Method of providing a hash value for a piece of data, electronic device and computer program

Abstract

A hash value provides for a time-stamp for a piece of data upon verification. Providing the hash value includes deriving one-time signing keys of signer's one-time signing key hash chain by a one-way function of a secret key of the signer and a function of an index of the one-time signing key, and providing the hash value for the piece of data by a hash function including the piece of data and the derived one-time signing key. An electronic device having a processor arranged to implement a functional module for deriving a one-time signing key and providing a hash value for a piece of data by a hash function including the piece of data and the derived one-time signing key is also disclosed. The functional module is arranged to perform the method. A computer program for implementing the method on the electronic device is also disclosed.

Claims

1. A method of verifying authenticity of a piece of data, the method comprising: deriving a plurality of one-time signing keys of signer's one-time signing key hash chain by, for each respective one of the one-time signing keys, using a one-way function that directly operates on a same secret key of the signer and a function of an index of the respective one-time signing key; providing a hash value for the piece of data by using a hash function that operates on parameters including the piece of data and one of the derived one-time signing keys; using the hash value for the piece of data to obtain a time stamp for the piece of data; using the time stamp and the one of the derived one-time signing keys to form a signature for the piece of data; and using the signature to verify authenticity of the piece of data to another entity, wherein the index is an index in the hash chain, all values of the hash chain are bound by a root of a hash tree on top of a sequence formed by the one-time signing keys, and wherein a public key of the signer includes the root.

2. The method of claim 1, wherein the function of the index is the index itself.

3. The method of claim 1, wherein the one-way function is a cryptographic message authentication code function.

4. The method of claim 1, wherein the one-way function is a hash function.

5. The method of claim 1, comprising registering the provided hash value.

6. The method of claim 1, comprising providing a one-time proof of knowledge of the one-time signing key to a signing authority entity without revealing the one-time signing key.

7. The method of claim 6, wherein the one-time proof of knowledge includes a hash path for the hash value, and the providing of the one-time proof of knowledge to the signing authority includes sending the index of the one-time signing key, the hash value and the hash path.

8. The method of claim 1, comprising sending a signing request to a signing authority for a plurality of pieces of data, wherein each piece of data is assigned a respective index consecutively by using one-time signing keys with time-forwarded one-time signing key indexes.

9. The method of claim 1, comprising applying a time fraction hash tree splitting a time slot corresponding to the index into time fractions such that the time slot is divided into fractions according to the number of leafs of the time fraction hash tree.

10. An electronic device comprising a processing circuitry arranged to verify authenticity of a piece of data, wherein the processing circuitry is arranged to perform a method comprising: deriving a plurality of one-time signing keys of signer's one-time signing key hash chain by, for each respective one of the one-time signing keys, using a one-way function that directly operates on a same secret key of the signer and a function of an index of the respective one-time signing key; providing a hash value for the piece of data by using a hash function that operates on parameters including the piece of data and one of the derived one-time signing keys; using the hash value for the piece of data to obtain a time stamp for the piece of data; using the time stamp and the one of the derived one-time signing keys to form a signature for the piece of data; and using the signature to verify authenticity of the piece of data to another entity, wherein the index is an index in the hash chain, all values of the hash chain are bound by a root of a hash tree on top of a sequence formed by the one-time signing keys, and wherein a public key of the signer includes the root.

11. The electronic device of claim 10, wherein the electronic device is a wireless device.

12. The electronic device of claim 10, wherein the electronic device is a network node.

13. A nontransitory computer readable storage medium comprising a computer program comprising instructions which, when executed on a processor of an electronic device, causes the electronic device to perform a method of verifying authenticity of a piece of data, the method comprising: deriving a plurality of one-time signing keys of signer's one-time signing key hash chain by, for each respective one of the one-time signing keys, using a one-way function that directly operates on a same secret key of the signer and a function of an index of the respective one-time signing key; providing a hash value for the piece of data by using a hash function that operates on parameters including the piece of data and one of the derived one-time signing keys; using the hash value for the piece of data to obtain a time stamp for the piece of data; using the time stamp and the one of the derived one-time signing keys to form a signature for the piece of data; and using the signature to verify authenticity of the piece of data to another entity, wherein the index is an index in the hash chain, all values of the hash chain are bound by a root of a hash tree on top of a sequence formed by the one-time signing keys, and wherein a public key of the signer includes the root.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above, as well as additional objects, features and advantages of the present invention, will be better understood through the following illustrative and non-limiting detailed description of preferred embodiments of the present invention, with reference to the appended drawings.

(2) FIG. 1 illustrates a hash tree structure.

(3) FIG. 2 illustrates a Merkle tree and a corresponding ash path.

(4) FIG. 3 schematically illustrates a KSI architecture.

(5) FIG. 4 illustrates a simplified view of the KSI architecture.

(6) FIG. 5 illustrates a model of signing documents in QI-KSI.

(7) FIG. 6 illustrates a QI-KSI signing protocol.

(8) FIG. 7 illustrates modified OTSKs in a QI-KSI solution.

(9) FIG. 8 schematically illustrates an approach for deriving the OTSKs directly via a one-way function.

(10) FIG. 9 illustrates a modified Trusted third party signing authority, TTP-SA, arranged to use a yet another Merkle sub-tree.

(11) FIG. 10 illustrates an example when a time slot is split into fractions.

(12) FIG. 11 illustrates an example of the approach of the fraction tree combined with an approach of delayed requests.

(13) FIG. 12 is a flow chart illustrating a method according to an embodiment.

(14) FIG. 13 schematically illustrates a wireless network with network nodes and a wireless device in which the invention may be implemented according to an embodiment.

(15) FIG. 14 schematically illustrates a computer-readable medium and a processing device.

DETAILED DESCRIPTION

(16) Certain embodiments disclosed herein relate generally to the technical field of security, and more particularly to the field of hash functions. For the easier understanding of the contribution by the invention, an introduction to mechanisms for providing hash functions used for time stamping is demonstrated below. For further facilitating the reading of this disclosure, commonly used abbreviations are listed below.

ABBREVIATIONS

(17) Abbreviation Explanation BLT Extension of KSI CRH Calendar root hash GW Gateway KSI Keyless Signature Infrastructure HMAC specific message authentication code algorithm construction MAC message authentication code algorithm (generic) PKI Public Key Infrastructure TSA Time-Stamp Authority PKI Public Key infrastructure QI-KSI Quantum-Immune KSI, e.g. BLT RH Root hash of a Merkle type of tree HP Hash path of a Merkle type of tree LRS Left-Right Sequence of a hash path AHP Aggregation hash path ARH Aggregation root hash CHP Calendar hash path CRH Calendar root hash TTP Trusted third party TTP-SA Trusted third party signing authority CA Certificate Authority SK Secret key PK Public key HC Hash chain OTSK One time signing key OTAK One time authentication key
Introduction to KSI

(18) KSI stands for the Keyless Signature Infrastructure. This section is based on open sources, such as publications of papers [1-5] mainly on the cryptographic e-print web-based database where the authors describe different aspects of the KSI. The term keyless signature that is used in references [1-5] could be seen as slightly misleading. Another term, in the field of cryptography, that could be used instead is a time stamp of a given hash value, from the client's perspective. For consistent terminology with earlier work, we will nevertheless stick with the term KSI in the text below.

(19) Merkle Trees and Hash Paths

(20) FIG. 1 illustrates a Merkle hash tree where H is a pre-defined hash function. The KSI is based on the well-known Merkle hash tree construction, a hash tree structure. The hash tree or Merkle tree is a tree in which every non-leaf node is labelled with the hash of the labels of its children nodes. Hash trees are useful because they allow efficient and secure verification of the contents of large data structures. Hash trees are a generalization of hash lists and hash chains. Demonstrating that a leaf node is a part of the given hash tree requires processing an amount of data proportional to the logarithm of the number of nodes of the tree; this contrasts with hash lists, where the amount is proportional to the number of nodes. FIG. 1 shows an example of such a tree with 4 leafs. The tree's leafs are digests of a pre-defined hash function H. The next layer includes two nodes with hash values h.sub.01 and h.sub.23 that are derived from the adjacent children leafs as the hash of the concatenation of the leafs' digests. The root hash (RH) is computed as the hash of the concatenation h.sub.01h.sub.23 (the order of the concatenation is important). This way, given the values on the tree's leafs one may compute the root hash that actually binds all the values of leafs together. i.e., changing any value in any leaf implies a change of the RH value.

(21) Another notion that we will use is the Hash Path (HP), which is an ordered sequence of hash values that helps to derive the root hash, starting from a chosen leaf value. FIG. 2 shows an example of a Merkle tree with 8 leafs, as illustrated in FIG. 2a, and the corresponding hash path for the leaf h.sub.3, as illustrated in FIG. 2b, that includes the sequence of missing nodes of the tree needed for the complete derivation of the RH. Note that the missing hash values in each node are added to the child's hash value either from the left (L) or from the right (R) side. The ordered sequence of L and R marks of a given HP is a left-right sequence (LRS) of a given HP.

(22) Thus, the path can be written as the sequence of 4 hash values {h.sub.3;h.sub.2(L);h.sub.01(L);h.sub.4567(R)}, and having the sequence of L-R marks one can compute the root hash explicitly.

(23) It is also worth to note that an LRS is 1-to-1 mapped to the index of the leaf, if the LRS is translated into the binary representation with the following rules: L-R marks closer to the root represent the most significant bits of the index, and closer to the leafs represent the least significant bits of the index; L is translated to the bit value 1 and R is translated to the bit value 0.

(24) Indeed, in the example illustrated in FIG. 2b of the hash path for h.sub.3 the L-R sequence is RLL, and it is translated to the correct index 011.sub.2=3.

(25) As a final comment we note that we actually can change the hash function as we move through the tree. In that case an identifier of the hash function used in each merging node has to be encoded into the path.

(26) KSI Architecture

(27) A basic drawing of the KSI architecture is shown in FIG. 3. That is, FIG. 3 illustrates KSI's global Merkle tree and its layers. KSI makes it possible for many users to collectively insert their hash values into the distributed Merkle tree and to compute the collective root hash, at a given time slot.

(28) The KSI system architecture includes several layers of aggregators, the functionality of each is basically to accept multiple hash values from the children connections, produce the local root hash, and push it to the upper layer for further aggregation. There are physically many aggregators on each layer that are distributed world-wide, but in the FIG. 3 there is only one hash path is shown, from the below single client to the top RH.

(29) A client or a device may push its own hash value using the entry point called the Gateway. The Core Network (CN) is the last station of accumulating hash values into the large Merkle tree, and CN thus computes the aggregation root hash (ARH).

(30) Additionally, CN has an extra modified Merkle tree to add the time stamping to ARE at a given time. The Calendar tree is organized such a way that it includes both the current ARE and the history of all previous ARHs in the past. The result of the Calendar tree is the Calendar Root Hash (CRH).

(31) As the result of aggregation, the client receives back the aggregation hash path (AHP) from the client's hash value to the aggregation root hash, and also the calendar hash path (CUP) from the ARE to the global time stamp hash value that is actually the CRH.

(32) The Core Network beats at regular intervals, for example, say once per second, which means that the CRH and the calendar tree are updated every second. CN also keeps the history of the global time-stamps for each second slotthe combination of ARHs and all historical CRHs in the past.

(33) This way, the client or anyone else can later verify that the combination of a saved aggregation hash path and the calendar hash path at a certain time t lead to the correct value. I.e., LRS of AHP could be served as a static identifier of the Gateway (if the connection of the Gateway to the KSI infrastructure is static), and LRS of CHP is used to verify the time when the hash paths were created.

(34) The global time stamp value CRH can be periodically published in a newspaper so that the Core Network cannot itself to modify the global time stamp back in time.

(35) For verification purposes, the CRH can be received either off-line, or on-line. For off-line use cases one could take the CRH through the printed publications (that may be periodically once per month). For on-line verification use cases, the CM can be signed by a trusted entity (perhaps, including a certificate), and then it can be downloaded by clients and/or applications at any time for verification purposes.

(36) In the general architecture of KSI the entry point for clients (and/or applications) is the Gateway (GW) that itself can be an aggregation layer, but additionally provides the client's front-end for various services based on KSI's time-stamping infrastructure. This way, the Gateway can be seen as a server-based service engine that should be located close to the customer, or actually be on the customer's side.

(37) The list of possible services that the Gateway may assist with includes: time-stamping of a given hash value, assistance in signing a document, etc. All those services are not really a part of KSI, but some of them are a part of QI-KSI.

(38) FIG. 4 illustrates a simplified view of KSI structure, and we may now refer to the simplified FIG. 4 of the KSI architecture.

(39) Identifier vs Identity

(40) KSI returns the aggregation hash path and the calendar hash path. The AHP may be considered as the identifier of the Gateway, since the L-R sequence in the global Merkle tree determines the way the Gateway was connected to the KSI. However, this identifier may be valid if certain conditions are valid: (a) The logical connection of the Gateway to KSI's leaf is static (b) A certificate that binds the Gateway's identity with the identifier is issued.

(41) Later we will see how the identifier is used in the QI-KSI signing model.

(42) Introduction to QI-KSI

(43) QI-KSI stands for Quantum-Immune KSI. This section is mainly based on the papers [2] and [4] identified in the introductory part of this disclosure.

(44) QI-KSI is an extension for KSI and provides two hash-based techniques. Hash-based cryptography is, as of today, believed to be quantum immune, so this is the reason for the name quantum-immune. QI-KSI proposes the technique for a hash-based authentication, and a hash-based digital signature architecture with the help of KSI's time-stamping service.

(45) Hash Chains for Authentication

(46) This is based on one-time passwords techniques. The client (and/or application) selects a random secret value z.sub.n (of size of the hash digest), and generates the hash chain (HC) z.sub.0z.sub.1 . . . z.sub.n as follows: z.sub.i=H(z.sub.i1), for i=0 . . . n1, and H is a chosen hash function.

(47) The value z.sub.0 is then shared with the server side (via some channel) to which the client is intended to authenticate himself.

(48) At any given time, the server holds a value z.sub.k (in the beginning, the server holds the value z.sub.0). When the client wants to authenticate himself, he uses and sends to the server the value z.sub.k+1. The server verifies that H(z.sub.k+1)=z.sub.k and if the values coincide then the authentication is successful. In the latter case, the server throws away z.sub.k and holds z.sub.k+1, instead, for future authentications.

(49) This way, one secret key z.sub.n can be served for n authentications.

(50) Hash Sequence Traversal Technique

(51) In this scheme, every time the client wants to authenticate himself, the value z.sub.k needs to be recomputed from z.sub.n. This may be a problem if n is large and there is no capacity to store or re-compute the whole hash chain. The solution to this problem is the technique called hash sequence traversal. Such a technique was proposed in [6] by D. Coppersmith and M. Jakobsson. In order to derive z.sub.k faster than just sequential hashing from z.sub.n to z.sub.k, the reversed order of hash chain z.sub.0z.sub.1 . . . z.sub.k . . . can be derived in average log(n) time if one could keep log(n) of intermediate hash values of the hash sequence. A short description of the M. Jakobsson and D. Coppersmith technique on the intuitive level can be given as follows. Assume the client can keep the value z.sub.n/2, then the derivation of any value z.sub.k would require at most n/2 hashes, instead of n. Now let us assume that the client keeps two intermediate values z.sub.n/2 and z.sub.n1/4. Thus, the elements of the first half of the hash chain z.sub.k, for kn/2, would require re-computation of at most n/4 hashes. When k becomes larger than n/2, the intermediate value z.sub.n/4 can be removed and a new value z.sub.n3/4 is derived linearly in time n hash operations, so that the elements of the second half of the hash chain z.sub.k, for k>n/2, can be calculated in at most n/4 hashes as well. It has been shown that having log(n) intermediate hash values, the total time to derive the reverse-order hash chain is log(n), in average.

(52) QI-KSI Signing Model

(53) The model of signing documents in QI-KSI is showed in FIG. 5. The client (or the Gateway, if the signing key is delegated), needs to create a secret signing key, and get a certificate from a CA on the public key. In this model, we look on the solution where a Trusted Third Party (TTP) behaves as a Signing Authority (TTP-SA) and takes part of the signing process and performs time-stamping of client's signing requests.

(54) In QI-KSI, the signer first creates his own pair of the secret key and the public key. The signer chooses a random secret key z.sub.n. Then, the sequence of values (hash chain) z.sub.0 . . . z.sub.n is computed as z.sub.1=H(z.sub.1+1) for i=0 . . . n1, and H is a chosen hash function.

(55) The value z.sub.0 is the public key and a relevant certificate for the public key z.sub.0 is generated by an external certificate authority (CA). The value z.sub.0 is bound with the user's identity in the validity time t.sub.0 seconds from a well-known date (number of seconds from the date 1970-01-01 and time 00:00:00) that determines the time after which the certificate is valid. To be more precise, a certificate should include at least the following fields: Cert:={Client's identity records; z.sub.0, t.sub.0, TTP-SA's identity and identifier}, where the TTP-SA's identifier can be the index of the leaf in the global KSI Merkle tree to which the TTP-SA is statically attached.

(56) QI-KSI signing key looks similar to the hash chain in the QI-KSI authentication method, but the difference comes from the meaning of the index k in the notation z.sub.k. The values z.sub.k, k=1 . . . n, are used as one-time signing keys (OTSK) each of which can be used only at a certain KSI's time frame that is exactly (t.sub.0+k)th second from the global starting time (recall, the Core Network beats and produces global time stamp values with the speed once per second).

(57) QI-KSI Signing Protocol

(58) QI-KSI signing protocol, see e.g. paper [2], is shown in FIG. 6. If the client wants to sign a piece of data, e.g. some message M, at a certain time slot t>t.sub.0, such that t=t.sub.0+i, then he takes the OTSK z.sub.i and computes x=H(H(M);z.sub.i) The value of x together with the user's ID is sent to the TTP-SA. TTP-SA checks that the client's certificate has not been revoked. Then TTP-SA pushes the hash of xID to KSI in order to get the time stamping. The returned blob S.sub.i contains the identifier of TTP-SA, that is its static LRS of AHP, the hash path and the calendar path. CA sends S.sub.i back to the user. After the time-stamp is returned, and the current time t becomes larger than t.sub.0+i seconds, the OTSK z.sub.i can be revealed. The signer then publishes the signature as <ID, i, z.sub.i, S.sub.i>.

(59) The verifier may check that z.sub.i is actually the i:th pre-image of z.sub.0, and the time stamp corresponds to t.sub.0+i.

(60) QI-KSI Improved OTSKs for Verification

(61) FIG. 7 illustrates modified OTSKs in a QI-KSI solution. In the QI-KSI signing protocol, the signer may derive the OTSK z.sub.i in log(n) time with the help of log(n) intermediate hash values using the hash sequence reversal technique, as it was described earlier.

(62) The problem comes for the verifier who wants to check the signature, as he only knows z.sub.i but needs to verify it against the public key z.sub.0. The verifier does not have those intermediate hash values and thus has to perform i hashes starting from z.sub.i and going all the way to z.sub.0.

(63) In order to reduce the time and/or complexity of the verification process, the following modification to OTSKs was proposed. This includes building yet another modified Merkle tree on top of OTSKs as shown in FIG. 7.

(64) The client's certificate additionally includes the root hash r, and the signature additionally includes the hash path from the OTSK z.sub.i to the root r. Thus, the verifier only needs to check that z.sub.i participated in the hash root generation, and the L-R sequence of the hash path is translated to the correct index i.

(65) For efficiency reasons, the signer needs to keep the relevant part of the hash-tree, and in the signing process the part of the hash tree that leads to the root hash r may be partly recomputed in log(n) time with log(n) intermediate hash values. That computation also requires the knowledge of other values z.sub.i in an efficient way, but then this part may be done with a hash chain traversal technique as demonstrated in U.S. provisional patent application No. 62/118,808.

(66) Synchronization with KSI

(67) It is important that S.sub.i returned by TTP-SA corresponds to the OTSK z.sub.i that has been used by the client. QI-KSI proposes the idea that the client actually needs to use 3 (or more) keys z.sub.i, z.sub.i+1 and z.sub.i2 and send a parallel request to TTP-SA for time-stamping. The signer will get 3 time stamps S's, but the stamp's time will correspond to only one of z.sub.i . . . z.sub.i+2.

(68) All this also means that the signer can produce one signature per 3 time slots, i.e., one signature per 3 seconds. However, as will be demonstrated below under the headline Further Options, efficiency may be improved also in this sense.

(69) The gist of this disclosure will now be presented, followed by some optional features, and thereafter further disclosure about methods and their implementations. It is readily understood from this disclosure that any combination with the demonstrated features of the KSI concept are applicable.

(70) Deriving the OTSKs Directly Via a One-Way Function

(71) FIG. 8 schematically illustrates an approach for deriving the OTSKs directly via a one-way function. It may be a desire to improve the part of deriving the one time signing keys, OTSK's, values z.sub.i of the signer's OTSK hash chain. The derivation of z.sub.i:s traditionally requires, even with the M. Jakobsson and D. Coppersmith technique of [6], the signer to spend additionally log(n) time for each z.sub.i, and to store additionally log(n) intermediate hash values. However, as described below, this can be done in O(1) time without storing intermediate hash values.

(72) We propose that instead of the hash chain z.sub.0 . . . z.sub.n, as discussed above, where z.sub.n is the secret key and z.sub.0 is the public key, the signer derives any of the OTSKs directly via a one-way function, given that all z.sub.is are bound by the root of a Merkle tree on top of the OTSKs sequence {z.sub.i}.

(73) Instead of the hash chain z.sub.0 . . . z.sub.n, the signer may derive any of the OTSKs as follows:

(74) z.sub.i=H(z.sub.sk;f.sub.i), for i=1 . . . n, where H is a one-way function, where z.sub.sk is a secret key of the signer, and f.sub.i is a function on the index i that generates different values for each i=1 . . . n. For example, this function can be as simple as fi=i, but it may be a more complex one. As an alternative, the z.sub.i:s may be generated as z.sub.i=HMAC(z.sub.sk;f.sub.i). The new scheme is shown in FIG. 8, where the upper part, i.e. above the dotted line, shows the verification of the OTSK values which is performed in the same way as demonstrated above, e.g. with reference to FIG. 7. The difference in this approach is thus the way the OTSK values are derived, i.e. by the one-way function.

(75) The signer's certificate then does not need to have z.sub.0, but it may comprise: the user's identity records, the root hash value r that combines all OTSKs, the value n that indicates the expiration time for the secret key z.sub.sk as well as determines the height of the tree, and the validation time t.sub.0, after which the certificate is valid. Since the LRS of the hash path encodes the index of z.sub.i uniquely, then this is the way to verify that z.sub.i is actually the OTSK that corresponds to the time t.sub.0+i

(76) The root hash thus still can prove that the hash path of OTSK z.sub.i was originated from the same secret source. The LRS of the hash path from z.sub.i to r determines the time slot when the OTSK z.sub.i can be used and be verified against the returned time-stamp.

(77) The use of z.sub.sk makes it faster and/or requires less processing/memory resources for the signer to derive the values z.sub.i for any i at any time without having to keep O(log(n)) intermediate hash values and spend O(log(n)) of time to derive z.sub.i, or calculate all hash values in the hash chain from z.sub.0, z.sub.n1, . . . , etc.

(78) Since in this modification the certificate now includes the expiration time (that is equal to t.sub.0+n), and the TTP-SA also checks for the validity of the signer's certificate, then this scheme will be as secure as the one proposed in QI-KSI above, and it is more efficient.

(79) After the expiration of the key usage time, the secret key z.sub.sk can be thrown away, whereas all created signatures remain valid in time and verifiable.

(80) By this, the signing process is faster and/or requires less storage resources (Cf. M. Jakobsson and D. Coppersmith technique) for the intermediate state, or requires less processing resources (Cf. traditional approach without M. Jacobsson and D. Coppersmith technique).

(81) The above mentioned approach is also applicable for deriving other OTSK values, as will be described below.

(82) Thus, for the QI-KSI signal model, there is provided a method to process for a hash tree infrastructure at predetermined intervals presented derived values of data to obtain a root hash value referred to as time-stamps that may be published such that the presented hash values to be processed depend on previously published root hash values, and a processes to compute and deliver a signature for the data after checking by a trusted signing authority wherein the derived values are the hash or mac of the data using an one-time signing key that is computed by a message authentication function. As demonstrated above, the one-time signing key may be computed as z.sub.i=H(z.sub.sk;f.sub.i), for i=1 . . . n, where H is a one-way function, where z.sub.sk is a secret key of the signer, and f.sub.i is a function on the index i that generates different values for each i=1 . . . n. The function may be f.sub.i=i.

(83) Further Options

(84) The approach of deriving the OTSKs directly by a one-way function has been shown above to provide an efficient way to provide the OTSK and thus hash value for a piece of data for use in the KSI context as previously known. Below, the applicability for further developments of the KSI approach and novel features thereof will be demonstrated.

(85) One-Time Proof of Knowledge for One-Time Signing Keys in Hash Based Signing Schemes

(86) FIG. 6 shows how the signing protocol uses TTP-SA. The TTP-SA issues a time stamp of the signing request only when the client's certificate is valid. This builds the trust for the verifier that at the time when the signature was actually created, the client's certificate has not been revoked. Therefore, the verifier does not need to check the status of the client's certificate during the verification time.

(87) A problem may be that TTP-SA does not know the content of the value xone part of the signing request, in the way that x (the value that the client derives and sends to TTP-SA; see section QI-KSI Signing Protocol above) can be anything and be generated by anyone.

(88) While issuing a signature, TTP-SA also does not know if the signing request comes from a legitimate user or from someone else. Hence, the TTP-SA may start to work and later when almost everything is ready find out that the user was not legitimate.

(89) It may thus be desirable to have a solution where the TTP-SA could verify that it is the authorized client who sends the signing request on his name, which would build a better trust in the signature.

(90) By using the hash path of a hash image of the actual OTSK as the proof that the user actually knows the not yet public secret OTSK, the TTP-SA may be better protected from doing work for non-legitimate requestors. The signer's signature may be shorter, and verification faster. The user sends this proof to the TTP-SA along with the signing request, so that the signing authority can verify the legitimacy of the signer before actually producing a signature fingerprint.

(91) The way to generate OTSKs by a user and the usage of such a proof-of-knowledge is not limited by the described use case, and the approach demonstrated here may be combined with any of the other approaches demonstrated in this disclosure. However, the benefit of deriving the OTSK by a one-way function as demonstrated above is evident when used together with this approach of providing one-time proof of knowledge to a signing authority.

(92) FIG. 7 illustrates how the hash chain is built (and FIG. 8 illustrates an alternative approach thereof) and its elements are used as OTSKs. For efficiency reasons on the verifier side, the combined root hash r of all OTSKs in the modified Merkle tree is public and included in the signer's certificate.

(93) By including the path from z.sub.i to the root r in the signature, the verifier is enabled to

(94) (a) check in O(log(n)) time that z.sub.i has been participated in the computation of the root value r and, by this way, to prove that z.sub.i is valid; and

(95) (b) the LRS of the hash path from z.sub.i to the root hash r also encodes the index i of the OTSK z.sub.i and, thus, the verifier can compare the time t.sub.0+i against the KSI's time-stamp's time slot, and that z.sub.i was used in the correct time slot.

(96) The hash path from r.sub.i's (where r.sub.i=H(z.sub.i)) to the public root hash r is actually the one-time proof of knowledge (OTPoK) of the secret OTSK z.sub.i, without revealing zi.

(97) By the client sending the OTPoK of the secret key to the TTP-SA along with the request, the TTP-SA may (additionally) verify that the OTPoK corresponds to the client's public key r that is stored in the client's certificate. The TTP-SA may add the value of r.sub.i into the time-stamping process.

(98) Thus, in the pair z.sub.i.fwdarw.r.sub.i the value r.sub.i authenticates to the TTP-SA the value of the OTSK z.sub.i.

(99) As a positive side effect, the signer's signature does not need to include the hash path from z.sub.1r, but only the OTSK z.sub.i, if TTP-SA includes r.sub.i as the part of the time-stamping computation. The verifier sort of exports the need to check of the hash path z.sub.i.fwdarw.r by letting the TTP-SA verify the hash path r.sub.i.fwdarw.r before issuing the time-stamp S.sub.i. The connection between z.sub.i and r.sub.i (and, thus, to r.sub.i.fwdarw.r) can be verified later on if the TTP-SA pushes the hash of the modified vector {x; usedID; r.sub.i} into KSI for time-stamping.

(100) After a key generation, the signer has the sequence of OTSKs {z.sub.1 . . . z.sub.n}, that are valid for signing at times t.sub.0+i time slot of KSI. The root hash r of a Merkle tree with the leafs values r.sub.is, i=1 . . . n, where r.sub.i=H(z.sub.i) for some one-way function H, as demonstrated above. The client's certificate may include the vector: {user ID; r; t.sub.0; TTP-SA's KSI identifier}

(101) Signing of a message M at some time t=t.sub.0+i, where t.sub.0<tt.sub.0+n, may then comprise the following protocol:

(102) 1. Signer computes x=H(H(M); z.sub.i) and sends to TTP-SA the vector {i; x; userID, HP r.sub.i.fwdarw.r}, where HP indicates hash path.

(103) 2. TTP-SA picks the right certificate that matches the pair {userID; r} and checks that it has not been revoked.

(104) 3. TTP-SA checks that HP r.sub.i.fwdarw.r is correct, and that LRS of that HP is mapping to the index i.

(105) 4. TTP-SA sends the hash of {x; userID; r.sub.i} to KSI in time t=t.sub.0+i, and receives the tune-stamping S.sub.i, that is AHP (aggregate HP) and CHP (calendar HP).

(106) 5. TTP-SA sends S.sub.i back to the signer.

(107) 6. The signer reveals the signature of the message M as <userID;i;z.sub.i;S.sub.i>

(108) The verification process is considered successful if:

(109) 1. H(x=H(H(M);z.sub.i), userID; r.sub.i=H(z.sub.i)) is the leaf of S.sub.i;

(110) 2. LRS of S.sub.i's AHP leads to the correct TTP-SA's KSI identifier that is bound in the signer's certificate;

(111) 3. S.sub.i's AHP and CHP lead to the correct CRH for the time t.sub.0+i.

(112) Thus, the approach may include that the signing authority receives a proof-of-possession before starting to process the request in the hash tree, computation and issuing of signature. The proof of possession may comprise sending the OTPoK of the secret key to the TTP-SA along with the request. The TTP-SA may verify that OTPoK corresponds to the client's public key that is stored in the client's certificate. The TTP-SA may add the value of r.sub.i into the time-stamping process.

(113) A device, application or session of a client may thus be arranged to transmit a proof-of-possession to a signing authority TTP-SA before the TTP-SA starts to process a request in the hash tree, compute and issue of signature. The transmission of the proof of possession may comprise sending the OTPoK of the secret key to the TTP-SA along with the request.

(114) A server operating a signing authority function may be arranged to receive a proof-of-possession from a client, to verify whether the OTPoK corresponds to the client's public key that is stored in the client's certificate, and omit computation and issuing of a signature when the OTPoK does not correspond to the client's public key and compute and issue signature when the OTPoK corresponds to the client's public key. The TTP-SA may add the value of r.sub.i into the time-stamping process.

(115) Sending Sequence of Signing Requests to TTP-SA Using OTSKs With Time-forwarded OTSKs Indexes

(116) This part of the disclosure relates to Time Fraction Sub-Trees in Hash Based Time Stamping Services for Faster Streaming of Requests of Services. Consider that KSI RH (root hash) is computed for each interval. Further, assume the intervals to be 1 second (but of course other interval settings are possible).

(117) An issue may be how QI-KSI, as demonstrated above, proposes to synchronize the OTSK z.sub.i with the KSI's tune. In the QI-KSI solution demonstrated above, when the signer sends a signing request to the TTP-SA, the client may take a group of OTSKs, for example three consecutive signing keys z.sub.i, z.sub.i+1 and z.sub.i+2, and send 3 signing requests to the TTP-SA simultaneously. The TTP-SA then can choose one out of the given three whose i corresponds to the current KSI's time, and push it to the KSI for time-stamping in the proper time slot. Since the client may reveal OTSK z.sub.i+2 only at time t>t.sub.0+i+2, this means that the client can produce a stream of signatures with the speed of 1 signature per 3 KSI's time slots (that is 1 signature per 3 seconds, with the above discussed design of the KSI's Core Network).

(118) For the use case where the client needs to sign a stream of data messages, the QI-KSI's way to synchronize the time between the signer and KSI is not optimal. It is a desire to provide a better synchronization solution so that the client does not waste OTSK keys and can perform signatures for a stream of data, e.g. with the speed in average of 1 signing per KSI's time slot (a second).

(119) Consider that the signer is enabled to send the sequence of signing requests to the TTP-SA using OTSKs with time-forwarded OTSKs indexes, and by this the client proposes the delay time before the actual time-stamping procedure, so that there is enough time for TTP-SA to receive the requests, prepare them and synchronize the time with KSI. In the use case where one needs to produce a stream of signatures, this synchronization scheme, as will be demonstrated in further detail below, utilizes the KSI resources (in particular, KSI's time slots) efficiently, which makes the signing speed to converge to 1 signature per one KSI time slot, in average.

(120) Assume that the possible resynchronization time between the signer's and KSI's clocks can be at most seconds (for instance, let be 5 seconds), including possible delays in communication between the signer and the TTP-SA. When the signer sends a signing request at his local time t.sub.sig, he actually may use the time-forwarded OTSK with the index t.sub.sigt.sub.0+, prepare and send a signing request to the TTP-SA.

(121) The TTP-SA may have a local queue with incoming signing requests that are already checked for the client's certificate and are waiting for being entered to KSI at the right tune for time-stamping. When the KSI time becomes aligned with the time of the first request in the queue, i.e., when the KSI's time becomes t.sub.sig+1, the TTP-SA pushes the corresponding hash value to the KSI infrastructure and receives the right time stamping.

(122) Thus, the client reveals the stream of signatures with the delay of seconds. In the use case of a stream of signatures, the performance may then converge to the speed 1 signature per KSI time slot.

(123) Note that in the above the clocking is described as being 1 second. However it is readily understood that it is equally applicable to other clocking interval settings.

(124) A trusted signing authority applying a hash tree signing system may have a local queue that comprises signing requests that use a time-forward OTSK that are already verified and which start further processing when the time with the hash tree system gets aligned. The OTSK may be determined by having the index t.sub.sigt.sub.0+.

(125) The sending of the sequence of signing requests to TTP-SA using OTSKs with time-forwarded OTSKs indexes benefits from being combined with the approach for deriving the OTSKs directly via a one-way function, and may also benefit from the approach for one-time proof of knowledge for one-time signing keys in hash based signing schemes, as well as with an approach comprising a combination of them.

(126) A device, application or session of a client may thus be arranged to transmit signing requests to a signing authority with time-forwarded OTSKs indexes.

(127) A server operating a signing authority function may be arranged to receive signing requests with time-forwarded OTSKs indexes, store them in a queue, and when the KSI time becomes aligned with the time of a request in the queue to push the corresponding hash value to a KSI infrastructure and receive the right time stamping Any calculations may be pre-calculated for the requests of the queue.

(128) Time Fraction Sub-Trees in Hash Based Time Stamping Service, or a Faster Streaming of Requests of Services

(129) Consider that KSI RH (root hash) is computed for each interval. Further, assume the intervals to be 1 second (but of course other interval settings are possible). As it was also mentioned in the section discussing synchronization with KSI above, the synchronization that is proposed in QI-KSI makes it possible to the client to make 1 signing per 3 seconds (3 KSI's time slots). However, in a use case when the client needs to sign a stream of data, this might be a performance bottleneck.

(130) The solution demonstrated above has mainly been discussed in view of a general case where an external service (KSI's time stamping, TTP SA service, other external modules that can, but not necessarily, be hash-based) is available once per a time slot (like in KSI, the service is available once per second). However, in the solution demonstrated below, the technique is demonstrated based on the example of the QI-KSI signing scheme for the sake of easier understanding for the reader.

(131) By extending the global KSI tree with a time fraction Merkle sub-tree on the TTP-SA node it is possible for one or more clients/gateways to perform signing for a stream of data items with the average speed faster than the speed of producing time stamps with KSI, i.e. faster than demonstrated with reference to the disclosure of sending sequence of signing requests to TTP-SA using OTSKs with time-forwarded OTSKs indexes above. It is to be noted that the approach demonstrated below may be combined with time-forwarded OTSKs indexes as demonstrated above for efficient provision of OTSK keys, e.g. for performing signatures for a stream of data.

(132) The approach makes it possible for the client to have only one hash chain of OTSKs, where each one-tune signing key corresponds to its own fraction of a second. That sub-tree will serve as a KSI's time slot splitter of a time slot into smaller time fractions.

(133) FIG. 9 illustrates a modified TTP-SA. We propose that the TTP-SA is arranged to use a yet another Merkle sub-tree with K leafs. The purpose is to split the KSI's 1 second time slot into K fractions of the second. Each leaf of the sub-tree corresponds to the certain fraction of the second, and thus the TTP-SA may accept multiple signing requests from one or multiple clients/gateways simultaneously, providing time-stamps with a better time-granularity than just 1 second.

(134) OTSKs of clients thus may be modified in such a way that now the client may create K sets of OTSKs. One set corresponds to and is used within one certain fraction of a second. FIG. 10 illustrates an example when a time slot is split into K fractions, where K=4 in the example.

(135) For example, if the TTP-SA's time-splitting sub-tree has 4 leafs, then TTP-SA is capable to perform 4 signatures per second, instead of 1 as of the original QI-KSI. The client generates 4 hash chains from 4 secret keys z.sub.n.sup.(0) . . . z.sub.n.sup.(3) and uses the OTSKs produced by z.sub.n.sup.(k) in the signing times t=t.sub.0+i+k/4 seconds, for i=1 . . . n, k=0 . . . 3 (for the example of K=4; K may be selected arbitrarily to achieve desired granularity).

(136) For each fraction of a second the TTP-SA returns, as the result of signing request, the same S.sub.i, but adds the hash path of the TTP-SA's time fraction sub-tree that is also included by the signer into the final signature.

(137) The verifier may apply: the LRS of AHP as the identifier for TTP-SA; the LRS of CHP to identify the time in seconds when the time-stamp was created; the LRS of the HP of the TTP-SA's time fraction sub-tree to identify the fraction of the second when the time stamp was created.

(138) Note that AHP and CHP parts of S.sub.i will be the same for all K signing requests within the same time slot. However, the HP of the time fraction tree will be different. Also note that since TTP-SA enters K hash values to the leafs of the time-fraction tree's HP, the signer or anyone else cannot ignore that HP since then the signature becomes invalid and non-verifiable.

(139) For synchronization purposes, the signer may still use the idea from the QI-KSI design demonstrated above, where for every fraction slot k=0 . . . K1, the signer uses 3 consecutive OTSKs z.sub.i.sup.(k), z.sub.i+1.sup.(k), z.sub.i+2.sup.(k). In this case, the average signing speed is 1 signature per 3/K seconds.

(140) A device, application or session of a client may thus be arranged to sign for a stream of data items by a time fraction tree splitting a time slot of a time stamping infrastructure into time fractions.

(141) A server operating a signing authority function may be arranged to receive multiple signing requests of a time slot of a time stamping infrastructure by a time fraction tree splitting the time slot of the time stamping infrastructure into time fractions.

(142) As indicated above, the approach of the fraction tree may be combined with the approach of delayed requests. FIG. 11 illustrates an example thereof. Assume that the TTP-SA has a time fraction sub-tree for splitting 1 second into K fractions. The signer may create only one OTSK hash chain, but now z.sub.k corresponds to the time (t.sub.0+k/K).sup.th second and (k modulo K).sup.th fraction of the second. The client sends a stream of signing requests using the time current time of the signer and the delay, t.sub.sig+, where is the maximum resynchronization time (for example, may be 3.25 seconds) between the client's and the KSI's clocks, including possible delays in communication and the processing time of the TTP-SA. i.e., the client sends the requests using z.sub.ks for not the current time, but for the current time plus some time offset .

(143) The TTP-SA server collects signing requests, verifies the client's certificate, and al locates the prepared hashes for the delayed collective time-stamping (with KSI) into a sorted (by time) queue. TTP-SA will push the top of the time fraction sub-tree to KSI infrastructure for time-stamping at a proper time. The hash root of the fraction tree can also be prepared by TTP-SA during the given delay . Thus, the queue of TTP-SA may be just a queue of hash values waiting for their turns to be time stamped.

(144) This way, TTP-SA has some time delay during which it can check the request itself (and the certificate), prepare the time fraction sub tree, calculate the root hash of that sub tree, and wait for the correct KSI's time to occur, in order to push the pre-computed hash into KSI for time stamping.

(145) Another solution could be that the possibility for a signer to add a signing request at a fraction of a KSI's time slot t closes shortly before the time t, such that TTP-SA would still have enough time to prepare the root hash of the time fraction tree before its root hash is to be pushed for KSI time-stamping at time t.

(146) The server returns S.sub.is together with the hash paths of its own sub-tree when the signing job for the group of requests is done, and continues to proceed with the next group of signing requests, taken from the local queue, checked and prepared in advance for the next second of the KSI's time slot.

(147) Thus, the client can publish the received stream of signatures with the time delay , and the average speed 1 signature per 1/K second utilizing OTSKs efficiently.

(148) A time stamp service provider applying a hash tree signing system of a hash-tree time-stamping part and a trusted signing authority (TTP-SA) may operate on given intervals for the TTP-SA, and there may be provided a time fraction sub-tree for splitting each interval into K fractions. The signer may create only one OTSK hash chain, where z.sub.k corresponds to the time (t.sub.0+(k div K)).sup.th time interval, e.g. second, and (k mod K).sup.th fraction of the interval.

(149) A device, application or session of a client may thus be arranged to sign for a stream of data items by a time fraction tree splitting a time slot of a time stamping infrastructure into time fractions, and be arranged to transmit signing requests to a signing authority with time-forwarded OTSKs indexes.

(150) A server operating a signing authority function may be arranged to receive multiple signing requests of a time slot of a time stamping infrastructure by a time fraction tree splitting the time slot of the time stamping infrastructure into time fractions, wherein the signing requests comprises time-forwarded OTSKs indexes, and the server is arranged to store them in a queue, and when the KSI time becomes aligned with the time of a request in the queue to push the corresponding hash value to a KSI infrastructure and receive the right time stamping. Any calculations may be pre-calculated for the requests of the queue.

(151) A server operating a signing authority function may be arranged to receive signing requests to a signing authority with time-forwarded OTSKs indexes, store them in a queue, and when the KSI time becomes aligned with the time of a request in the queue to push the corresponding hash value to a KSI infrastructure and receive the right time stamping. Any calculations may be pre-calculated for the requests of the queue.

(152) The generation of further OTSKs, as of the optional approach demonstrated above, further emphasizes the benefits of deriving OTSKs directly by the one-way function.

(153) Methods and Implementations

(154) FIG. 12 is a flow chart illustrating methods according to embodiments. Variants, details and explanations have already been provided above, and the flow chart should be considered as a rough, schematic and simplified illustration of the approach and some of its options.

(155) One or more OTSKs are derived 100 by a one-way function. The respective OTSK is used to provide 102 a hash value using a hash function including the OTSK and a piece of data which is intended for time signing. One or more of the following options may be included in the method: registering the hash value such that the piece of data at least later on may be verified regarding its presence at a time corresponding to an index of the OTSK used for providing the hash value; providing a one-time proof of knowledge, OTPoK, to a signing authority that the OTSK was in possession of the signer at a certain time without revealing the OTSK; and sending a signing request to the signing authority using OTSKs with time-forwarded OTSK indexes such that signing of the hashes of the pieces of data may be queued at the signing authority and the slots corresponding to OTSK indexes can be efficiently used. Further options and variants have been demonstrated above.

(156) A device, application or session of a client may thus be arranged to derive a one-time signing key z.sub.i as z.sub.i=H(z.sub.sk;f.sub.i), for i=1 . . . n, where H is a one-way function, where z.sub.sk is a secret key of the signer, and f.sub.i is a function on the index i that generates different values for each i=1 . . . n. The function may be f.sub.i=i.

(157) FIG. 13 illustrates a wireless network comprising a more detailed view of network node 200 and wireless device (WD) 210, in accordance with a particular embodiment. For simplicity, FIG. 13 only depicts network 220, network nodes 200 and 200a, and WD 210. Network node 200 comprises processor 202, storage 203, interface 201, and antenna 201a. Similarly, WD 210 comprises processor 212, storage 213, interface 211 and antenna 211a. These components may work together in order to provide network node and/or wireless device functionality, such as providing wireless connections in a wireless network and allowing for a change in estimated DL CC. In different embodiments, the wireless network may comprise any number of wired or wireless networks, network nodes, base stations, controllers, wireless devices, relay stations, and/or any other components that may facilitate or participate in the communication of data and/or signals whether via wired or wireless connections.

(158) Network 220 may comprise one or more of IP networks, public switched telephone networks (PSTNs), packet data networks, optical networks, wide area networks (WANs), local area networks (LANs), wireless local area networks (WLANs), wired networks, wireless networks, metropolitan area networks, and other networks to enable communication between devices.

(159) Network node 200 comprises processor 202, storage 203, interface 201, and antenna 201a. These components are depicted as single boxes located within a single larger box. In practice however, a network node may comprises multiple different physical components that make up a single illustrated component (e.g., interface 201 may comprise terminals for coupling wires for a wired connection and a radio transceiver for a wireless connection). Similarly, network node 200 may be composed of multiple physically separate components (e.g., a NodeB component and a RNC component, a BTS component and a BSC component, etc.), which may each have their own respective processor, storage, and interface components. In certain scenarios in which network node 200 comprises multiple separate components (e.g., BTS and BSC components), one or more of the separate components may be shared among several network nodes. For example, a single RNC may control multiple NodeB's. In such a scenario, each unique NodeB and BSC pair, may be a separate network node. In some embodiments, network node 200 may be configured to support multiple radio access technologies (RATs). In such embodiments, some components may be duplicated (e.g., separate storage 203 for the different RATs) and some components may be reused (e.g., the same antenna 201a may be shared by the RATs).

(160) Processor 202 may be a combination of one or more of a microprocessor, controller, microcontroller, central processing unit, digital signal processor, application specific integrated circuit, field programmable gate array, or any other suitable computing device, resource, or combination of hardware, software and/or encoded logic operable to provide, either alone or in conjunction with other network node 200 components, such as storage 203, network node 200 functionality. For example, processor 202 may execute instructions stored in storage 203. Such functionality may include providing various wireless features discussed herein to a wireless devices, such as WD 210, including any of the features or benefits disclosed herein.

(161) Storage 203 may comprise any form of volatile or non-volatile computer readable memory including, without limitation, persistent storage, solid state memory, remotely mounted memory, magnetic media, optical media, random access memory (RAM), read-only memory (ROM), removable media, or any other suitable local or remote memory component. Storage 203 may store any suitable instructions, data or information, including software and encoded logic, utilized by network node 200. Storage 203 may be used to store any calculations made by processor 202 and/or any data received via interface 201.

(162) Network node 200 also comprises interface 201 which may be used in the wired or wireless communication of signalling and/or data between network node 200, network 220, and/or WD 210. For example, interface 201 may perform any formatting, coding, or translating that may be needed to allow network node 200 to send and receive data from network 220 over a wired connection. Interface 201 may also include a radio transmitter and/or receiver that may be coupled to or a part of antenna 201a. The radio may receive digital data that is to be sent out to other network nodes or WDs via a wireless connection. The radio may convert the digital data into a radio signal having the appropriate channel and bandwidth parameters. The radio signal may then be transmitted via antenna 201a to the appropriate recipient (e.g., WD 210).

(163) Antenna 201a may be any type of antenna capable of transmitting and receiving data and/or signals wirelessly. In some embodiments, antenna 201a may comprise one or more omni-directional, sector or panel antennas operable to transmit/receive radio signals between, for example, 2 GHz and 66 GHz. An omni-directional antenna may be used to transmit/receive radio signals in any direction, a sector antenna may be used to transmit/receive radio signals from devices within a particular area, and a panel antenna may be a line of sight antenna used to transmit/receive radio signals in a relatively straight line.

(164) WD 210 may be any type of wireless endpoint, mobile station, mobile phone, wireless local loop phone, smartphone, user equipment, desktop computer, PDA, cell phone, tablet, laptop, VoIP phone or handset, which is able to wirelessly send and receive data and/or signals to and from a network node, such as network node 200 and/or other WDs. WD 210 comprises processor 212, storage 213, interface 211, and antenna 211a. Like network node 200, the components of WD 210 are depicted as single boxes located within a single larger box, however in practice a wireless device may comprises multiple different physical components that make up a single illustrated component (e.g., storage 213 may comprise multiple discrete microchips, each microchip representing a portion of the total storage capacity).

(165) Processor 212 may be a combination of one or more of a microprocessor, controller, microcontroller, central processing unit, digital signal processor, application specific integrated circuit, field programmable gate array, or any other suitable computing device, resource, or combination of hardware, software and/or encoded logic operable to provide, either alone or in combination with other WD 210 components, such as storage 213, WD 210 functionality. Such functionality may include providing various wireless features discussed herein, including any of the features or benefits disclosed herein.

(166) Storage 213 may be any form of volatile or non-volatile memory including, without limitation, persistent storage, solid state memory, remotely mounted memory, magnetic media, optical media, random access memory (RAM), read-only memory (ROM), removable media, or any other suitable local or remote memory component. Storage 213 may store any suitable data, instructions, or information, including software and encoded logic, utilized by WD 210. Storage 213 may be used to store any calculations made by processor 212 and/or any data received via interface 211.

(167) Interface 211 may be used in the wireless communication of signalling and/or data between WD 210 and network node 200. For example, interface 211 may perform any formatting, coding, or translating that may be needed to allow WD 210 to send and receive data from network node 200 over a wireless connection. Interface 211 may also include a radio transmitter and/or receiver that may be coupled to or a part of antenna 211a. The radio may receive digital data that is to be sent out to network node 201 via a wireless connection. The radio may convert the digital data into a radio signal having the appropriate channel and bandwidth parameters. The radio signal may then be transmitted via antenna 211a to network node 200.

(168) Antenna 211a may be any type of antenna capable of transmitting and receiving data and/or signals wirelessly. In some embodiments, antenna 211a may comprise one or more omni-directional, sector or panel antennas operable to transmit/receive radio signals between 2 GHz and 66 GHz. For simplicity, antenna 211a may be considered a part of interface 211 to the extent that a wireless signal is being used.

(169) In some embodiments, the components described above may be used to implement one or more functional modules used in a collision-blocking method for hash tree based time stamping. The functional modules may comprise software, computer programs, sub-routines, libraries, source code, or any other form of executable instructions that are run by, for example, a processor. In general terms, each functional module may be implemented in hardware and/or in software. Preferably, one or more or all functional modules may be implemented by processors 212 and/or 202, possibly in cooperation with storage 213 and/or 203. Processors 212 and/or 202 and storage 213 and/or 203 may thus be arranged to allow processors 212 and/or 202 to fetch instructions from storage 213 and/or 203 and execute the fetched instructions to allow the respective functional module to perform any features or functions disclosed herein. The modules may further be configured to perform other functions or steps not explicitly described herein but which would be within the knowledge of a person skilled in the art.

(170) The methods according to the present invention is suitable for implementation with aid of processing means, such as computers and/or processors, especially for the case where the processing element 202, 212 demonstrated above comprises a processor handling security functions. Therefore, there is provided computer programs, comprising instructions arranged to cause the processing means, processor, or computer to perform the steps of any of the methods according to any of the embodiments described above and those roughly summarized with reference to FIG. 12. The computer programs preferably comprises program code which is stored on a computer readable medium 300, as illustrated in FIG. 14, which can be loaded and executed by a processing means, processor, or computer 302 to cause it to perform the methods, respectively, according to embodiments of the present invention, preferably as any of the embodiments described with reference to FIG. 12. The computer 302 and computer program product 300 can be arranged to execute the program code sequentially where actions of the any of the methods are performed stepwise. The processing means, processor, or computer 302 is preferably what normally is referred to as an embedded system. Thus, the depicted computer readable medium 300 and computer 302 in FIG. 14 should be construed to be for illustrative purposes only to provide understanding of the principle, and not to be construed as any direct illustration of the elements.