Abstract: A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set.

Abstract: A distributed certificate authority includes a CA and a number of Sub-CAs (2610). The Sub-CAs have secret certificate validation data, but different data are provided to different Sub-CAs for each certificate. If a Sub-CA is compromised, the Sub-CA validity proof will be withheld by the CA to alert the verifiers not to use the data from this Sub-CA. Also, the secret data are encrypted when distributed to the Sub-CAs. A decryption key (DK.j.k) for each “partition” of time is distributed to each Sub-CA at or shortly before the start of the partition. A compromised Sub-CA can be reactivated at the end of the partition because the adversary does not get the decryption keys for the future partitions.

Abstract: In the setup phase, the certification authority (CA 120) generates validation proof data structures for greater time than the maximum validity period of any digital certificate. Therefore, new certificates can be added to the existing data structures after the setup phase.

Abstract: A computer system (110) provides validity status proofs each of which proves the validity or invalidity of a set (F) of one or more digital certificates (104). The computer system may decide to cache a validity proof for a set F to later provide the cached proof to other parties. The caching decision is based on the caching priority of the set F. The priority may depend on the number of certificates in the set F, the sum of the remaining validity periods for the certificates in the set, and other factors.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set. A verifier (110) may decide to cache the validity proof for a set provide the cached proof to other parties. The caching decision is based on the caching priority of the set F.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set. A verifier (110) may decide to cache the validity proof for a set provide the cached proof to other parties. The caching decision is based on the caching priority of the set F.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set. A verifier (110) may decide to cache the validity proof for a set provide the cached proof to other parties. The caching decision is based on the caching priority of the set F.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set. A verifier (110) may decide to cache the validity proof for a set provide the cached proof to other parties. The caching decision is based on the caching priority of the set F.

Abstract: A certification authority (CA, 120) generates decryption key data (K?Fj) for each set (F) in the complement cover (804) for a plurality of digital certificates. The CA encrypts all or a portion of the validity proof data (cj(i)) for each digital certificate (140.i) for each time period j for which the validity proof is to be provided. For each certificate, the decryption can be performed with decryption keys (Kij) that can be obtained from the decryption key data (K?Fj) for any set containing the certificate. The CA distributes the encrypted portions of the validity proof data to prover systems that will provide validity proofs in the periods j. To perform certificate re-validation in a period j, the CA constructs the complement cover for the set of the revoked certificates, and distributes the decryption key data (K?Fj) for the sets in the complement cover.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: A certification authority (CA, 120) generates decryption key data (K?Fj) for each set (F) in the complement cover (804) for a plurality of digital certificates. The CA encrypts all or a portion of the validity proof data (cj(i)) for each digital certificate (140.i) for each time period j for which the validity proof is to be provided. For each certificate, the decryption can be performed with decryption keys (Kij) that can be obtained from the decryption key data (K?Fj) for any set containing the certificate. The CA distributes the encrypted portions of the validity proof data to prover systems that will provide validity proofs in the periods j. To perform certificate re-validation in a period j, the CA constructs the complement cover for the set of the revoked certificates, and distributes the decryption key data (K?Fj) for the sets in the complement cover.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Authentication of elements (e.g. digital certificates 140) as possessing a pre-specified property (e.g. being valid) or not possessing the property is performed by (1) assigning a distinct integer pi to each element, and (2) accumulating the elements possessing the property or the elements not possessing the property using a P-th root u1/P (mod n) of an integer u modulo a predefined composite integer n, where P is the product of the integers associated with the accumulated elements. Alternatively, authentication is performed without such accumulators but using witnesses associated with such accumulators. The witnesses are used to derive encryption and/or decryption keys for encrypting the data evidencing possession of the property for multiple periods of time. The encrypted data are distributed in advance. For each period of time, decryption keys are released which are associated with that period and with the elements to be authenticated in that period of time.

Abstract: Different targets (c0, N1) of a digital certificate are mapped into a “super-target” using methods allowing a certificate validity verifier (110) to compute the super-target. The certificate includes the super-target instead of the targets. Also, a certificate with multiple targets can be signed with a redactable signature by the certification authority (CA 120). When the certificate's owner provides the certificate to a verifier together with a validity proof, the owner redacts the certificate to delete unnecessary targets. A single validity proof (ci(F)) may be provided to certificate owners for a set (F) of the certificates via a multicast transmission if a multicasting group (2010) is formed to correspond to the set. A verifier (110) may decide to cache the validity proof for a set provide the cached proof to other parties. The caching decision is based on the caching priority of the set F.