WO1993009620A1 - Method, sender apparatus and receiver apparatus for modulo operation - Google Patents

Method, sender apparatus and receiver apparatus for modulo operation Download PDF

Info

Publication number
WO1993009620A1
WO1993009620A1 PCT/EP1992/002449 EP9202449W WO9309620A1 WO 1993009620 A1 WO1993009620 A1 WO 1993009620A1 EP 9202449 W EP9202449 W EP 9202449W WO 9309620 A1 WO9309620 A1 WO 9309620A1
Authority
WO
WIPO (PCT)
Prior art keywords
sender
receiver
mod
values
value
Prior art date
Application number
PCT/EP1992/002449
Other languages
French (fr)
Inventor
David Naccache
Original Assignee
Thomson Consumer Electronics S.A.
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Thomson Consumer Electronics S.A. filed Critical Thomson Consumer Electronics S.A.
Priority to US08/199,213 priority Critical patent/US5479511A/en
Priority to EP92922272A priority patent/EP0611506B1/en
Priority to DE69218961T priority patent/DE69218961T2/en
Publication of WO1993009620A1 publication Critical patent/WO1993009620A1/en

Links

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
    • G06Q20/30—Payment architectures, schemes or protocols characterised by the use of specific devices or networks
    • G06Q20/36—Payment architectures, schemes or protocols characterised by the use of specific devices or networks using electronic wallets or electronic money safes
    • G06Q20/367—Payment architectures, schemes or protocols characterised by the use of specific devices or networks using electronic wallets or electronic money safes involving electronic purses or money safes
    • G06Q20/3674—Payment architectures, schemes or protocols characterised by the use of specific devices or networks using electronic wallets or electronic money safes involving electronic purses or money safes involving authentication
    • 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
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3234—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving additional secure or trusted devices, e.g. TPM, smartcard, USB or software token

Definitions

  • the present invention relates to a method, to a sender appa ⁇ ratus and to a receiver apparatus for modulo operation.
  • d-th roots modulo X are used where X is a com ⁇ posite number having at least two large prime factors.
  • is 64 bytes.
  • a sender e.g. a smart-card
  • communicates with a receiver only few data are transmitted in order to save time. But this results in an increased number of computation operations in the sender and/or receiver.
  • the invention is applicable when a first cryptographic device (sender) communicates with a second cryptographic device (receiver) , especially when the devices use a modulo-based protocol. Thereby the required number of modular operations is reduced or even eliminated. It can be avoided to do modular operations by the first device.
  • said first device e.g. a smart-card
  • said second device e.g. a powerful processor acting as a verifier
  • S D mod X
  • Number A is a secret of the sender.
  • Number i may have a value of 10.
  • the first and the second variant can be modified.
  • This modi ⁇ fication fits especially to smart-card applications. It al ⁇ lows the sender to perform squarings or a multiplication (which result is E) with only
  • Fig. 1 shows an inventive communication protocol between the sender and the receiver
  • Fig. 2 shows a sender and a receiver.
  • Fig. 1 shows an interface 10 between a sender, e.g. a weak processor in a smart-card, and a receiver, e.g. a pay TV de ⁇ coder, which may contain a powerful processor for calculating the modulo function.
  • of E and E(j), respectively, is less than four times the length
  • a receiver device 27 and a sender device 28 are depicted.
  • the sender device contains a first microprocessor 25, first memory means 26 which are connected to microproces ⁇ sor 25 and a first connector 24 for data exchange with re ⁇ DCver device 27.
  • the receiver device 27 contains a second microprocessor 22, second memory means 21 which are connected to microprocessor 22 and a second connector 23 for data exchange with sender device 28.
  • First connector 24 and second connector 23 represent the in ⁇ terface 10 in Fig. 1.
  • the first memory means 26 store inter ⁇ mediate calculation results and/or values X and/or B or Lo (E)/High(E) .
  • First microprocessor 25 computes data as shown in the left side of Fig. 1.
  • the second memory means 21 store value X and/or intermediate results.
  • Second microprocessor 22 computes data as shown in the right side of Fig. 1.
  • the invention can be used for identification (VideoCrypt or EuroCrypt Pay TV system) and/or digital signature (credit cards) and/or encryption, especially together with one or more of the following systems for getting in the receiver modulo calculated results without respective modulo calcula ⁇ tion in the sender i

Abstract

In access control systems, e.g. pay TV systems, square, or more general, d-th roots modulo X are used where X is a composite number having at least two large prime factors. If a sender, e.g. a smart-card, communicates with a receiver only few data are transmitted in order to save time. But this results in an increased number of computation operations in the sender and/or receiver. The invention is applicable when a first cryptographic device (28) communicates with a second cryptographic device (27), especially when the devices use a modulo-based protocol. Thereby the required number of modular operations is reduced or even eliminated. It can be avoided to do modular operations by the first device. This is particularly advantageous when said first device has a weaker computational power (e.g. less RAM and/or ROM capacity, slower clock rate) than said second device.

Description

Method/ sender apparatus and receiver apparatus for modulo operation
The present invention relates to a method, to a sender appa¬ ratus and to a receiver apparatus for modulo operation.
Background
In access control systems, e.g. pay TV systems, square, or more general, d-th roots modulo X are used where X is a com¬ posite number having at least two large prime factors. Typi¬ cally the length of such a number X (denoted |X|) is 64 bytes.
If a sender, e.g. a smart-card, communicates with a receiver only few data are transmitted in order to save time. But this results in an increased number of computation operations in the sender and/or receiver.
Invention
It is one object of the invention to disclose a method for time-reduced modulo operations. This object is reached by the inventive method disclosed in claim 1.
In principle the inventive method consists in secure sending of a number S = D mod X or of a set of numbers S(j) = D(j) mod X, j = l,...,i, from a sender device 28 to a receiver device 27, whereby X is a product of at least two big prime numbers and D is greater than X, comprising the following steps:
- picking a random number A or a set of random numbers A(j) by said sender device;
- calculating in said sender a value E = D+A*X or a set of values E(j) = D(j)+A(j)*X, whereby X is stored in said send¬ er,, or calculating in said sender a set of values E(j) = D(j)*B, whereby a fixed number B = A*X is stored in said sender;
- transmitting via an interface 10 said value and said val¬ ues, respectively, from said sender to said receiver;
- calculating by said receiver S = E mod X or S(j) = E(j) mod X, whereby the number X is stored in said receiver device.
Advantageous additional embodiments of the inventive method are resulting from the respective dependent claims.
It is a further object of the invention to disclose a sender apparatus which utilizes the inventive method. This object is reached by the inventive apparatus disclosed in claim 6.
In principle the inventive sender apparatus consists in first computation means 25, first memory means 26 which are connected to said first computation means and first data ex¬ change means 24 which are connected to said first computation means, whereby either said first memory means store said modulus X and said first computation means select said random number A or random num¬ bers A(j) and calculate said value E = D+A*X or calculate said set of values E(j) = D(j)+A(j)*X or said first memory means store said fixed number B and said first computation means calculate said set of values E(j) = D(j)+B and whereby said first data exchange means 24 send said value E or said set of values E(j) to said receiver device 27.
Advantageous additional embodiments of the inventive sender apparatus are resulting from the respective dependent claims.
It is a further object of the invention to disclose a receiv¬ er apparatus which utilizes the inventive method. This object is reached by the inventive apparatus disclosed in claim 7. In principle the inventive receiver apparatus consists in second computation means 22, second memory means 21 which are connected to said second computation means and second data exchange means 23 which are connected to said second computation means, whereby said second memory means store said modulus X and said second computation means calculate the modulo function S = E mod X of said value E or calculate a set of modulo functions S(j) = E(j) mod X of said set of values E(j) .
Advantageous additional embodiments of the inventive receiver apparatus are resulting from the respective dependent claims.
The invention is applicable when a first cryptographic device (sender) communicates with a second cryptographic device (receiver) , especially when the devices use a modulo-based protocol. Thereby the required number of modular operations is reduced or even eliminated. It can be avoided to do modular operations by the first device.
This is particularly advantageous when said first device, e.g. a smart-card, has' a weaker computional power (e.g. less RAM and/or ROM capacity, slower clock rate) than said second device (e.g. a powerful processor acting as a verifier) .
There are such access control systems where all the numbers appearing in the first ("weaker") device have a size n*|X| bytes before modular reduction, where n is a very small inte¬ ger, typically 2 or 3.
There are different variants of the inventive method. First variant:
Let D be a number of length n*|X| bytes.
The sender wishes to communicate S = D mod X to the receiver. For avoiding the modular reduction the sender chooses a ran¬ dom number A, computes E = D+A*X and sends this value E to the receiver. Since A is random the value of D is hidden in E and the receiver can calculate S by: S — E mod X, because E mod X = D mod X + A*X mod X = D mod X.
Second variantΪ
The sender wishes to communicate a set of i numbers S(j) =
D(j) mod X to the receiver.
Number A is a secret of the sender. The sender keeps in a ROM a pre-calculated constant B, B = A*X.
As before, let D(l) , ... ,D(i) be a set of numbers (all bigger than X) such that the set of values S(j) is to be send to the receiver. Then these D(i) can be hidden by sending to the receiver E(l) = D(l)+B,— ,E(i) = D(i)+B. The receiver will recover S(j) by calculating:
S(j) — E(j) mod X, because
E(j) mod X = D(j) mod X + B mod X = D(j) mod X.
Number i may have a value of 10.
The first and the second variant can be modified. This modi¬ fication fits especially to smart-card applications. It al¬ lows the sender to perform squarings or a multiplication (which result is E) with only |X| RAM bytes.
For doing so the sender computes only the [X| lower bytes of E (denoted Low(E)) and sends them to the receiver. This com¬ putation of Low(E) requires only [X| RAM cells. After the receiver gets Low(E) , the sender can reuse his |X| RAM bytes to compute the |X[ higher bytes of E (denoted High(E)). When the receiver gets High(E) it calculates E = Concatenation (High(E) ,Low(E) ) and continues its calculations as before. Drawings
Preferred embodiments of the invention will now be described with reference to the accompanying drawings, in which:
Fig. 1 shows an inventive communication protocol between the sender and the receiver; Fig. 2 shows a sender and a receiver.
Preferred embodiments
Fig. 1 shows an interface 10 between a sender, e.g. a weak processor in a smart-card, and a receiver, e.g. a pay TV de¬ coder, which may contain a powerful processor for calculating the modulo function. The microprocessor in the sender prepares a first number D or a first set of numbers D(j) . Then it chooses a random number A and calculates E = D+A*X or it adds value B to each number D(j) and sends E and the set E(j) , respectively, via interface 10 to the receiver side. The receiver calculates S = E mod X or S(j) = E(j) mod X from the received numbers.
Advantageous the final length |E| or |E(j) | of E and E(j), respectively, is less than four times the length |x| of X.
In Fig. 2 a receiver device 27 and a sender device 28 are depicted. The sender device contains a first microprocessor 25, first memory means 26 which are connected to microproces¬ sor 25 and a first connector 24 for data exchange with re¬ ceiver device 27.
The receiver device 27 contains a second microprocessor 22, second memory means 21 which are connected to microprocessor 22 and a second connector 23 for data exchange with sender device 28.
First connector 24 and second connector 23 represent the in¬ terface 10 in Fig. 1. The first memory means 26 store inter¬ mediate calculation results and/or values X and/or B or Lo (E)/High(E) . First microprocessor 25 computes data as shown in the left side of Fig. 1.
The second memory means 21 store value X and/or intermediate results. Second microprocessor 22 computes data as shown in the right side of Fig. 1.
The invention can be used for identification (VideoCrypt or EuroCrypt Pay TV system) and/or digital signature (credit cards) and/or encryption, especially together with one or more of the following systems for getting in the receiver modulo calculated results without respective modulo calcula¬ tion in the sender i
- Fiat-Shamir;
- Feige-Fiat-Shamir;
- Quisquater-Guillou;
- Fischer-Micali-Rackoff;
Naccache (EP-A-91400111, EP-A-91400301) ;
RSA;
Rabin.
These systems are published according to the following list:
- Fiat-Shamir, "How to prove yourself: Practical solutions to identification and signature problems", A.Odlyzko editor, Advances in Cryptology, Proc. of Crypto '86, August 11 - 15, (Lecture Notes in Computer Science 263) , pp. 186 - 194, Springer Verlag, 1987, Santa Barbara, California, USA
- Feige-Fiat-Shamir, "Zero knowledge proofs of identity", Journal of Cryptology, 1(2), pp. 77 - 94, 1988
- Quisquater-Guillou, "A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmis¬ sion and memory", C.G. Gϋnther editor, Advances in Cryptology, Proc. of Crypto '88, August 16 - 20, (Lecture Notes in Computer Science 330), pp. 123 - 128, Springer Verlag, 1988, Santa Barbara, California, USA - Fischer-Micali-Rackoff, Unedited papers mentioned in the bibliography of Fiat-Shamir
- RSA: Rivest-Shamir-Adeleman, "A method of obtaining Digital Signatures and Public-key Cryptosystems", CACM, pp. 120 - 126, Vol. 21, No. 2, Feb. 1978
- Rabin, "Digitalized Signatures", Foundations of secure Com¬ putations, R.A. DeMillo et al. editors, Academic Press, pp. 155 - 166, London, 1987

Claims

Claims
1. Method for secure sending of a number S = D mod X or of a set of numbers S(j) = D(j) mod X, j = l,...,i, from a sender device (28) to a receiver device (27) , whereby X is a product of at least two big prime numbers and D is greater than X, characterized in the following steps:
- picking a random number A or a set of random numbers A-(J) by said sender device;
- calculating in said sender a value E = D+A*X or a set of values E(j) = D(j)+A(j)*X, whereby X is stored in said sender, or calculating in said sender a set of val¬ ues E(j) = D(j)*B, whereby a fixed number B = A*X is stored in said sender;
- transmitting via an interface (10) said value and said values, respectively, from said sender to said receiver;
- calculating by said receiver S = E mod X or S(j) = E(j) mod X, whereby the number X is stored in said re¬ ceiver device.
2. Method according to claim 1, characterized in that the transmitted length of value E or of each of values E(j) is less than four times the length of X.
3. Method according to claim 1 or 2, characterized in that the length of X is in the range from 64 to 128 bytes.
4. Method according to any of claims 1 to 3, characterized in that said sender device (28) calculates, using |X| cells of memory means (26) , and transmits in a first step [X[ lower bytes and in a second step |X| higher bytes of said value E or of each of said values E(j) , whereby said receiver device (27) reconstructs said value E or of each of said values E(j) by concatenating High(E) and Low(E) or High(E(j)) and Low(E(j) ) .
5. Method according to any of claims 1 to 4, characterized in that said sender device (28) is a smart-card.
6. Sender apparatus (28) for a method according to any of claims 1 to 5, consisting of first computation means (25) , first memory means (26) which are connected to said first computation means and first data exchange means (24) which are connected to said first computation means, whereby either said first memory means store said modulus X and said first computation means select said random number A or random numbers A(j) and calculate said value E = D+A*X or calculate said set of values E(j) = D(j)+A(j)*X or said first memory means store said fixed number B and said first computation means calculate said set of val¬ ues E(j) = D(j)+B and whereby said first data exchange means (24) send said value E or said set of values E(j) to said receiver device (27) .
7. Receiver apparatus (27) for a method according to any of claims 1 to 5, consisting of second computation means (22) , second memory means (21) which are connected to said second computation means and second data exchange means (23) which are connected to said second computation means, whereby said second memory means store said modulus X and said second computation means calculate the modulo function S = E mod X of said value E or calculate a set of modulo functions S(j) = E(j) mod X of said set of values E(j) .
8. Sender device according to claim 6, characterized in that said sender device (28) is a smart-card or a cred¬ it-card or a passport or a door-key.
9. Receiver device according to claim 7, characterized in that said receiver device (27) is a pay TV decoder or a credit-card verifier or a passport verifier or an electronic lock.
PCT/EP1992/002449 1991-11-05 1992-10-27 Method, sender apparatus and receiver apparatus for modulo operation WO1993009620A1 (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
US08/199,213 US5479511A (en) 1991-11-05 1992-10-27 Method, sender apparatus and receiver apparatus for modulo operation
EP92922272A EP0611506B1 (en) 1991-11-05 1992-10-27 Method, sender apparatus and receiver apparatus for modulo operation
DE69218961T DE69218961T2 (en) 1991-11-05 1992-10-27 METHOD, TRANSMITTER AND RECEIVER DEVICE FOR MODULO OPERATION

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
EP91402958 1991-11-05
EP91402958.2 1991-11-05

Publications (1)

Publication Number Publication Date
WO1993009620A1 true WO1993009620A1 (en) 1993-05-13

Family

ID=8208635

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/EP1992/002449 WO1993009620A1 (en) 1991-11-05 1992-10-27 Method, sender apparatus and receiver apparatus for modulo operation

Country Status (8)

Country Link
US (1) US5479511A (en)
EP (1) EP0611506B1 (en)
AU (1) AU2883692A (en)
DE (1) DE69218961T2 (en)
ES (1) ES2101124T3 (en)
HK (1) HK1000987A1 (en)
SG (1) SG44714A1 (en)
WO (1) WO1993009620A1 (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0682327A2 (en) * 1994-05-09 1995-11-15 Yeda Research And Development Company, Ltd. Method and apparatus for memory efficient variants of public key encryption and identification schemes for smart card applications
EP0723251A2 (en) * 1995-01-20 1996-07-24 Tandem Computers Incorporated Method and apparatus for user and security device authentication

Families Citing this family (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5377270A (en) * 1993-06-30 1994-12-27 United Technologies Automotive, Inc. Cryptographic authentication of transmitted messages using pseudorandom numbers
US5363448A (en) * 1993-06-30 1994-11-08 United Technologies Automotive, Inc. Pseudorandom number generation and cryptographic authentication
US5680131A (en) * 1993-10-29 1997-10-21 National Semiconductor Corporation Security system having randomized synchronization code after power up
DE19600081C2 (en) * 1996-01-03 1999-11-18 Ibm Ensuring data integrity for data carrier cards
US5838790A (en) * 1996-04-19 1998-11-17 Juno Online Services, L.P. Advertisement authentication system in which advertisements are downloaded for off-line display
WO1999014880A2 (en) * 1997-09-16 1999-03-25 Koninklijke Philips Electronics N.V. A method and device for executing a decrypting mechanism through calculating a standardized modular exponentiation for thwarting timing attacks
FR2862454A1 (en) * 2003-11-18 2005-05-20 Atmel Corp RANDOM MODULAR REDUCTION METHOD AND EQUIPMENT THEREFOR
FR2885711B1 (en) * 2005-05-12 2007-07-06 Atmel Corp METHOD AND MODULAR AND RANDOM EQUIPMENT FOR POLYNOMIAL REDUCTION
US7849125B2 (en) 2006-07-07 2010-12-07 Via Telecom Co., Ltd Efficient computation of the modulo operation based on divisor (2n-1)
US8600047B2 (en) * 2008-05-07 2013-12-03 Irdeto Corporate B.V. Exponent obfuscation
US8443086B2 (en) * 2011-06-22 2013-05-14 National Chiao Tung University Decentralized structured peer-to-peer network and load balancing methods thereof
EP2795477B1 (en) 2011-12-19 2018-07-25 Uthisme LLC Privacy system
FR3066845B1 (en) 2017-05-24 2019-06-14 Idemia Identity And Security METHOD FOR ELECTRONIC SIGNATURE OF A DOCUMENT WITH A PREDETERMINED SECRET KEY

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0428252A2 (en) * 1989-11-14 1991-05-22 News Datacom Ltd. A system for controlling access to broadcast transmissions

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE1159501B (en) * 1961-05-12 1963-12-19 Siemens Ag Method and circuit arrangement for the secure transmission of message characters
DE1175019B (en) * 1963-03-29 1964-07-30 Telefunken Patent Cipher system
US4306111A (en) * 1979-05-31 1981-12-15 Communications Satellite Corporation Simple and effective public-key cryptosystem
US5231668A (en) * 1991-07-26 1993-07-27 The United States Of America, As Represented By The Secretary Of Commerce Digital signature algorithm

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0428252A2 (en) * 1989-11-14 1991-05-22 News Datacom Ltd. A system for controlling access to broadcast transmissions

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
PHILIPS TELECOMMUNICATION REVIEW vol. 47, no. 3, September 1989, HILVERSUM NL pages 1 - 19 R.C. FERREIRA 'THE SMART CARD: A HIGH SECURITY TOOL IN EDP' *
PROCEEDINGS OF CRYPTO 90 11-15 August 1990, BERLIN (DE) pages 502-513; D. de WALEFFE and J.-J. QUISQUATER: "CORSAIR: A SMART CARD FOR PUBLIC KEY CRYPTOSYSTEMS" *
RECHERCHE OPERATIONNELLE vol. 24, no. 3, 1990, pages 307 - 313 D. NACCACHE DE PAZ AND H. MSILTI 'A NEW MODULO COMPUTATION ALGORITHM' *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0682327A2 (en) * 1994-05-09 1995-11-15 Yeda Research And Development Company, Ltd. Method and apparatus for memory efficient variants of public key encryption and identification schemes for smart card applications
EP0682327A3 (en) * 1994-05-09 1999-11-03 Yeda Research And Development Company, Ltd. Method and apparatus for memory efficient variants of public key encryption and identification schemes for smart card applications
EP0723251A2 (en) * 1995-01-20 1996-07-24 Tandem Computers Incorporated Method and apparatus for user and security device authentication
EP0723251A3 (en) * 1995-01-20 1998-12-30 Tandem Computers Incorporated Method and apparatus for user and security device authentication

Also Published As

Publication number Publication date
ES2101124T3 (en) 1997-07-01
EP0611506A1 (en) 1994-08-24
SG44714A1 (en) 1997-12-19
DE69218961D1 (en) 1997-05-15
AU2883692A (en) 1993-06-07
DE69218961T2 (en) 1997-07-24
US5479511A (en) 1995-12-26
EP0611506B1 (en) 1997-04-09
HK1000987A1 (en) 1998-05-15

Similar Documents

Publication Publication Date Title
Pedersen Electronic payments of small amounts
Beth Efficient zero-knowledge identification scheme for smart cards
US4969189A (en) Authentication system and apparatus therefor
EP0385511B1 (en) Cipher-key distribution system
CA2196356C (en) Transaction verification protocol for smart cards
EP0257585B1 (en) Key distribution method
CA2228958C (en) Data card verification system
EP0570388B1 (en) Method, identification device and verification device for identification and/or performing digital signature
US4661658A (en) Offline PIN validation with DES
US5245657A (en) Verification method and apparatus
US5299262A (en) Method for exponentiating in cryptographic systems
US6708893B2 (en) Multiple-use smart card with security features and method
EP0682327A2 (en) Method and apparatus for memory efficient variants of public key encryption and identification schemes for smart card applications
EP0611506B1 (en) Method, sender apparatus and receiver apparatus for modulo operation
WO1998034202A9 (en) Data card verification system
JPH0750375B2 (en) Entity identification and signature generation method and device
US7228418B1 (en) Authentication and signature method for messages using reduced size of binary units of information content and corresponding systems
US7382875B2 (en) Cryptographic method for distributing load among several entities and devices therefor
Rihaczek Teletrust
Fan et al. A user efficient fair blind signature scheme for untraceable electronic cash
EP0578059B1 (en) Method for executing number-theoretic cryptographic and/or error-correcting protocols
US20020188850A1 (en) Method for accelerated transmission of electronic signature
Huang et al. An untraceable electronic cash system using fair blind signatures
CA2543094C (en) Transaction verification protocol for smart cards
Watanabe et al. An improvement of the digital cash protocol of Okamoto and Ohta

Legal Events

Date Code Title Description
AK Designated states

Kind code of ref document: A1

Designated state(s): AU CA CS HU JP KR US

AL Designated countries for regional patents

Kind code of ref document: A1

Designated state(s): AT BE CH DE DK ES FR GB GR IE IT LU MC NL SE

DFPE Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101)
WWE Wipo information: entry into national phase

Ref document number: 1992922272

Country of ref document: EP

WWE Wipo information: entry into national phase

Ref document number: 08199213

Country of ref document: US

WWP Wipo information: published in national office

Ref document number: 1992922272

Country of ref document: EP

NENP Non-entry into the national phase

Ref country code: CA

WWG Wipo information: grant in national office

Ref document number: 1992922272

Country of ref document: EP