Computation on lwe-encrypted values

A device for performing a computation on LWE-encrypted values, wherein an LWE-encrypted value is an encryption of a value based on a Learning With Errors problem, wherein the encryption supports a programmable bootstrapping operation, wherein the programmable bootstrapping operation evaluates an LWE decryption in an exponent of a GLWE-encrypted monomial, wherein a GLWE-encrypted polynomial is an encryption of a polynomial based on a Generalized Learning With Errors problem, the device comprising:

• a storage for storing a set of auxiliary keys for performing the computation, wherein the auxiliary keys do not allow to decrypt the LWE-encrypted values, wherein the auxiliary keys comprise a set of bootstrapping keys for performing the programmable bootstrapping operation;
• a processor system configured to compute an LWE-encrypted product value based on one or more LWE-encrypted input values by:
• applying a cryptographic key switching operation to the set of LWE-encrypted input values to determine one or more GLWE-encrypted input polynomials, wherein a coefficient of an input polynomial is a linear combination of the set of input values;
• applying an encrypted polynomial multiplication based on the one or more GLWE-encrypted input polynomials to obtain a GLWE-encrypted output polynomial;
• applying a cryptographic sample extraction operation based on the GLWE-encrypted output polynomial, thereby obtaining the LWE-encrypted product value as an encryption of a polynomial coefficient.