09-28 | Racal-Milgo, Inc. | RSA Public-key data encryption system having large random prime number generating microprocessor or the like |
US4405829A (en) * | 1977-12-14 | 1983-09-20 | Massachusetts Institute Of Technology | Cryptographic communications system and method |
US4424414A (en) * | 1978-05-01 | 1984-01-03 | Board Of Trustees Of The Leland Stanford Junior University | Exponentiation cryptographic apparatus and method |
US4514592A (en) | 1981-07-27 | 1985-04-30 | Nippon Telegraph & Telephone Public Corporation | Cryptosystem |
US4995082A (en) * | 1989-02-24 | 1991-02-19 | Schnorr Claus P | Method for identifying subscribers and for generating and verifying electronic signatures in a data exchange system |
US5046094A (en) | 1989-02-02 | 1991-09-03 | Kabushiki Kaisha Toshiba | Server-aided computation method and distributed information processing unit |
US5136647A (en) | 1990-08-02 | 1992-08-04 | Bell Communications Research, Inc. | Method for secure time-stamping of digital documents |
US5321752A (en) * | 1991-09-05 | 1994-06-14 | Canon Kabushiki Kaisha | Method of and apparatus for encryption and decryption of communication data |
US5343527A (en) | 1993-10-27 | 1994-08-30 | International Business Machines Corporation | Hybrid encryption method and system for protecting reusable software components |
US5351298A (en) | 1991-09-30 | 1994-09-27 | Smith Peter J | Cryptographic communication method and apparatus |
US5761310A (en) | 1995-07-26 | 1998-06-02 | De La Rue Cartes Et Systemes Sas | Communication system for messages enciphered according to an RSA-type procedure |
US5835598A (en) * | 1995-04-12 | 1998-11-10 | Deutsche Telekom Ag | Public key method of encoding data |
US5974151A (en) * | 1996-11-01 | 1999-10-26 | Slavin; Keith R. | Public key cryptographic system having differential security levels |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5046194A (en) * | 1989-07-31 | 1991-09-10 | Alaniz Irma P | Suit for weight lifters |
US5848159A (en) * | 1996-12-09 | 1998-12-08 | Tandem Computers, Incorporated | Public key cryptographic apparatus and method |
-
1997
- 1997-01-16 US US08/784,453 patent/US5848159A/en not_active Ceased
- 1997-12-08 JP JP52677298A patent/JP2001510583A/en not_active Ceased
- 1997-12-08 IL IL13023997A patent/IL130239A/en not_active IP Right Cessation
- 1997-12-08 WO PCT/US1997/022026 patent/WO1998026536A1/en active Application Filing
- 1997-12-08 EP EP97953075.5A patent/EP0950302B1/en not_active Expired - Lifetime
- 1997-12-08 AU AU56893/98A patent/AU5689398A/en not_active Abandoned
-
1998
- 1998-10-26 US US09/328,726 patent/US7231040B1/en not_active Expired - Fee Related
-
2000
- 2000-10-20 US US09/694,416 patent/USRE40530E1/en not_active Expired - Lifetime
Patent Citations (15)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4200770A (en) * | 1977-09-06 | 1980-04-29 | Stanford University | Cryptographic apparatus and method |
US4218582A (en) * | 1977-10-06 | 1980-08-19 | The Board Of Trustees Of The Leland Stanford Junior University | Public key cryptographic apparatus and method |
US4405829A (en) * | 1977-12-14 | 1983-09-20 | Massachusetts Institute Of Technology | Cryptographic communications system and method |
US4424414A (en) * | 1978-05-01 | 1984-01-03 | Board Of Trustees Of The Leland Stanford Junior University | Exponentiation cryptographic apparatus and method |
US4351982A (en) | 1980-12-15 | 1982-09-28 | Racal-Milgo, Inc. | RSA Public-key data encryption system having large random prime number generating microprocessor or the like |
US4514592A (en) | 1981-07-27 | 1985-04-30 | Nippon Telegraph & Telephone Public Corporation | Cryptosystem |
US5046094A (en) | 1989-02-02 | 1991-09-03 | Kabushiki Kaisha Toshiba | Server-aided computation method and distributed information processing unit |
US4995082A (en) * | 1989-02-24 | 1991-02-19 | Schnorr Claus P | Method for identifying subscribers and for generating and verifying electronic signatures in a data exchange system |
US5136647A (en) | 1990-08-02 | 1992-08-04 | Bell Communications Research, Inc. | Method for secure time-stamping of digital documents |
US5321752A (en) * | 1991-09-05 | 1994-06-14 | Canon Kabushiki Kaisha | Method of and apparatus for encryption and decryption of communication data |
US5351298A (en) | 1991-09-30 | 1994-09-27 | Smith Peter J | Cryptographic communication method and apparatus |
US5343527A (en) | 1993-10-27 | 1994-08-30 | International Business Machines Corporation | Hybrid encryption method and system for protecting reusable software components |
US5835598A (en) * | 1995-04-12 | 1998-11-10 | Deutsche Telekom Ag | Public key method of encoding data |
US5761310A (en) | 1995-07-26 | 1998-06-02 | De La Rue Cartes Et Systemes Sas | Communication system for messages enciphered according to an RSA-type procedure |
US5974151A (en) * | 1996-11-01 | 1999-10-26 | Slavin; Keith R. | Public key cryptographic system having differential security levels |
Non-Patent Citations (26)
Title |
---|
A. J. Menezes et al., "Handbook of Applied Cryptography", 1997, Library of Congress catalog No. 96-27609, pp. 89, 612-613. |
Bruce Schneier: "Applied Cryptography" Second Edition, Jan. 1, 1996, John Wiley & sons, USA, XP002283138, pp. 466-474. |
C. Couvruer et al., "An Introduction to Fast Generation of Large Prime Numbers," 1982, Philips Journal of Research, vol. 37, Nos. 5-6, pp. 231-264. |
Captain Nemo, RSA Moduli Should Have 3 Prime factors, Aug. 1996. * |
Cetin Kaya Koc, "High-Speed RSA Implementation (Version 2.0)," Nov. 1994, RSA White Paper, RSA Laboratories. |
D. Boneh et al., "Generating a Product of Three Primes with an Unknown Factorization," Computer Science Department, Stanford University, date unknown. |
Donald Knuth, The Art of Computer Programming, vol. 2, Addison-Wesley Publishing Company 1969. * |
European Search Report, dated Oct. 11, 2004; App No. EP 95 3075. |
International Search Report (PCT), ISA/US; Apr. 6, 1998. * |
Itakura and Nakamura, A Public-Key Cryptosystem Suitable for Digital Multisignatures, NEC Res. & Develop. No. 71 Oct. 1983. * |
J. J. Quisquater et al., "Fast Decipherment Algorithm for RSA Public-Key Cryptosystem" Oct. 1982, Electronic Letters, vol. 19, No. 21. |
J. J. Quisquater et al., "Fast Generation of Large Prime Numbers" Jun. 1982, Library of Congress, Catalog No. 72-179437, IEEE Catalog No. 92CH1767-3 IT, pp. 114-115. |
Kenneth H. Rosen, "Elementary Number Theory and Its Applications," 2nd Edition, Copyright 1988 by Bell Telephone Laboratories and Kenneth H. Rosen, p. 97 (4 p.). |
Knuth, The Art of Computer Programming vol. 2, 1969. * |
M.O. Rabin, "Digitalized Signatures and Public-Key Functions as Intractable as Factorization," Jan. 1979, MIT Laboratory for Computer Science. |
Menezes et al., Handbook of Applied Cryptography, CRC Press, 1997, Chapter 8, "Public-Key Encryption", pp. 283-319. |
Micali et al., "Accountable-Subgroup Multisignatures", CCS '01, Proceedings of the Eighth ACM Conference on Computer and Communications Security, @ACM 2001, Aug. 15, 2001, pp. 1-18. |
P. J. Flinn et al. Using the RSA Algorithm for Encryption and Digital Signatures: Can you Encrypt, Decrypt, Sign and Verify without Infringing the RSA Patent? Jul. 9, 1997, Alston & Bird LLP, http://www.cyberlaw.com/rsa.html. |
PKCS #1: RSA Encryption Standard (Version 1.5), Nov. 1993, RSA Laboratories Technical Note. |
R. Lidl et al., "Permutation Polynomials in RSA-Cryptosystems," 1984, Advances in Cryptology-Crypto '83, pp. 293-301. |
Rivest et al., "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems," Feb. 1978, Communications of the ACM, vol. 21. |
Rivest, et. al. A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, kACM 1979. * |
Rivest, Shamir, and Aldeman, A Method for Obtaining Digital Signatures and Public Key Cryptosystems, Communications of th ACM, 21(2), Feb. 1978. * |
S. A. Vanstone and R. J. Zuccherato, Using four-prime RSA in which some of the bits are specified. * |
S.A. Vanstone et al., "Using Four-Prime RSA in Which Some of the Bits are Specified," Dec. 8, 1994, Electronics Letter, vol. 30, No. 25. pp. 2118-2119. |
Y. Desmedt et al., "Public-Key Systems Based on the Difficulty of Tampering (Is There a Difference Between DES and RSA?)," 1986, Lecture Notes in Computer Science, Advances in Cryptology-Crypto '86 Proceedings. |
Also Published As
Publication number | Publication date |
---|---|
JP2001510583A (en) | 2001-07-31 |
US7231040B1 (en) | 2007-06-12 |
EP0950302A1 (en) | 1999-10-20 |
EP0950302B1 (en) | 2013-05-08 |
AU5689398A (en) | 1998-07-03 |
IL130239A0 (en) | 2000-06-01 |
EP0950302A4 (en) | 2004-11-24 |
WO1998026536A1 (en) | 1998-06-18 |
US5848159A (en) | 1998-12-08 |
IL130239A (en) | 2003-11-23 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
USRE40530E1 (en) | Public key cryptographic apparatus and method | |
EP0997016B1 (en) | Method and apparatus for fast elliptical encryption with direct embedding | |
US4405829A (en) | Cryptographic communications system and method | |
EP0634038B1 (en) | A cryptographic communications method and system | |
US6377688B1 (en) | Cryptographic communication method and system | |
US5581616A (en) | Method and apparatus for digital signature authentication | |
US7499551B1 (en) | Public key infrastructure utilizing master key encryption | |
US7027598B1 (en) | Residue number system based pre-computation and dual-pass arithmetic modular operation approach to implement encryption protocols efficiently in electronic integrated circuits | |
EP1031204B1 (en) | Cryptographic system and method with fast decryption | |
US6813358B1 (en) | Method and system for timed-release cryptosystems | |
GB2407238A (en) | System which blinds a message prior to forwarding to encryption/decryption agent with function which can be reversed after en/decryption | |
US20130236012A1 (en) | Public Key Cryptographic Methods and Systems | |
US7894608B2 (en) | Secure approach to send data from one system to another | |
CN113411345A (en) | Method and device for secure session | |
US6721771B1 (en) | Method for efficient modular polynomial division in finite fields f(2{circumflex over ( )}m) | |
US6111952A (en) | Asymmetrical cryptographic communication method and portable object therefore | |
US7248692B2 (en) | Method of and apparatus for determining a key pair and for generating RSA keys | |
US7305093B2 (en) | Method and apparatus for securely transferring data | |
US6038318A (en) | Optimized machine computation of exponential functions and modulo functions | |
US6772184B2 (en) | Method for efficient modular division over prime integer fields | |
US6826586B2 (en) | Method for efficient computation of point doubling operation of elliptic curve point scalar multiplication over finite fields F(2m) | |
Rushdi et al. | A pedagogical multi-key multi-stage package to secure communication channels | |
US20020025043A1 (en) | Private retrieval of digital objects | |
CN109889330B (en) | Anti-quantum computing blind signature method and system based on asymmetric key pool | |
JPH1155244A (en) | Method for restoring key and device therefor |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AS | Assignment |
Owner name: HEWLETT-PACKARD DEVELOPMENT COMPANY, L.P., TEXAS Free format text: CHANGE OF NAME;ASSIGNOR:COMPAQ INFORMATION TECHNOLOGIES GROUP, L.P.;REEL/FRAME:017036/0650 Effective date: 20021001 |
|
FPAY | Fee payment |
Year of fee payment: 12 |
|
AS | Assignment |
Owner name: HEWLETT PACKARD ENTERPRISE DEVELOPMENT LP, TEXAS Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:HEWLETT-PACKARD DEVELOPMENT COMPANY, L.P.;REEL/FRAME:037079/0001 Effective date: 20151027 |
|
AS | Assignment |
Owner name: ENTIT SOFTWARE LLC, CALIFORNIA Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:HEWLETT PACKARD ENTERPRISE DEVELOPMENT LP;REEL/FRAME:042746/0130 Effective date: 20170405 |
|
AS | Assignment |
Owner name: MICRO FOCUS LLC, CALIFORNIA Free format text: CHANGE OF NAME;ASSIGNOR:ENTIT SOFTWARE LLC;REEL/FRAME:052010/0029 Effective date: 20190528 |