Quandle-based cryptography

A system for secure computation, comprising:

• a memory to store an input variable comprising one or more first elements of a quandle;
• and
• at least one processor to receive a specification of an arithmetic computation to be performed over the input variable, to encrypt the input variable using a first operation of the quandle performed over the input variable together with an encoding variable comprising one or more non-unity second elements of the quandle, to cause the arithmetic computation to be applied to the encrypted input variable to produce an encrypted output variable, and to decrypt the encrypted output variable using the encoding variable and a second operation of the quandle to obtain a result of the arithmetic computation over the variable.

A computer software product, comprising a non-transitory computer-readable medium in which program instructions are stored, which instructions, when read by a computer, cause the computer to receive a specification of an input variable comprising one or more first elements of a quandle and an arithmetic computation to be performed over the input variable, to encrypt the input variable using a first operation of the quandle performed over the input variable together an with encoding variable comprising one or more non-unity second elements of the quandle, to cause the arithmetic computation to be applied to the encrypted input variable to produce an encrypted output variable, and to decrypt the encrypted output variable using the encoding variable and a second operation of the quandle to obtain a result of the arithmetic computation over the variable.