Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3297—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving time stamps, e.g. generation of time stamps
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/50—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using hash chains, e.g. blockchains or hash trees

Definitions

• This invention relates to digital signatures in computer documents, and more particularly to time stamping digital signatures so that the latest time will be unambiguously known.
• Time stamping is a set of techniques enabling the ascertaining of when an electronic document was created or signed.
• the real importance of time-stamping comes about with the legal use of long lifetime documents.
• a problem with time stamping signed documents comes about when, for example, the signer repudiates the document and the cryptographic primitives become unreliable.
• the security of the signature becomes questionable. For example, a signer might claim she had lost her signature key, repudiate the signing, and bring the authenticity of a signature into question in order to escape responsibility for a document.
• RTA Relative Temporal Authentication
• RTA gives the verifier with two time stamped documents the ability to verify which of the two was created first.
• An example of an existing time stamping technique is a simple time stamping protocol.
• a weakness of this approach is the unreliability of documents with old time stamps after a signature key leakage, which may make it impossible to verify the time t on the document. This implies that for a reasonable solution the TSS must be unconditionally trusted. It is therefore widely accepted that a secure time stamping system cannot rely solely on the keys or on any other secret information of that sort.
• the time-stamping procedure is divided into rounds.
• the time-stamp R,. for round r is a cumulative hash of the time stamp R. . , for round r-1 and of all the documents submitted to the TSS during the round r.
• a binary tree T r is built. Every participant P ( who wants to time-stamp at least one document in this round, submits to the TSS a hash y which is a hash of all the documents he wants to time-stamp in this round.
• the leaves of T r are labeled by the submitted data items y j .
• Each inner node k of T r is recursively labeled by numerical values H k ⁇ H ⁇ , H, ⁇ , where k L and k R are correspondingly the left and the right child nodes of k, and H is a collision-resistant hash function.
• the TSS has to store only the time-stamps R. for rounds (Fig. 1). All the remaining information, required to verify whether a certain document was time-stamped during a fixed round is included into the time certificates.
• a time certificate of a document comprises the information required to verify whether a certain document was time stamped during a fixed round, i. e., for restoring the label of the predecessor node needed to know the labels of the sibling nodes.
• the time certificates for y 3 in Figure 1 is (r;(y 4 ,L),(H 4 ,R)).
• the verifying procedure of the time stamp of y 3 consists of verifying the equality:
• R r H(H(H 4 ,H(y 3 ,y 4 )),R r.1 ).
• the size of the time certificate and thereby also the number of computational steps during the verification is logarithmic on the number of documents submitted.
• the values of R_ are stored into a database and some of them are published in a newspaper.
• the schemes are feasible but provide the RTA for the documents issued during the same round only if we unconditionally trust the TSS to maintain the order of time-stamps in T r . Therefore, this method either increases the need for trust or otherwise limits the maximum temporal duration of rounds to the insignificant units of time (one second in Digital Notary system). However, if the number of submitted documents during a round is too small, the expenses of time-stamping a single document may become unreasonably large.
• the present invention comprises a method of time-stamping a digital document using a binary linking scheme where the value of the catenate certificate L n is generated by applying a one-way hash function H to a catenation comprising the value of the catenate certificate L n _j and the value of another suitably chosen catenate certificate L f(n) , with /being a fixed deterministic function algorithm, i.e.
• L n H (n,XJL n _,,L f(n) ).
• a method is also presented of certifying the moment of signing, not only the moment of submitting.
• a principal P Before signing a document X a principal P generates nonce N and time-stamps it.
• a nonce is meant sufficiently long random bit-string, such that the probability it has been already time-stamped is negligible.
• the verifier has to compare both these time-stamps with the time-stamps trusted by the verifier (which may be nonces generated by the verifier herself).
• the verifier may conclude that the signature was created in the time- frame between the moments of issuance o ⁇ L(N) and ofL(S) respectively. If these moments are close enough, the signing time can be ascertained with necessary precision. In this solution there are no supplementary duties to the TSS or to the other principals.
• a time-stamping procedure is also defined, as follows: (1) the client sends to the TSS the data item X to be time-stamped; (2) the TSS answers immediately by sending then current L n and the necessary data for verifying the one-way dependency between L n and the time-stamp for the previous round. The TSS signs L n and sends the signature D ⁇ n, LJ to the client; (3) if the round is over, the client may apply the TSS for the data necessary to verify a one-way relationship between L n and the time-stamp for round. Therefore, the TSS is not able to rearrange the time-stamps during a round. This means the present scheme reduces the need for trusting the TSS in maintaining the temporal order of time-stamped documents.
• Fig. 1 is flow chart of a tree linking system for the certification of Digital
• Fig. 2 is flow chart of a binary linking system (BLS) for the certification of Digital Signatures.
• BLS binary linking system
• Fig. 3 is flow chart of a BLS with the shortest verification links between digital signatures.
• Fig. 4 is a flow chart of an Accumulated Linking System (ALS) which may be used in the invention.
• ALS Accumulated Linking System
• Fig. 5 is flow chart of a Time Stamp system of the invention.
• Table I is a definition of a recursive linking system for digital signature verification.
• Table II shows how recursive linking may be programmed on a computer.
• Table III is a proof that a further reduction in the complexity of linking digital signatures is not feasible beyond the invention.
• Table IV-A and IV-B comprise proofs of the sufficiency of the invention for verification of digital signatures as disclosed. Description of the Preferred Embodiment
• time-stamping systems applicable in legal situations. Later the approach will be justified and compared to older systems.
• a time-stamping system consists of a set of principals with the time- stamping server (TSS) together with a triple (S, V, A) of protocols.
• the stamping protocol S allows each participant to post a message.
• the verification protocol V is used by a principal having two time-stamps to verify the temporal order between those time-stamps.
• the audit protocol A is used by a principal to verify whether the TSS carries out his duties. Additionally, no principal (in particular, TSS) should be able to produce fake time-stamps without being caught.
• a time-stamping system has to be able to handle time-stamps which are anonymous and do not reveal any information about the content of the stamped data.
• the TSS is not required to identify the initiators of time-stamping requests.
• time-stamping The main security objective of time-stamping is temporal authentication - ability to prove that a certain document has been created at a certain moment of time.
• the creation of a digital data item is an observable event in the physical world, the moment of its creation cannot be ascertained by observing the data itself.
• the best one can do is to check the relative temporal order of the created data items (i.e., prove the RTA) using one-way dependencies defining the arrow of time, analogous to the way in which the growth of entropy defines the arrow of time in the physical world.
• H is a collision-resistant one-way hash function
• the system utilizes collision- resistant one-way hash functions.
• a collision-resistant one-way hash function is a function H which has the properties of compression, ease of computation, preimage resistance, 2nd-preimage resistance and collision resistance.
• a (p, H)-linking scheme is a procedure to link a family (H of data items together using auxiliary linking items L n satisfying the recursive formula
• L n : H(H n , L n 1, ... ,Ln ⁇ p.1(n) ),
• a sequence (m j ) ⁇ i 1 , where m ; p m i+1 is called a verifying chain between m, and m ⁇ with length ⁇ .
• H n H(n,XJ, where X tract denotes the n-th time-stamped document.
• the linking item L n is also referred to as a time-stamp of X tract. Note that a one-way relationship between L n and L m (n ⁇ m) does not prove that in the moment of creating X tract the bit-string ⁇ did not exist, but we do know that X propel did exist at the moment of creating L m .
• RTA By using RTA it is possible to determine not only the submitting time of the signature but also the time of signing the document.
• the verifier may conclude that the signature was created in the time-frame between the moments of issuance of L(N) and of L( ⁇ ) respectively. If these moments are close enough, the signing time can be ascertained with necessary precision.
• a time-stamping system must have properties enabling users to verify whether an arbitrary time-stamp is correct or not. Possession of two documents with corresponding time-stamps is not enough to prove the RTA between the documents because everyone is able to produce fake chains of time-stamps.
• a time-stamping system should allow the user (1) to determine whether the time-stamps possessed by an individual have been tampered with; and (2) in the case of tampering, to determine whether the time-stamps were tampered with by the TSS or tampered after the issuing (generally by unknown means). In the second case, there is no one to bring an action against.
• the principals interested in legal use of time-stamps should themselves verify their correctness immediately after the issuing (using signatures and other techniques discussed later) because if the signature of the TSS becomes unreliable, the signed time-stamps cannot be used as evidence.
• the clients In order to increase the trustworthiness of the time-stamping services it should be possible for the clients to periodically inspect the TSS. Also, in the case when the TSS is not guilty he should have a mechanism to prove his innocence, i.e., that he has not issued a certain time-stamp during a certain round.
• the TSS must publish regularly, in an authenticated manner, the time-stamps for rounds [BdM91] in mass media. If the time-stamping protocol includes (by using collision-resistant one-way hash functions) (1) the message digest of any time-stamp issued during the r-th round, into the time-stamp for r-th round, and (2) the message digest of the time-stamp for round r - 1 into any time-stamp issued during the r-th round, it will be difficult for anyone to forge a time-stamp without detection.
• the forgery detection procedures should be simple. Forgeries should be determinable either during the stamping protocol (when the time-stamp, signed by the TSS, fails to be correct) or later when it is unable to establish the temporal order between two otherwise correct time-stamps.
• the values SU r are also referred to as the time-stamps for rounds. Note that the time-stamps requested from the TSS during the verification protocol should belong to the set of time-stamps for rounds because only these time-stamps are available in the time-stamping server.
• a (P, ⁇ , ⁇ ,H)-linking scheme is said to be an Accumulated Linking Scheme (ALS) with rank m, if
• a (p, H)-linking scheme enables accumulated time-stamping if for arbitrary positive m there exists ⁇ , such that the (p, ⁇ , p, H)-scheme is an ALS with rank m.
• the duration of the rounds can be flexibly enlarged in order to guarantee that only a negligible fraction of the time-stamps are kept in the memory of the time-stamping server.
• n the total number of time-stamps issued till the moment of the current run of stamping/verification protocol.
• the number of the evaluations of the hash function during the verification protocol should be O(log n).
• the number of time-stamps examined during a single run of the verification protocol should be O(log n);
• the size of an individual time-stamp should be small.
• the TSS maintains the following three databases:
• the fourth database (the complete database of time-stamps) is also stored but not on-line (it may be stored into an archive of CDs). Requests to this database are possible, but costly (e.g., requiring human interaction).
• the time-stamps in D p are stored to a separate CD (this procedure may be audited). Thereafter Dp is emptied.
• the time- stamp Rr for the current round is computed, added to Dr and published in a newspaper or similar publication (two processes which should be audited).
• the database Dc is copied into Dp and a new database Dc is created.
• Client sends X freely to the TSS.
• the TSS signs the pair (n, L n ) and sends (n, L n , Sig ⁇ ss (n,L n )) back to the client. 4.
• the client verifies the signature of TSS and checks whether
• L ⁇ r H (H' ⁇ r ,L ⁇ r. ,)(where H' ⁇ H ⁇ L ⁇ . ,)) and publishing L er and his public key K ⁇ ss in the newspaper or the like.
• the client may now continue, during a limited period, the protocol in order to get the complete individual time-stamp for
• the client sends a request to the TSS.
• tail (n) (H ⁇ r . together H ⁇ r.2 , ..., H n+2 ,H n+1 ).
• the TSS answers by sending (tail (n), sig ⁇ ss (tail (n))) to the client.
• the client checks whether
• the signature key of TSS is trusted to authenticate him and therefore, his signature on an invalid head (n) or tail (n) can be used as an evidence in the court.
• the client is responsible for doing it when the signature key of TSS can still be trusted. Later, the signature of TSS may become unreliable and therefore only the one-way properties can be used.
• the verifier sends a request to the TSS.
• the TSS answers by sending the tuple V mn (m)) and the signature sig ⁇ ss (V mn )to the verifier.
• the verifier validates the signature, finds L ⁇ r(m) using (3), finds L r (n) -1 using the formula
• L r(n) - ⁇ H (H ⁇ r(n) _ ⁇ , H (H ⁇ r(n ⁇ ) , L ⁇ r(m) )(7)). and finally, compares the value of L n in s n with the value given by (2).
• time-stamps issued by the TSS there should be some mechanism to audit the TSS.
• One easy way to do it is to periodically ask for time-stamps from the TSS and verify them. If these time-stamps are linked inconsistently (i.e., Eq. (2) and (3) hold for both time-stamps but the verification protocol fails), the TSS can be proven to be guilty.
• the TSS has to find the shortest verifying chains between ⁇ r(n) resort, and n and between N and ⁇ .
• the n-th individual time-stamp consists of the minimal amount of data necessary to verify the mutual one-way dependencies between all Lj which lay on these chains. It can be shown that if f satisfies the implication
• the length of the n-th time-stamp in this scheme does not exceed 2 -3 • log(n)- x bits, where x is the output size of the hash function H.
• the maximum length of rounds grows proportionally to O(log n).
• the average length of rounds is constant and therefore it is practical to publish the time-stamps for rounds after constant units of time. This can be achieved easily with the following procedure. If the "deadline" for a round is approaching and there are still q time-stamps not issued yet, assign random values to the remaining data items H».
• Remark 1 Denote by ord n the greatest power of 2 dividing n. In the ALS presented above, it is reasonable to label time-stamps in the lexicographical order with pairs (n, p), where 0 ⁇ p ⁇ ord n and n > 0. Then,
• ⁇ (i) : (2 1 " 1 i, k - 1 + ord i), for i ⁇ 1.
• C 2 be verifying chains from z to x and w to y respectively. It is obvious that C, and C 2 have a common element. Thus, if m ⁇ n then the verifying chains tail (m) and head (n) have a common element c which implies the existence of a verifying chain.
• Example 2 For the chains given in Example 1, the common element is 7 and the verifying chain between 4 and 10 is (4, 5, 6, 7, 10).
• Corollary 1 Due to the similarity between the verification and the stamping procedure, for an arbitrary pair of time-stamped documents the number of steps executed (and therefore, also the number of time-stamps examined) during a single run of the verification protocol is O(log n).
• the Theorem 2 can be straightforwardly generalized to claim that the number of examined time-stamps must be greater than any fixed constant.
• a binary linking scheme can alternatively be defined as a directed countable graph which is connected, contains no cycles and where all the vertices have two outgoing edges (links). Let us construct an infinite family of such graphs Tk in the following way:
• Tl consists of a single vertex which is labeled with the number 1. This vertex is both the source and the sink of the graph Tl
• Tk be already constructed. Its sink is labeled by 2 k -l .
• the graph Tk+1 consists of two copies of Tk, where the sink of the second copy is linked to the source of the first copy, and an additional vertex labeled by 2 k+1 -l which is linked to the source of the second copy. Labels of the second copy are increased by 2 k -l.
• the sink of Tk+1 is equal to the sink oft the first copy
• the source of Tk+1 is equal to the vertex labeled by 2 k+1 -l.
• l(a,b) be the length of the shortest verifying chain from b to a. If k>2 and 0 ⁇ a ⁇ b ⁇ 2 k then l(a,b) ⁇ 3k-5.
• RTA Relative Temporal Authentication
• An embodiment of the present invention comprises a method of time stamping a digital document using binary linking.
• a catenate certificate L n is generated by applying a one-way hash function H to a concatenation of the value of the catenate certificate L submit .
• ⁇ and the value of a suitably chosen catenate certificate L ⁇ n) where f is a fixed deterministic function, such as:
• L n H(n, X n , L n.1 ,L f(n) ).
• the indices are such that for each k the time certificate L n(k) is generated exclusively with values of L j , where n(k-l) ⁇ j ⁇ n(k), and of L n(j) with j ⁇ k. Treating intervals between the issuance of different L n(k) as "rounds", the anti-monotonic property insures that the time stamp for a round is not linked directly to the inner time stamps of other rounds.
• the moment of signing is certified.
• a principal P Before signing a document X a principal P generates nonce N and time stamps it.
• a nonce is a long random bit string, with an arbitrary length judged sufficient to reduce the probability of a conflict with another time stamp to insignificance.
• the time stamping events are identical; that is, the TSS does not know or need to know whether the time stamping is for a nonce or for meaningful data.
• the verifier compares both time stamps with other time stamps trusted by the verifier; which may be nonces developed for this purpose.
• the verifier can conclude that the signature was created in the time frame between the moments of issuance of L(N) and of L(S), respectively. If these moments are close enough in time, the signing time can be ascertained with precision. In this embodiment there are no supplementary duties for the TSS or other principals. In yet another embodiment, limited reliance on the TSS allows for a simplified system:
• the TSS responds immediately with the current L n and the necessary data for verifying the one-way dependency between L n and the time stamp for the previous round, signs to create an L n , and sends the signature D TSS (n,L n ) to the client, and
• the client may apply to the TSS for the data necessary to verify a one-way relationship between Ln and the time stamp for the round.
• the above embodiment thereby reduces the need for trusting the TSS in maintaining the temporal order of time stamped documents by preventing the TSS from having an opportunity to rearrange the documents.

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