`Sudia
`
`54) ENHANCED CRYPTOGRAPHIC SYSTEM
`AND METHOD WITH KEY ESCROW
`FEATURE
`
`Inventor: Frank Wells Sudia, New York, N.Y.
`Assignee: Certco LLC, New York, N.Y.
`
`Appl. No.: 08/802,603
`Filed:
`Feb. 19, 1997
`Related U.S. Application Data
`
`Division of application No. 08/272.203, Jul. 8, 1994, aban
`doned, which is a continuation-in-part of application No.
`08/181859, Jan. 13, 1994, abandoned.
`Int. Cl. ...................................................... H04L 9/32
`... 380/25; 380/30
`Field of Search .................................... 380/30, 4, 25,
`380/49
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`4,200,770 4/1980 Hellman et al..
`4,218,582 8/1980 Hellman et al..
`4,405,829 9/1983 Rivest et al..
`4,558,176 12/1985 Arnold et al. .............................. 380/4
`4,771,461 9/1988 Matyas ...................................... 380/24
`4,868,877 9/1989 Fischer.
`4,995,082 2/1991 Schnorr.
`5,001,752 3/1991 Fischer.
`5,005,200 4/1991 Fischer.
`5,136,643 8/1992 Fischer.
`5,150,411
`9/1992 Maurer.
`5,164,988 11/1992 Matyas et al..
`5,199,070 3/1993 Matsuzaki et al..
`5,214,700 5/1993 Pinkas et al..
`5,214,702 5/1993 Fischer.
`5,222,140 6/1993 Beller et al..
`5,261,002 11/1993 Perlman et al..
`5,276,737
`1/1994 Micali.
`5,313,521
`5/1994 Torii et al..
`5,315,658 5/1994 Micali.
`5,499.295 3/1996 Cooper ...................................... 380/23
`5,787,172 7/1998 Arnold ...................................... 380/21
`
`USOO60.09177A
`Patent Number:
`11
`(45) Date of Patent:
`
`6,009,177
`Dec. 28, 1999
`
`OTHER PUBLICATIONS
`American National Standard X9.30, “Public Key Cryptog
`raphy Using Irreversible Algorithms for the Financial Ser
`vices Industry: Part 1: The Digital Signature Algorithm
`(DSA)” (American Bankers Assn., Washington, D.C.,
`1993).
`American National Standard X9.30, “Public Key Cryptog
`raphy Using Irreversible Algorithms for the Financial Ser
`vices, Industry: Part 2: The Secure Hash Algorithm (SHA)”
`(American Bankers Assn., Washington, D.C., 1993).
`American National Standard X9.30, “Public Key Cryptog
`raphy Using Irreversible Algorithms for the Financial Ser
`vices, Industry: Part 3: Certificate Management for DSA’
`(American Bankers Assn., Washington, D.C., 1993).
`Silvio Micali, “Fair Public Key Cryptosystems”, Laboratory
`for Computer Science of the Massachusetts Institute of
`Technology, Oct. 13, 1993.
`Donn B. Parker, “Crypto and Avoidance of Business Infor
`mation Anarchy First Annual AC Conference on Computer
`and Communication Security, Nov. 3-5, 1993, Reston, VA.
`(List continued on next page.)
`Primary Examiner-Gilberto Barrón, Jr.
`Attorney, Agent, or Firm-Steptoe & Johnson LLP
`57
`ABSTRACT
`The invention provides a cryptographic System and method
`with a key escrow feature that uses a method for verifiably
`Splitting users’ private encryption keys into components and
`for Sending those components to trusted agents chosen by
`the particular users, and provides a System that uses modern
`public key certificate management, enforced by a chip
`device that also self-certifies. The methods for key escrow
`and receiving an eScrow certificate are also applied herein to
`a more generalized case of registering a trusted device with
`a trusted third party and receiving authorization from that
`party enabling the device to communicate with other trusted
`devices. Further preferred embodiments provide for rekey
`ing and upgrading of device firmware using a certificate
`System, and encryption of Stream-oriented data.
`
`18 Claims, 25 Drawing Sheets
`
`Ks-ttp
`241-1 KKStpp swa
`
`244,
`A USER'S REG, REEST
`
`KSmfgr
`KSiswa
`
`REG, F EWIE
`WITH TRUSTE
`THIRD PARY
`
`8, TTP's RESPONSE
`
`246
`
`
`
`242 EWE ERT
`OWIE Yp
`DEVICE SER No.
`KSidew
`-mfgr.
`
`
`
`
`
`TT's GRANT
`SFWARE AND/OR PLB,
`E. ALITHIRIZATION key LeAES cop.
`TT NAME
`TRS. SFTWARE
`App I, ATA
`TRUSE KEYS
`LSER IN
`APPLIC, ATA
`DEVICE INF
`tto -
`-247
`KSidew
`24g
`-ttP - - - - - - - - -
`NAME
`HEiver
`AR5UAERADE'' - UPGRADE AUTH-24
`ALTH CER
`SW
`
`
`
`
`
`
`
`24.)
`
`242
`
`Wre
`
`RUST
`KSew
`KS devemf gr
`KSimfgr
`kStswa
`
`TRANSACTIONCS)
`USER'S ALTH
`249
`242 TTP's GRANT
`TRANS, DATA
`F ATH,
`User INF
`--
`KSidew
`- Pl
`-dew
`
`
`
`FURTH PARTY
`(eg TRADING
`pARTNER)
`KSiswa
`Kshttp
`
`SAMSUNG EX. 1037 - 1/53
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`
`6,009,177
`Page 2
`
`OTHER PUBLICATIONS
`CCITT Recommendation X.509, “The Directory-Authen
`tication Framework, International Standards Organization
`(ISO), Melbourne, Australia 1988.
`Dorothy E. Denning, “The Clipper Encryption System”,
`American Scientist, Jul.-Aug., 1993, pp. 319-323.
`Martin E. Hellman, “Commercial Encryption', IEEE Net
`work Magazine, Apr. 1987, vol. 1, No. 2, pp. 6-10.
`
`David B. Newman, Jr., Jim K. Omura and Raymond L.
`Pickholtz, “Public Key Management for Network Security”,
`IEEE Network Magazine, Apr. 1987, vol. 1, No. 2, pp.
`11-16.
`
`IBM Technical Disclosure Bulletin, “Cyrptographic Micro
`code Loading Controller for Secure Function”, vol. 34, No.
`4B, Sep. 1991, pp. 34–36.
`
`SAMSUNG EX. 1037 - 2/53
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`
`U.S. Patent
`
`Dec. 28, 1999
`
`Sheet 1 of 25
`
`6,009,177
`
`DIFFIE-HELLMAN AND MICALI ABBREVIATIONS
`
`X
`X1 , , ,
`x i
`
`RECIPIENTS PRIVATE KEY (EXPONENT )
`NUMBERED FRAGMENTS OF PRIVATE KEY
`i-th FRAGMENT OF PRIVATE KEY
`SENDER" S. EPHEMERAL PRIVATE KEY C EXPONENT )
`PLELIC BASE NUMBER
`PUBLIC PRIME MOLLUS NUMBER
`INTERMEDIATE NUMBER = ox mod P
`OHx
`INTERMEDIATE NUMBER = oy mod P
`OH
`DIFFIE-HELLMAN OERIVED MESSAGE KEY
`Kd
`V1, ... n MICALI INTERMEDIATE NUMBER, s axi mod P
`
`THER SYMMETRIC KEY ABBREVIATIONS
`
`
`
`Kmsg
`
`C
`
`RANDOM OR DERIVED MESSAGE KEY
`PLAINTEXT MESSAGE
`CIFPHERTEXT MESSAGE
`
`FIG. BSEESA, ASMETRIC
`
`PUBLIC PRIVATE
`
`
`
`SIGNATURE
`
`ENCRYPTION
`
`KKS dev>mfor
`
`FIG. CRESSEATE
`
`PBLIC SIGNATURE KEY
`OF THE DEVICE
`SIGNED BY MANUFACTURER
`(USING MFGR PRIVATE KEY: KS-mfgr)
`
`SAMSUNG EX. 1037 - 3/53
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`US. Patent
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`Dec. 28, 1999
`
`Sheet 2 0f 25
`
`6,009,177
`
`
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`SAMSUNG EX. 1037 - 4/53
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`U.S. Patent
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`Dec. 28, 1999
`
`Sheet 3 of 25
`
`6,009,177
`
`FIG. F
`SHORTHAND NOTATION - SIGNING
`
`<doto) dev
`
`{dotod KS dev
`
`-dev
`
`FIG. G
`SHORTHAND NOTATION - ENCRYPTION
`<dotoxsender = ( dota ) KEsender
`
`FIG. 2
`INTERACTIVE DIFFIE-HELLMAN KEY OERIVATIVE
`PRIOR AGREEMENT ON (NON-SECRET )
`PRIME P AND VALUE a
`PARTY A
`GENERATE SECRET 21
`GENERATE SECRET
`RANDOM NUMBER x
`RANDOM NUMBER y
`COMPUTE
`COMPUTE
`ax mod p
`oy mod p
`COMPUTE KEY
`COMPUTE KEY
`(oy) mod
`c ox)y mod
`COMMON KEY axy mod p KNDWN BY A AND B
`BUT NOT DEDUCIBLE BY AN EAVESOROPPER
`
`PARTY B
`
`
`
`22
`
`24
`
`23
`
`
`
`
`
`
`
`
`
`
`
`
`
`221
`
`223
`FIG. 22
`DEVICE OWNER'S
`CERTIFICATE ( EXAMPLE)
`
`
`
`
`
`
`
`VERSION NO ,
`DEVICE SERIA No.
`OWNER NAME
`OWNER UNIQUE ID
`KS
`WNER
`PURCHASE DATE
`
`220
`
`222
`
`224
`
`225
`
`MFGR SIGNATURE
`
`SAMSUNG EX. 1037 - 5/53
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`US. Patent
`
`])ec.28,1999
`
`Sheet 4 0f 25
`
`6,009,177
`
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`])ec.28,1999
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`Sheets 0f25
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`6,009,177
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`US. Patent
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`Dec. 28, 1999
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`Sheet6 0f25
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`6,009,177
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`U.S. Patent
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`Dec. 28, 1999
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`Sheet 7 of 25
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`6,009,177
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`SAMSUNG EX. 1037 - 9/53
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`U.S. Patent
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`Dec. 28, 1999
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`Sheet 8 of 25
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`6,009,177
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`FIG
`
`MICAL ESCROW PROCESS EXAMPLE -
`USER OPERATIONS
`
`SECRET
`GENERATE OH PARAMETERS g2 RANDOM
`NUMBERS
`PRIVATE KEY COMPONENTS
`x1, x2, x
`3
`
`PUBLIC CONSTANTS
`PRIME
`Pl
`BASE
`a
`
`USERS PRIVATE KEY X
`( x1 + x2 + x3) mod P-O-X
`
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`STORE PRIVATE
`KEY
`SECURELY
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`OH INTERMEDIATE NO ,
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`
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`93
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`94
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`SAMSUNG EX. 1037 - 10/53
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`D
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`])ec.28,1999
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`Sheet10 0f25
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`6,009,177
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`
`
`
`
`
`U.S. Patent
`
`Sheet 11 0f 25
`
`6,009,177
`
`Dec. 28, 1999
`FIG. 2
`
`ESCROW CERTIFICATE ( EXAMPLE X
`
`VERSION NO ,
`CERTIFICATE SERIAL No.
`ESCROW CENTER NAME
`ESCROW CENTER COUNTRY CODE
`KE ec (FOR LEAF USE)
`USER NAME
`KEt user (FOR MESSAGES)
`KStdev ( To VERIFY LEAF
`VALIDITY PERIOO
`
`ESCROW CENTER SIGNATURE
`
`123
`21
`
`122
`
`124
`
`25
`
`FIG. 3
`
`CLIPPER LEAF PACKET C CONJECTURED)
`* msgkdv
`CHECKSUM OF Kmsg
`
`
`
`
`
`OEVICE SERIA No,
`
`CHECKSUM OF LEAF
`
`Kfam
`
`
`
`
`
`SYMMETRIC MESSAGE KEY
`EMBEDOED SYMMETRIC DEVICE KEY
`SYMMETRIO CLIPPER FAMILY KEY
`
`SAMSUNG EX. 1037 - 13/53
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`
`
`U.S. Patent
`
`Dec. 28, 1999
`
`Sheet 12 of 25
`
`6,009,177
`
`FIG. 4
`DEVICE CERTIFICATE : <KS devemfgr. C EXAMPLE)
`
`
`
`
`
`VERSION NO ,
`MFGR NAME
`DEVICE SERIAL. No,
`OEVICE TYPE/MOOEL
`MFG DATE
`KS todev
`ATTRIBUTE CODES (OPTIONAL )
`
`MFGR SIGNATURE
`
`FIG. 18
`MESSAGE CONTROL HEADER C EXAMPLE)
`( IN RSA - KEY - TRANSPORT FORMAT )
`
`
`
`
`
`VERSION NO ,
`(MESSAGE KEY) KErecip
`SENDER ESCROW CENTER NAME ( 21 )
`SENDER ESCROW CENTER COUNTRY COOE
`RECIPIENT ESCROW CENTER NAME ( eC2)
`RECIPIENT ESCROW CENTER COUNTRY CODE
`(SENDER ESCROW CERT, NO, ) KE ec 1
`(MESSAGE KEY) KEtsender (TD HIMSELF)
`C RECIP, ESCROW CERT. No, ) KEtec2
`TIMESTAMP (OPTIONAL )
`
`SENOER DEVICE SIGNATURE
`
`B1
`
`181
`
`181
`81
`
`SAMSUNG EX. 1037 - 14/53
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`SAMSUNG EX. 1037 - 15/53
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`
`US. Patent
`
`])ec.28,1999
`
`Sheet 14 0f 25
`
`6,009,177
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`SAMSUNG EX. 1037 - 17/53
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`SAMSUNG EX. 1037 - 17/53
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`
`
`US. Patent
`
`Dec. 28, 1999
`
`Sheet 16 0f 25
`
`6,009,177
`
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`US. Patent
`
`])ec.28,1999
`
`Sheet 17 0f 25
`
`6,009,177
`
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`SAMSUNG EX. 1037 - 19/53
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`SAMSUNG EX. 1037 - 19/53
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`
`
`U.S. Patent
`
`Dec. 28, 1999
`
`Sheet 18 of 25
`
`6,009,177
`
`TAMPER-RESISTANT DEVICE
`
`CPU
`CRYPTO
`CDPROCESSOR
`
`21 O
`
`MEMORY:
`KST dev
`<KS dev>mfg
`KS swo
`FIRM NAME
`OTHER KEYS
`& CERTS
`DEVICE
`
`CLOCK BATTERYC
`
`
`
`TRUSTED TIME-SETTING
`ENT (eg POST OFFICE)
`2 1
`TIME-SET
`INSTRUCTION
`THE TIME IS NOW
`3: O5PM JAN 3, 1994
`SET YOURSELF AND
`PROCEEO
`SIGNED,
`POST OFFICE
`
`TIME-SET AUTH, CERT,
`"POST OFFICE" IS. A
`TRUSTED TIME-SETTER
`SIGNED, SYSTEMWIDE
`AUTHORITY
`
`212
`
`VERIFIES
`
`(NOTE: TIMESTAMP WILL
`BE NULL IF CLOCK
`NOT CALIBRATED )
`
`ANY DATA STRUCTURE
`CONTAINING A CONTEMP
`ORANEOUS TIMESTAMP
`
`213
`JAN 3, 1994 - 3:05PM
`
`214
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`SIGNED, DEVICE
`
`25
`
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`IS TRUSTED
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`
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`SELF-CERTIFYING TRUSTED TIMESTAMP DEVICE
`
`SAMSUNG EX. 1037 - 20/53
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`
`
`U.S. Patent
`
`Dec. 28, 1999
`
`Sheet 19 of 25
`
`6,009,177
`
`239
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`231
`
`232
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`REUEST
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`
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`FIG. 23
`OWNER REKEY INSTRUCTIONS PROCESS
`
`SAMSUNG EX. 1037 - 21/53
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`
`
`US. Patent
`
`hS
`
`77
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`SAMSUNG EX. 1037 - 22/53
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`SAMSUNG EX. 1037 - 22/53
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`U.S. Patent
`
`Dec. 28, 1999
`
`Sheet 21 of 25
`
`6,009,177
`
`
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`
`SAMSUNG EX. 1037 - 23/53
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`SAMSUNG EX. 1037 - 24/53
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`
`US. Patent
`
`Dec. 28, 1999
`
`Sheet 23 0f 25
`
`6,009,177
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`US. Patent
`
`Dec. 28, 1999
`
`Sheet24 0f25
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`6,009,177
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`
`US. Patent
`
`Dec. 28, 1999
`
`Sheet25 0f25
`
`6,009,177
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`
`6,009,177
`
`1
`ENHANCED CRYPTOGRAPHC SYSTEM
`AND METHOD WITH KEY ESCROW
`FEATURE
`
`CROSS-REFERENCE TO RELATED
`APPLICATION
`This is a division of application Ser. No. 08/272,203, filed
`Jul. 8, 1994, now abandoned which is a continuation-in-part
`of application Ser. No. 08/181859, filed Jan. 13, 1994, now
`abandoned.
`
`2
`149. The sender cryptographic device uses the DES algo
`rithm to encrypt the message when loaded with the cipher
`key (a DES cipher key is 56 bits long) for that session of
`communication (the Session key). The recipient crypto
`graphic device uses an inverse of the DES algorithm to
`decrypt the encrypted message when loaded with the same
`cipher key as was used for encryption. However, the
`adequacy of Symmetric key cryptosystems in general has
`been questioned because of the need for the Sender and the
`recipient to exchange the cipher key over a Secure channel
`to which no unauthorized third party has access, in advance
`of the desired communications between the Sender and
`recipient. This process of first Securely exchanging cipher
`keys and only then encrypting the communication is often
`Slow and cumberSome, and is thus unworkable in Situations
`requiring spontaneous or unsolicited communications, or in
`Situations requiring communications between parties unfa
`miliar with each other. Moreover, interception of the cipher
`key by an unauthorized third party will enable that party to
`eavesdrop on both ends of the encrypted conversation.
`The Second class of cryptographic algorithms, asymmet
`ric key algorithms, uses different cipher keys for encrypting
`and decrypting. In a cryptosystem using an asymmetric key
`algorithm, the user makes the encryption key public and
`keeps the decryption key private, and it is not feasible to
`derive the private decryption key from the public encryption
`key. Thus, anyone who knows the public key of a particular
`user could encipher a message to that user, whereas only the
`user who is the owner of the private key corresponding to
`that public key could decipher the message. This public/
`private key System was first proposed in Diffie and Hellman,
`“New Directions in Cryptography,” IEEE Transactions on
`Information Theory, Nov. 1976, and in U.S. Pat. No. 4,200,
`770 (Hellman et al.), both of which are hereby incorporated
`by reference.
`An early type of asymmetric key algorithm allows Secure
`communication over an insecure channel by interactive
`creation by the communicating parties of a cipher key for
`that Session of communication. Using the asymmetric key
`algorithm, two interacting users Simultaneously and inde
`pendently generate a Secure cipher key that cannot be
`deduced by an eavesdropper and that is to be used Sym
`metrically to encode that Session of communications
`between the users. This interactive method of generating a
`secure cipher key was described by Diffie and Hellman in
`their 1976 paper. Under this prior art method, known as the
`Interactive Diffie-Hellman Scheme, shown in FIG. 2, each of
`the two users A,B randomly chooses a Secret number 21,22
`and then computes an intermediate number 23.24 using two
`publicly-known numbers and the secret number 21.22 cho
`Sen by that user. Each user next transmits the intermediate
`number 23.24 to the other user and then computes the secret
`(Symmetric) cipher key 25 using his own Secret number
`21,22 and the intermediate number 24.23 just received from
`the other user. The interactively generated cipher key 25 is
`then used symmetrically by both users as a DES or other
`Symmetric cipher key to encrypt and decrypt that Session of
`communications over an otherwise insecure channel in the
`manner of Symmetric key algorithm communications. This
`interactive process requires only a few Seconds of real time,
`and all digital communications, including digitized Sound or
`Video transmissions, in a particular Session can be encrypted
`merely by pushing a button at the outset of a Session to
`initiate the interactive key exchange process. Because all the
`numbers chosen in the Interactive Diffie-Heilman key gen
`eration Scheme are very large, the computations are infea
`Sible to invert and the Secret cipher key cannot be computed
`
`BACKGROUND OF THE INVENTION
`This invention relates to cryptographic communications
`Systems. More particularly, this invention relates to the
`Secure generation, certification, Storage and distribution of
`cryptographic keys used in cryptographic communications
`Systems. Still more particularly, this invention relates to a
`System of cryptographic key escrow and public-key certifi
`cate management enforced by a Self-certifying chip device.
`The development and proliferation of Sophisticated com
`puter technology and distributed data processing Systems
`has led to a rapid increase in the transfer of information in
`digital form. This information is used in financial and
`banking matters, electronic mail, electronic data interchange
`and other data processing Systems. Transmission of this
`information over unsecured or unprotected communication
`channels risks exposing the transmitted information to elec
`tronic eavesdropping or alteration. Cryptographic commu
`nications Systems preserve the privacy of these transmis
`Sions by preventing the monitoring by unauthorized parties
`of messages transmitted over an insecure channel. Crypto
`graphic communications Systems also ensure the integrity of
`these transmissions by preventing the alteration by unau
`thorized parties of information in messages transmitted over
`an insecure channel. The cryptographic communications
`Systems can further ensure the integrity and authenticity of
`the transmission by providing for recognizable, unforgeable
`and document-dependent digitized signatures that can pre
`vent denial by the Sender of his own message.
`Cryptographic Systems involve the encoding or encrypt
`ing of digital data transmissions, including digitized voice or
`Video transmissions, to render them incomprehensible by all
`but the intended recipient. A plaintext message consisting of
`digitized Sounds, letters and/or numbers is encoded numeri
`cally and then encrypted using a complex mathematical
`algorithm that transforms the encoded message based on a
`given Set of numbers or digits, also known as a cipher key.
`The cipher key is a Sequence of data bits that may either be
`randomly chosen or have special mathematical properties,
`depending on the algorithm or cryptosystem used. Sophis
`ticated cryptographic algorithms implemented on computers
`can transform and manipulate numbers that are hundreds or
`thousands of bits in length and can resist any known method
`of unauthorized decryption. There are two basic classes of
`cryptographic algorithms: Symmetric key algorithms and
`asymmetric key algorithms.
`Symmetric key algorithms use an identical cipher key for
`both encrypting by the Sender of the communication and
`decrypting by the receiver of the communication. Symmet
`ric key cryptosystems are built on the mutual trust of the two
`parties sharing the cipher key to use the cryptosystem to
`protect against distrusted third parties. The best known
`Symmetric key algorithm is the National Data Encryption
`Standard (DES) algorithm first published by the National
`Institute of Standards and Technology. See Federal Register,
`Mar. 17, 1975, Vol. 40, No. 52 and Aug. 1, 1975, Vol. 40, No.
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`by an eavesdropper, thus preserving the privacy of the
`communication. Because the computations are infeasible to
`invert, each user knows that any communication received
`using this algorithm was not altered and could have been
`Sent only by the other user, thus preserving the integrity and
`authenticity of the communication. This interactive key
`eXchange method, however, requires the parties to interact in
`real time in order to create the cipher key and may not be
`useful for unsolicited communications or unfamiliar parties.
`In particular, the Interactive Diffie-Rellman key exchange
`Scheme does not work for Store-and-forward electronic-mail
`Style messaging or for long-term Storage of documents in an
`electronic data Storage System, because the recipient is not
`on-line to negotiate the Session key.
`A modified, non-interactive form of the Diffie-Hellman
`Scheme, known as Certified Diffie-Hellman, can be used
`when the communicating parties are not on-line together.
`The initial, certification step of the Certified Diffie-Hellman
`Session key generation Scheme is shown in FIG. 3. One user,
`the recipient-to-be, randomly chooses a Secret number 31
`(his private key) and then computes an intermediate number
`33 using two publicly-known numbers 32 and the secret
`number 31 chosen by that user. That user then sends proof
`of identification along with the intermediate number and the
`two public numbers, which numbers together form his
`public key 34, to a certifying authority that then issues a
`public key certificate 35 digitally signed 36 by the issuing
`certifying authority binding the user's identity to the user's
`Diffie-Hellman public key information 34. The public key
`34 publicized by that user remains the same until he decides
`to rekey and choose another private key 31. MeSSaging using
`the Certified Diffie-Hellman method is shown in FIG. 4. In
`order to transmit a message to that-user, a Sending user first
`obtains the receiving user's certificate 35 and verifies the
`certifying authority's Signature 36. The Sender next com
`35
`putes the Session key 42 for that communication Session
`using the recipient's intermediate number 33 (from the
`recipient's certificate) and the Sender's own Secret number
`41 (his private key), which he chooses at random. The
`Sender then encrypts a message 43 using the Session key 42
`and places his own intermediate number 40 unencrypted at
`the head of the communication. Upon receiving the
`communication, the recipient computes the Session key 42
`using the Sender's unencrypted intermediate number 40 and
`his own Secret number 31 (or private key), and then uses the
`Session key 42 to decrypt the message 43. AS with the
`Interactive Diffie-Hellman Scheme, the Session key gener
`ated in the Certified Diffie-Hellman scheme is then used by
`both parties to encrypt and decrypt communications during
`that Session over an otherwise insecure channel using a
`conventional symmetric algorithm, such as DES. The Cer
`tified Diffie-Hellman scheme, however, requires that a
`trusted entity or a certifying authority sign the receiving
`user's public key certificate So that a Sending user can trust
`that the information contained within is correct. In addition,
`the private key randomly chosen by the sender, with which
`he computes both the Session key and the intermediate
`number for that communication, must not be identical to the
`private key that is connected to the Sender's own public key
`certificate; in order to avoid others learning his permanent
`60
`private key numbers (corresponding to the public key num
`bers that have been certified), the sender should keep them
`distinct from any ephemeral private keys or intermediate
`numbers that are generated only for Specific messages.
`Another asymmetric key algorithm, named the RSA algo
`rithm after the inventors Rivest, Shamir and Adleman, is
`described in U.S. Pat. No. 4,405,829 (Rivest et al.), which is
`
`4
`hereby incorporated by reference, and involves the difficulty
`of factoring a number that is the product of two large prime
`numbers. As with the Interactive Diffie-Hellman Scheme, the
`RSA algorithm is relatively straightforward to compute but
`practically infeasible to invert. Thus, it is not feasible to
`derive the private key from the public key and, in this way,
`the privacy of the communication is preserved. Once a
`message is encrypted with the public key using the RSA
`algorithm, only the private key can decrypt it, and Vice
`versa. As with the Certified Diffie-Hellman Scheme, the RSA
`algorithm requires a trusted entity to certify and publicize
`the users public keys. In contrast to