A method comprising: obtaining, at a computer coupled with a communication network, a first set of information (227b, 327b) regarding a first physical material to be verified, the first set of information comprising hundreds of values for channels of a spectrum of electromagnetic radiation emitted by the first physical material in response to an irradiation of the first physical material, the hundreds of values representing physical characteristics of the first physical material to be verified, and wherein the first set of information uniquely identifies the physical material; obtaining, at the computer coupled with the communication network, a second set of information (227a, 327b) regarding the first physical material to be verified, wherein obtaining the second set of information comprises retrieving, from a distributed digital ledger, the second set of information, wherein the second set of information comprises a) hundreds of previously produced values for channels of the spectrum of electromagnetic radiation emitted by the first physical material in response to a previous irradiation of the first physical material and b) a second digital signature of at least the hundreds of previously produced values, wherein the second digital signature is generated by encrypting at least the hundreds of previously produced values using a private key portion of an asynchronous encryption key pair used by a verification computer system; sending, by the computer, the first and second sets of information over the communication network to a verification computer system to verify an identity or provenance of the first physical material; receiving, at the computer, verification information from the verification computer system, the verification information comprising a first digital signature by the verification computer system of the first set of information, wherein the verification computer system is configured to verify the identity or the provenance of the first physical material based on a determination that the spectra of electromagnetic radiation are substantially the same in the first set of information and the second set of information, and wherein the verification comprises verifying the second digital signature of at least the hundreds of previously produced values using a public key portion of the asynchronous encryption key pair used by the verification computer system; if the first physical material is verified, adding, by the computer, the first set of information and the first digital signature to the distributed digital ledger along with the second set of information previously added to the distributed ledger. obtaining, at a computer coupled with a communication network, a first set of information (227b, 327b) regarding a first physical material to be verified, the first set of information comprising hundreds of values for channels of a spectrum of electromagnetic radiation emitted by the first physical material in response to an irradiation of the first physical material, the hundreds of values representing physical characteristics of the first physical material to be verified, and wherein the first set of information uniquely identifies the physical material; obtaining, at the computer coupled with the communication network, a second set of information (227a, 327b) regarding the first physical material to be verified, wherein obtaining the second set of information comprises retrieving, from a distributed digital ledger, the second set of information, wherein the second set of information comprises a) hundreds of previously produced values for channels of the spectrum of electromagnetic radiation emitted by the first physical material in response to a previous irradiation of the first physical material and b) a second digital signature of at least the hundreds of previously produced values, wherein the second digital signature is generated by encrypting at least the hundreds of previously produced values using a private key portion of an asynchronous encryption key pair used by a verification computer system; sending, by the computer, the first and second sets of information over the communication network to a verification computer system to verify an identity or provenance of the first physical material; receiving, at the computer, verification information from the verification computer system, the verification information comprising a first digital signature by the verification computer system of the first set of information, wherein the verification computer system is configured to verify the identity or the provenance of the first physical material based on a determination that the spectra of electromagnetic radiation are substantially the same in the first set of information and the second set of information, and wherein the verification comprises verifying the second digital signature of at least the hundreds of previously produced values using a public key portion of the asynchronous encryption key pair used by the verification computer system; if the first physical material is verified, adding, by the computer, the first set of information and the first digital signature to the distributed digital ledger along with the second set of information previously added to the distributed ledger.