Method for deriving a partial signature with partial verification

A method comprising:

• verifying a partial signature for a subset I of a set of n messages, called first subset of messages, the number of messages of the first subset I being strictly smaller than n, said partial signature being intended to prove validity of a signature of the set of messages for the messages of the first subset I of messages, said verifying, implemented by an entity for verifying a partial signature, comprising:
• receiving the first subset I of messages and the partial signature) specific to the first subset I of messages, said partial signature comprising a constant number of elements comprising at least anonymized elements of the signature of the set of messages, a first verification element calculated from a second subset of messages of the set of n messages, the second subset of messages being composed of the messages of the set of n messages other than those of the first subset I of messages and a second verification element to prove that the first verification element is well formed, the second verification element being a function of derived values from at least the elements of the partial signature other than the second verification element,
• calculating the derived values by using a function for calculating derived values, and
• verifying a first equation and of a second equation, said first equation comprising the messages of the first subset I of messages, the anonymized elements of the signature of the set of messages, the first verification element and elements of the public key, the second equation comprising the first signature verification element, the second signature verification element, elements of the public key and the derived values.

A partial signature derivation entity comprising:

• a processor;
• and
• a non-transitory computer readable medium comprising instructions stored thereon which when executed by the processor configure the partial signature derivation entity to derive a partial signature for a subset I of a set of n messages, called first subset of messages, the number of messages of the first subset I being strictly smaller than n, said partial signature proving validity of a signature of the set of messages for the messages of the first subset I of messages, wherein the deriving comprises:
• receiving the set of messages and a signature of said set of messages, said signature comprising signature elements of the set of messages,
• generating anonymized elements of the signature,
• generating a first verification element calculated from a second subset of messages of the set of messages, the second subset of messages being composed of the messages of the set of messages other than those of the first subset I of messages,
• generating a second verification element intended to prove that the first verification element is well formed, and
• sending to a verification entity the partial signature specific to the first subset I of messages, said partial signature comprising a constant number of elements comprising at least the anonymized elements of the signature of the set of messages, the first verification element and the second verification element, said partial signature being verifiable with only the messages from the first subset I of messages,
• wherein the second verification element is a function of derived values calculated from at least the elements of the partial signature other than the second verification element.

A partial signature verification entity comprising:

• a processor;
• and
• a non-transitory computer readable medium comprising instructions stored thereon which when executed by the processor configure the partial signature derivation entity to verify a partial signature for a subset I of a set of n messages, called first subset of messages, the number of messages of the first subset I being strictly smaller than n, said partial signature proving validity of a signature of the set of messages for the messages of the first subset I of messages, wherein the verifying comprises:
• receiving the first subset I of messages and the partial signature specific to the first subset I of messages, said partial signature comprising a constant number of elements comprising at least anonymized elements of the signature of the set of messages, a first verification element calculated from a second subset of messages of the set of messages, the second subset of messages being composed of the messages of the set of messages other than those of the first subset I of messages and a second verification element intended to prove that the first verification element is well formed, the second verification element being a function of derived values from at least the elements of the partial signature other than the second verification element,
• calculating derived values by using a function of calculating derived values, and
• verifying a first equation and a second equation, said first equation comprising the messages of the first subset I of messages, the anonymized elements of the signature of the set of messages, the first verification element and elements of the public key, the second equation comprising the first signature verification element, the second signature verification element, elements of the public key and the derived values.