Evaluating convolutions using encrypted data

A method, comprising:

• receiving from a client device an input ciphertext including at least encrypted coefficients of an input polynomial, wherein the encrypted coefficients have been encrypted according to a Fully Homomorphic Encryption (FHE) scheme after encoding one or more input datasets of real numbers into a plaintext polynomial;
• encoding a kernel into one or more kernel polynomials using kernel values from the kernel as kernel coefficients in the one or more kernel polynomials;
• performing a convolution on the input ciphertext at least in part by separately multiplying the input polynomial by the one or more kernel polynomials to result in one or more corresponding convolved polynomials;
• using at least a plurality of coefficients in each of the one or more convolved polynomials to derive an output ciphertext representing an output of the convolution on the input ciphertext using the kernel;
• and
• performing a modified bootstrapping on the output ciphertext by at least:
• converting coefficients of the output ciphertext into a plurality of slots of an input vector according to the FHE scheme;
• performing a modular reduction approximated by a scaled sine function on each slot of the plurality of slots to generate a plurality of reduced slots;
• and
• evaluating an activation function for the plurality of reduced slots to generate an output vector.

A client device, comprising:

• an interface configured to communicate with a server;
• and
• at least one processor, individually or in combination, configured to:
• encode one or more input datasets of real numbers into a plaintext polynomial with integral coefficients that do not include an imaginary component in a ring of polynomials expressed as =[X]/(XN+1) with N being a power of two and [X] denoting integral coefficients of the polynomials in the ring;
• generate an input ciphertext by encrypting the plaintext polynomial using a first key according to a Fully Homomorphic Encryption (FHE) scheme, wherein the input ciphertext includes at least encrypted coefficients of an input polynomial;
• and
• send the input ciphertext to the server via the interface for the server to perform at least one convolution on the input polynomial.

A method, comprising:

• encoding one or more input datasets of real numbers into a plaintext polynomial by:
• separately multiplying the real numbers of the one or more input datasets by a scaling factor;
• determining coefficients of the plaintext polynomial by rounding each of the corresponding products of the real numbers and the scaling factor to a nearest integer;
• and
• using the determined coefficients as coefficients in the plaintext polynomial, wherein the plaintext polynomial is in a ring of polynomials expressed as =[X]/(XN+1) with N being a power of two and [X] denoting integral coefficients of the polynomials in the ring;
• generating an input ciphertext by encrypting the plaintext polynomial using a first key according to a Fully Homomorphic Encryption (FHE) scheme, wherein the input ciphertext includes at least encrypted coefficients of an input polynomial;
• and
• sending the input ciphertext to a server to perform at least one convolution on the input polynomial using at least one kernel.

A system, comprising:

• a client device including at least one processor, individually or in combination, configured to:
• encode one or more input datasets of real numbers into a plaintext polynomial with integral coefficients that do not include an imaginary component, wherein the plaintext polynomial is in a ring of polynomials expressed as =[X]/(XN+1) with N being a power of two and [X] denoting integral coefficients of the polynomials in the ring;
• and
• generate an input ciphertext by encrypting the plaintext polynomial using a first key according to a Fully Homomorphic Encryption (FHE) scheme, wherein the input ciphertext includes at least encrypted coefficients of an input polynomial;
• and
• a server including means for:
• receiving the input ciphertext from the client device;
• performing a convolution on the input ciphertext using a kernel by at least in part separately multiplying the input polynomial by one or more kernel polynomials to result in one or more corresponding convolved polynomials, wherein the one or more kernel polynomials include kernel coefficients encoded using kernel values for the kernel;
• and
• using at least a plurality of coefficients in each of the one or more convolved polynomials to derive an output ciphertext representing an output of the convolution on the input ciphertext using the kernel.