US 4,405,829 A · Cryptographic communications system and method

Abstract

A cryptographic communications system and method. The system includes a communications channel coupled to at least one terminal having an encoding device and to at least one terminal having a decoding device. A message-to-be-transferred is enciphered to ciphertext at the encoding terminal by first encoding the message as a number M in a predetermined set, and then raising that number to a first predetermined power (associated with the intended receiver) and finally computing the remainder, or residue, C, when the exponentiated number is divided by the product of two predetermined prime numbers (associated with the intended receiver). The residue C is the ciphertext. The ciphertext is deciphered to the original message at the decoding terminal in a similar manner by raising the ciphertext to a second predetermined power (associated with the intended receiver), and then computing the residue, M', when the exponentiated ciphertext is divided by the product of the two predetermined prime numbers associated with the intended receiver. The residue M' corresponds to the original encoded message M.

Claims40

Dependent claims

A cryptographic communications system comprising:

A. a communications channel,
B. an encoding means coupled to said channel and adapted for transforming a transmit message word signal M to a ciphertext word signal C and for transmitting C on said channel,
where M corresponds to a number representative of a message and
0.ltoreq.M.ltoreq.n-1
where n is a composite number of the form
n=p.multidot.q
where p and q are prime numbers, and
where C corresponds to a number representative of an enciphered form of said message and corresponds to
C.ident.M.sup.e (mod n)
where e is a number relatively prime to 1 cm(p-1,q-1), and
C. a decoding means coupled to said channel and adapted for receiving C from said channel and for transforming C to a receive message word signal M'
where M' corresponds to a number representative of a deciphered form of C and corresponds to
M'.ident.C.sup.d (mod n)
where d is a multiplicative inverse of e(mod(1 cm((p-1),(q-1)))).

11 more elements

A communications system for transferring message signals M.sub.i, comprising k terminals, wherein each terminal is characterized by an encoding key E.sub.i =(e.sub.i, n.sub.i) and decoding key D.sub.i =(e.sub.i, n.sub.i), where i=1,2, . . . ,k, and wherein

Mi corrresponds to a number representative of a message signal to be transmitted from the i.sup.th terminal, and
0.ltoreq.M.sub.i .ltoreq.n.sub.i -1,
n.sub.i is a composite number of the form
n.sub.i =p.sub.i .multidot.q.sub.i
p.sub.i and q.sub.i are prime numbers,
e.sub.i is relatively prime to 1 cm(p-1,q-1),
d.sub.i is a multiplicative inverse of
e.sub.i (mod(1 cm((p.sub.i -1), (q.sub.i -1))))
wherein a first terminal includes means for encoding a digital message word signal M.sub.a for transmission from said first terminal (i=A) to a second terminal (i=B), said first terminal including:
means for transforming said message word signal M.sub.A to a signed message word signal M.sub.As, M.sub.As corresponding to a number representative of an encoded form of said message word signal M.sub.A, whereby:
M.sub.As .ident.M.sub.A.sup.d.sbsp.A (mod n.sub.A).

8 more elements

A communications system for transferring a message signal M.sub.i comprising k terminals, wherein each terminal is characterized by an encoding key E.sub.i =(e.sub.i, n.sub.i) and decoding key D.sub.i =(e.sub.i, n.sub.i), where i=1,2, . . . ,k, and wherein

M.sub.i corresponds to a number representative of a message signal to be transmitted from the i.sup.th terminal,
n.sub.i is a composite number of the form
n.sub.i =p.sub.i .multidot.q.sub.i
P.sub.i and q.sub.i are prime numbers,
e.sub.i is relatively prime to 1 cm(p.sub.i -1,q.sub.i -1),
d.sub.i is a multiplicative inverse of
e.sub.i (mod(1 cm((p.sub.i -1),(q.sub.i -1))))
wherein a first terminal includes means for encoding a digital message word signal M.sub.A for transmission from said first terminal (i=A) to a second terminal (i=B), said first terminal including:
means for transforming said message word signal M.sub.A to one or more message block word signals M.sub.A ', each block word signal M.sub.A being a number representative of a portion of said message word signal M.sub.A in the range 0.ltoreq.M.sub.A .ltoreq.n.sub.B -1, means for transforming each of said message block word signals M.sub.A " to a ciphertext word signal C.sub.A, C.sub.A corresponding to a number representative of an encoded form of said message block word signal M.sub.A ", whereby:
C.sub.A .ident.M.sub.A ".sup.e.sbsp.B (mod n.sub.B).

7 more elements

A communications system having a plurality of terminals coupled by a communications channel, including a first terminal characterized by an associated encoding key E.sub.A =(e.sub.A, n.sub.A) and decoding key D.sub.A =(d.sub.A, n.sub.A), and including a second terminal, wherein

n.sub.A is a composite number of the form
n.sub.A =p.sub.A .multidot.q.sub.A
p.sub.A and q.sub.A are prime numbers,
e.sub.A is relatively prime to 1 cm(p.sub.A -1, q.sub.A -1),
d.sub.A is a multiplicative inverse of
e.sub.A (mod(1 cm((p.sub.A -1), (q.sub.A -1)))),
wherein said first terminal comprises:
encoding means coupled to said channel and adapted for transforming a transmit message word signal M.sub.A to a signed message word signal M.sub.As and for transmitting M.sub.As on said channel,
where M.sub.A corresponds to a number representative of a message and
0.ltoreq.M.sub.A .ltoreq.n.sub.A -1
where M.sub.As corresponds to a number representative of a signed form of said message and corresponds to
M.sub.As .ident.M.sub.A.sup.d.sbsp.A (mod n.sub.A)
wherein said second terminal comprises:
decoding means coupled to said channel and adapted for receiving M.sub.As from said channel and for transforming M.sub.As to a receive message word signal M.sub.A '
where M.sub.A ' corresponds to a number representative of an unsigned form of M.sub.A and corresponds to
M.sub.A '.ident.M.sub.As.sup.e.sbsp.A (mod n.sub.A).

13 more elements

A cryptographic communications system having a plurality of terminals coupled by a communications channel, including a first terminal characterized by an associated encoding key E.sub.A =(e.sub.A,n.sub.A) and decoding key D.sub.A =(d.sub.A,n.sub.A), and including a second terminal wherein

n.sub.A is a composite number of the form
n.sub.A =p.sub.A .multidot.q.sub.A
p.sub.A and q.sub.A are prime numbers,
e.sub.A is relatively prime to 1 cm(p.sub.A -1,q.sub.A -1),
d.sub.A is a multiplicative inverse of
e.sub.A (mod(1 cm((p.sub.A -1),(q.sub.A -1)))),
wherein said second terminal comprises:
blocking means for transforming a message-to-be-transmitted from said second terminal to said first terminal, to one or more transmit message word signals M.sub.B,
where M.sub.B corresponds to a number representative of said message in the range
0.ltoreq.M.sub.B .ltoreq.n.sub.A -1
encoding means coupled to said channel and adapted for transforming each transmit message word signal M.sub.B to a ciphertext word signal C.sub.B and for transmitting C.sub.B on said channel,
where C.sub.B corresponds to a number representative of an enciphered form of said message and corresponds to
C.sub.B .ident.M.sub.B.sup.e.sbsp.A (mod n.sub.A)
wherein said first terminal comprises:
decoding means coupled to said channel and adapted for receiving said ciphertext word signals C.sub.B from said channel and for transforming each of said ciphertext word signals to a receive message word signal M.sub.B, and
means for transforming said receive message word signals M.sub.B ' to said message,
where M.sub.B ' is a number representative of a deciphered form of C.sub.B and corresponds to
M.sub.B '.ident.C.sub.B.sup.d.sbsp.A (mod n.sub.A).

15 more elements

A method for establishing cryptographic communications comprising the step of:

encoding a digital message word signal M to a ciphertext word signal C, where M corresponds to a number representative of a message and
0.ltoreq.M.ltoreq.n-1
where n is a composite number of the form
n=p.multidot.q
where p and q are prime numbers, and
where C is a number representative of an encoded form of message word M,
wherein said encoding step comprises the step of:
transforming said message word signal M to said ciphertext word signal C whereby
C.ident.M.sup.e (mod n)
where e is a number relatively prime to (p-1).multidot.(q-1).

7 more elements

A method for transferring a message signal M.sub.i in a communications system having k terminals, wherein each terminal is characterized by an encoding key E.sub.i =(e.sub.i, n.sub.i) and decoding key D.sub.i =(e.sub.i, n.sub.i), where i=1,2, . . . ,k, and wherein

M.sub.i corresponds to a number representative of message-to-be-transmitted from the i.sup.th terminal, and
0.ltoreq.M.sub.i .ltoreq.n.sub.i -1,
n.sub.i is a composite number of the form
n.sub.i =p.sub.i .multidot.q.sub.i
p.sub.i and q.sub.i are prime numbers,
e.sub.i is relatively prime to 1 cm(p.sub.i -1,q.sub.i -1),
d.sub.i is a multiplicative inverse of
e.sub.i (mod(1 cm((p.sub.i -1),(q.sub.i -1))))
comprising the step of:
encoding a digital message word signal M.sub.A for transmission from a first terminal (i=A) to a second terminal (i=B), said encoding step including the sub-step of:
transforming said message word signal M.sub.A to a signed message word signal M.sub.As, M.sub.A corresponding to a number representative of an encoded form of said message word signal M.sub.A, whereby:
M.sub.As .ident.M.sub.A.sup.d.sbsp.A (mod n.sub.A).

9 more elements

M.sub.i corresponds to a number representative of a message-to-be-transmitted from the i.sup.th terminal,
n.sub.i is a composite number of the form
n.sub.i =p.sub.i .multidot.q.sub.i
p.sub.i and q.sub.i are prime numbers,
e.sub.i is relatively prime to 1 cm(p.sub.i -1,q.sub.i -1),
d.sub.i is a multiplicative inverse of
e.sub.i (mod(1 cm((p.sub.i -1),(q.sub.i -1)))
comprising the step of:
encoding a digital message word signal M.sub.A for transmission from a first terminal (i=A) to a second terminal (i=B), said encoding step including the sub-step of:
transforming said message word signal M.sub.A to one or more message block word signals M.sub.A ", each block word signal M.sub.A " corresponding to a number representative of a portion of said message word signal M.sub.A in the range 0.ltoreq.M.sub.A ".ltoreq.n.sub.B -1,
transforming each of said message block word signals M.sub.A " to a ciphertext word signal C.sub.A, C.sub.A corresponding to a number representative of an encoded form of said message block word signal M.sub.A ", whereby:
C.sub.A .ident.M.sub.A ".sup.e.sbsp.B (mod n.sub.B).

9 more elements

A method for establishing cryptographic communications comprising the step of:

encoding a digital message word signal M to a ciphertext word signal C, where M corresponds to a number representative of a message and
0.ltoreq.M.ltoreq.n-1
where n is a composite number and
where C corresponds to a number representative of an encoded form of message word M,
wherein said encoding step comprises the step of:
transforming said message word signal M to said ciphertext word signal C whereby
C.ident.a.sub.e M.sup.e +a.sub.e-1 M.sup.e-1 + . . . +a.sub.0 (mod n)
where e and a.sub.e, a.sub.e-1, . . . a.sub.0 are numbers.

5 more elements

Dependencies are inferred from the claim text.

Cryptographic communications system and method

Life of this patent

Cryptographic communications system and method

Life of this patent

Abstract

Claims40