Method, sender apparatus and receiver apparatus for modulo operation
First Claim
1. A method for encrypted communication of a message from a sender device to a receiver device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than or equal to 1, X being a product of at least two big prime numbers and each D (j) being greater than X, said method comprising the steps of:
- storing the value X in a first memory device of said sender device and in a second memory device of said receiver device;
producing in a first processor associated with said sender device a set of values E(j)=D(j)+A(j)*X from a set of random numbers A(j);
transmitting a signal representative of said values E(j) from said sender device to said receiver device via an interface;
processing said signal in a second processor associated with said receiver device for generating a set of numbers S(j)=E(j) mod X; and
recovering said message from said set of numbers S(j)=E(j) mod X.
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Abstract
An access control system involves a first cryptographic device communicating with a second cryptographic device using a modulo-based protocol. To transmit a message from the first device to the second device, a random number is combined with the number representing the message without using a modulo operation. As a result, the message is hidden. By performing a modulo operation in the second device on the received hidden message, the original message can be recovered. Modular operations by the first device can be avoided reducing the number of modular operations.
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Citations
16 Claims
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1. A method for encrypted communication of a message from a sender device to a receiver device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than or equal to 1, X being a product of at least two big prime numbers and each D (j) being greater than X, said method comprising the steps of:
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storing the value X in a first memory device of said sender device and in a second memory device of said receiver device; producing in a first processor associated with said sender device a set of values E(j)=D(j)+A(j)*X from a set of random numbers A(j); transmitting a signal representative of said values E(j) from said sender device to said receiver device via an interface; processing said signal in a second processor associated with said receiver device for generating a set of numbers S(j)=E(j) mod X; and recovering said message from said set of numbers S(j)=E(j) mod X. - View Dependent Claims (2, 3, 4, 5)
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6. A method for encrypted communication of a message from a sender device to a receiver device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than 1, X being a product of at least two big prime numbers and each D (j) being greater than X, said method comprising the steps of:
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storing the value X in a first memory device of said sender device and in a second memory device of said receiver device; generating in a first processor associated with said sender device a random number A and a number B=A*X; storing said number B in said first memory device of said sender device; producing in a first processor associated with said sender device a set of values E(j)=D(j)*B; transmitting a signal representative of said values E(j) from said sender device to said receiver device via an interface; processing said signal in a second processor associated with said receiver device for generating a set of numbers S(j)=E(j) mod X; and recovering said message from said set of numbers S(j)=E(j) mod X. - View Dependent Claims (7, 8, 9, 10)
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11. A sender device for encrypted communication of a message to a receiver device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than or equal to 1, X being a product of at least two big prime numbers and each D(j) being greater than X, comprising:
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memory means for storing X; a processor coupled to said memory means for generating a set of values E(j)=D(j)+A(j)*X from a set of random numbers A(j); data exchange means coupled to said processor for sending a signal representative of said values E(j) to said receiver device, said number X being stored in said receiver device and a set of values S(j)=E(j) mod X being generated in said receiver device for recovering said message from said set of values S(j)=E(j) mod X. - View Dependent Claims (13)
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12. A sender device for encrypted communication of a message to a receiver device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than 1, X being a product of at least two big prime numbers and each D(j) being greater than X, comprising:
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memory means for storing X; a processor coupled to said memory means for generating a number B=A*X from a random number A and for generating a set of values E(j)=D(j)*B, said number B being stored in said memory means; data exchange means coupled to said processor for sending a signal representative of said values E(j) to said receiver device, said number X being stored in said receiver device and a set of values S(j)=E(j) mod X being generated in said receiver device for recovering said message represented by said values D(j) mod X.
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14. A receiver device for evaluating an encrypted communication of a message from a sender device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than or equal to 1, X being a product of at least two big prime numbers and each D(j) being greater than X, said receiver device comprising:
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memory means for storing X; data exchange means for receiving a signal generated in said sender device, said signal being representative of a set of values E(j)=D(j)+A(j)*X generated in said sender device by generating a set of random numbers A(j) and generating therefrom said values E(j); a processor coupled to said memory means and to said data exchange means for processing said signal to generate a set of values S(j)=E(j) mod X for recovering said message. - View Dependent Claims (16)
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15. A receiver device for evaluating an encrypted communication of a message from a sender device, said message being represented by a set of numbers S(j)=D(j) mod X, j=1, . . . ,i, i being an integer greater than 1, X being a product of at least two big prime numbers and each D(j) being greater than X, said receiver device comprising:
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memory means for storing X; data exchange means for receiving a signal from said sender device, said signal being representative of a set of values E(j)=D (j)* B generated in said sender device by generating a random number A and a number B=A*X, said number B being stored in said sender device; a processor coupled to said memory means and to said data exchange means for processing said signal to generate a set of values S(j)=E(j) mod X for recovering said message.
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Specification