Signature verifications using Merkle signature schemes
Examples relate to machine readable storage storing instructions arranged, when processed, to realise methods of verifying as valid a received signature, associated with a respective received message, generated using a Merkle Signature Scheme comprising a Merkle Tree, the Merkel Tree comprising a root node, a number of leaf nodes and a number of intermediate nodes disposed between the root node and the leaf nodes; the instructions comprising instructions to: calculate a hash value in response to receiving the respective message; determine that the calculated hash value corresponds to a stored previously verified hash value calculated in response to a previously received message, and verify the received signature as valid based on the stored previously verified hash value.
1. A non-transitory machine-readable storage storing machine-instructions arranged, when processed by a processor, to
verify as valid a signature generated using a Merkle Signature Scheme comprising a Merkle Tree, the Merkle Tree comprising:
a root node;
a number of leaf nodes; and
a plurality of intermediate nodes disposed between the root node and the leaf nodes;
wherein verifying the signature as valid includes:
receiving the signature and a message associated with the signature;
deriving a candidate public key from the signature and the message;
calculating a hash value in response to receiving the message;
calculating a first hash value using the candidate public key;
determining that the first hash value corresponds to a stored previously verified second hash value, wherein the stored previously verified second hash value was calculated in response to a previously received message; and
verifying the candidate public key as valid based on the stored previously verified second hash value, wherein verifying the candidate public key verifies the signature.
2. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to calculate a hash value related to the root node in response to receiving the message.
3. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to, in response to receiving the message, calculate a hash value associated with an authentication path related to the message.
4. The non-transitory machine-readable storage of claim 1 , wherein the Merkle Tree is a multi-tree Merkle Tree comprising a number of subtrees, and wherein each subtree comprises an independent subtree root node, and wherein the number of leaf nodes and a number of intermediate nodes are disposed between the subtree root node and leaf nodes, and further wherein the root node is associated with one of the subtrees.
5. The non-transitory machine-readable storage of claim 4 , comprising further instructions that, when executed by the processor, cause the processor to, in response to receiving the message, calculate the hash value associated with a respective root node of a subtree of the number of subtrees.
6. The non-transitory machine-readable storage of claim 1 , wherein the Merkle tree comprises:
2 h one-time key pairs (sk j , pk j ), where 0≤j<2 h , and
wherein the previously stored previously verified second hash value associated with the previously received message comprises:
one or more than one of a plurality of hash values q 1 , . . . , q 2 h+1 −1 where q i =H(q 2i ∥q 2i+1 ) for 1≤i<2 h , q 2 h +j =H(pk (j) ) for 0≤j<2 h and an overall public key is Y=q 1 .
7. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to calculate, verify and store the second hash value calculated in response to the previously received message.
8. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to terminate traversing of the Merkle Tree at a node of a subtree corresponding to the first hash value that corresponds to the stored previously verified second hash value in response to verifying the received signature as valid based on the stored previously verified second hash value associated with the previously received message.
9. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to:
traverse the Merkle Tree from a leaf node associated with the message having a respective authentication path comprising at least respective intermediate nodes, wherein traversing the Merkle Tree includes:
calculating a hash value in response to receiving the message;
determining that the first hash value corresponds to a stored previously verified second hash value calculated in response to the previously received message; and
verify the received signature as valid based on the stored previously verified second hash value calculated in response to the previously received message and
terminate the traversing of the Merkle Tree in response to the verification of the received signature as valid based on the stored previously verified second hash value calculated in response to the previously received message, wherein terminating at a root node of a subtree corresponds to the first hash value corresponding to the stored previously verified second hash value.
10. The non-transitory machine-readable storage of claim 1 , comprising further instructions that, when executed by the processor, cause the processor to:
traverse the Merkle Tree from a leaf node associated with the message having a respective authentication path comprising at least respective intermediate nodes, wherein traversing the Merkle Tree includes:
calculating a hash value in response to receiving the message;
determining that the first hash value corresponds to a stored previously verified second hash value calculated in response to the previously received message; and
verifying the received signature as valid based on the stored previously verified second hash value; and
terminating traversing of the Merkle Tree in response to verifying the received signature as valid based on the stored previously verified second hash value associated with the previously received message, wherein terminating being at an intermediate node corresponding to the first hash value corresponding to the stored previously verified second hash value.
11. A computing device comprising:
a non-transitory memory storing instructions for verifying code as authentic, wherein the code comprises an associated received signature generated using a hash based signature scheme comprising a tree structure, and wherein the tree structure comprises:
a root node;
a number of leaf nodes; and
a number of intermediate nodes disposed between the root node and the leaf nodes; and
a processor in communication with the non-transitory memory, wherein the processor is to:
receive a portion of data associated with the code and the signature, wherein the portion of data associated with the code is one of a number of portions of data associated with the code;
derive a candidate public key from the signature and the portion of data associated with the code;
calculate a first hash value in response to receiving the portion of data associated with the code;
determine that the first hash value corresponds to a stored previously verified second hash value calculated in response to receiving a previously received portion of data associated with the code; and
verify the candidate public key as valid based on the previously verified second hash value calculated in response to receiving the previously received portion of data associated with the code, wherein verifying the candidate public key verifies the signature.
12. The computing device of claim 11 , wherein the processor is further to verify the code as authentic in response to verifying as authentic each portion of data of the number of portions of data.
13. A non-transitory computer-readable medium comprising instructions that, when executed by a processor, cause the processor to:
verify as valid a current composite signature associated with a currently received message, wherein the current composite signature comprises a number of signatures;
verify as valid a previously received composite signature, comprising a number of previously received signatures, associated with a previously received message including verifying as valid the number of previously received signatures;
verify as valid a signature of the number of signatures of the current composite signature; and
establish that a further signature of the number of signatures of the current composite signature is common to a previously received signature that was previously verified as valid, the previously received signature being one of the number of previously received signatures.
14. The non-transitory computer-readable medium of claim 13 , comprising further instructions that, when executed by the processor, cause the processor to:
verify as valid a previously received composite signature, comprising a number of previously received signatures, associated with the previously received message including instructions to verify as valid the number of previously received signatures; and
verify as valid a previously received signature associated with a root node of a subtree of a Merkle tree used to verify as valid the current composite signature.
15. The non-transitory computer-readable medium of claim 13 , comprising further instructions that, when executed by the processor, cause the processor to store in a data structure a previously received signature that was verified as valid.