Ternary and higher multi-value digital scramblers/descramblers

Apparatus for scrambling an unknown ternary signal with a known ternary signal, the unknown and known ternary signals being able to assume one of three states, comprising:

• a scrambling ternary logic device having a first input, a second input and an output:
• the unknown ternary signal being connected to the first input of the scrambling ternary logic device;
• the known ternary signal being connected to the second input of the scrambling ternary logic device;
• the scrambling ternary logic device implementing a ternary logic function, sc, that satisfies the following equations:
• (1) A sc B=C, where A is the unknown signal, B is the known ternary signal and C is the output from the ternary logic device;
• (2) C sc B=A, if C and B were input to the ternary logic device;
• and
• (3) A sc C=B;
• if A and C were input to the ternary logic device;
• whereby a scrambled ternary signal is provided on the output of the scrambling ternary logic device.

A method of scrambling an unknown x-value signal with a known x-value signal, the known and unknown x-value signals being able to assume one of x states, wherein x is greater than or equal to 3, comprising:

• inputting the unknown x-value signal to a first input of a scrambling x-value logic device;
• inputting the known x-value signal to a second input of the scrambling x-value logic device;
• the scrambling x-value logic device implementing a x-value logic function, fc, that satisfies the following equations:
• (1) A fc B=C, where A is the unknown signal, B is the known x-value signal and C is the output from the x-value logic device;
• (2) C fc B=A, if C and B were input to the x-value logic device;
• and
• (3) A fc C=B;
• if A and C were input to the x-value logic device;
• and
• outputting a scrambled x-value signal from an output of the scrambling x-value logic device.

Apparatus for scrambling an unknown x-value signal with a known x-value signal, the unknown and known x-value signals being able to assume one of x states, comprising:

• a scrambling x-value logic device having a first input, a second input and an output:
• the unknown x-value signal being connected to the first input of the scrambling x-value logic device;
• the known x-value signal being connected to the second input of the scrambling x-value logic device;
• the scrambling x-value logic device implementing a x-value logic function, fc, that satisfies the following equations:
• (1) A fc B=C, where A is the unknown signal, B is the known x-value signal and C is the output from the x-value logic device;
• (2) C fc B=A, if C and B were input to the x-value logic device;
• and
• (3) A fc C=B;
• if A and C were input to the x-value logic device;
• whereby a scrambled x-value signal is provided on the output of the scrambling x-value logic device.

A method of scrambling an unknown x-value signal, the unknown x-value signal being able to assume one of x states, x being greater than or equal to 3, comprising:

• inputting the unknown x-value signal to a first input of a first scrambling x-value logic device and a first known x-value signal to a second input of the first scrambling x-value logic device;
• inputting an output from the first scrambling x-value logic device to a first input of a second scrambling logic device and a second known x-value signal to a second input of the second scrambling x-value logic device;
• inputting an output from the second scrambling x-value logic device to a first input of a third scrambling logic device and a second known x-value signal to a second input of the third scrambling x-value logic device;
• the first, second and third scrambling x-value logic device implementing a x-value logic function, fc, that satisfies the following equations:
• (1) A fc B=C, where A is the signal on the first input of the device, B is the second input of the device and C is the output from the device;
• (2) C fc B=A, if C and B were input to the device;
• and
• (3) A fc C=B;
• if A and C were input to the device;
• and
• outputting a scrambled x-value signal on an output of the third scrambling x-value logic device.

Apparatus for scrambling an unknown x-value signal, the unknown x-value signal being able to assume one of x states, x being greater than or equal to 3, comprising:

• a first scrambling x-value logic device having a first input, a second input and an output,
• a second scrambling x-value logic device having a first input, a second input and an output,
• a third scrambling x-value logic device having a first input, a second input and an output,
• wherein the unknown x-value signal is connected to the first input of the first scrambling x-value logic device, a first known x-value signal is connected to the second input of the first scrambling x-value logic device, the output from the first scrambling x-value logic device is connected to the first input of the second scrambling logic device, a second known x-value signal is connected to the second input of the second scrambling x-value logic device, the output from the second scrambling x-value logic device is connected to the first input of the third scrambling logic device and a third known x-value signal is connected to the second input of the third scrambling x-value logic device;
• the first, second and third scrambling x-value logic device implementing a x-value logic function, fc, that satisfies the following equations:
• (1) A sc B=C, where A is the signal on the first input of the device, B is the second input of the device and C is the output from the device;
• (2) C sc B=A, if C and B were input to the device;
• and
• (3) A sc C=B;
• if A and C were input to the device;
• and
• wherein a scrambled x-value signal is provided on the output of the third scrambling x-value logic device.

A method of scrambling an unknown x-value signal, the unknown x-value signal being able to assume one of x states, x being greater than or equal to 3, comprising:

• inputting the unknown x-value signal to a first set of serially connected odd number of x-value logic devices;
• inputting one or more known x-value signals to the first set of serially connected odd number of x-value logic devices;
• each of the odd number of x-value logic devices implementing a x-value logic function that satisfies the following equations:
• (1) A fc B=C, where A is the signal on the first input of the device, B is the second input of the device and C is the output from the device;
• (2) C fc B=A, if C and B were input to the device;
• and
• (3) A fc C=B;
• if A and C were input to the device;
• and
• outputting a scrambled x-value signal on an output.