Cascading multivariate quadratic identification schemes for chain of trust

At least one non-transitory computer-readable medium comprising instructions that, when executed by a processor, cause a computing system to:

• generate a respective public/private key pair for each component of a plurality of components of a computing environment, wherein each respective public/private key pair is generated using a multivariate quadratic function F;
• provide a response from a first component of the plurality of components to a challenge from a second component of the plurality of components, wherein the response comprises at least a first commitment value and a second commitment value, wherein each of the first and second commitment values is determined using a public key of a respective public/private key pair of a third component of the plurality of components, and at least one of the first and second commitment values is determined using a polar function G, wherein the polar function G is a polar form of the multivariate quadratic function F;
• and
• add the first component to a chain of trust for the computing environment if the first commitment value is equal to a first expected commitment value and the second commitment value is equal to a second expected commitment value.

At least one non-transitory computer-readable medium comprising instructions that, when executed by a processor, cause a computing system to:

• generate a secret key si for a component, of a computing environment;
• calculate a public key vi, wherein the public key vi is a multivariate quadratic function F of the secret key si, wherein v F(si), i represents a current prover i, and vi is a public key for the current prover i;
• determine a value for each element of a tuple using the secret key si the multivariate quadratic function F, and a polar function G, wherein the polar function G is a polar form of the multivariate quadratic function F;
• calculate a first commitment value and a second commitment value, wherein calculating the first and second commitment values comprises using a string commitment function, at least one element of the tuple and a public key vi−1, wherein i−1 represents a previous prover i−1, vi−1 is a public key for the previous prover i−1, and vi−1 is determined as the multivariate quadratic function F of a corresponding secret key for the previous prover i−1;
• provide the public key vi−1 and the first and second commitment values to a verifier;
• and
• add the component to a chain of trust for the computing environment if the first and second commitment values are equal to a first expected commitment value and a second expected commitment value.

A method comprising:

• generating, in a computing system, a public/private key pair for each component of a plurality of components of the computing system, wherein each public/private key pair is generated using a multivariate quadratic function F;
• providing a response from a first component of the plurality of components to a challenge from a second component of the plurality of components, wherein the response comprises at least a first commitment value and a second commitment value, wherein each of the first and second commitment values is determined using a public key of a respective public/private key pair of a third component of the plurality of components and at least one of the first and second commitment values for the first component is determined using a polar function G, wherein the polar function G is a polar form of the multivariate quadratic function F;
• and
• adding the first component to a chain of trust for the computing system if the first commitment value is equal to a first expected commitment value and the second commitment value is equal to a second expected commitment value.