This invention relates to applications of information security technologies and, in particular, relates to a key exchange technique that allows a plurality of users, who make up a group, to share a common key.
A key exchange technique that allows a plurality of users, who make up a group, to share a common key has been proposed. An example of a system that implements such a key exchange technique is shown in
Therefore, a protocol in Non-patent Literature 1 has been proposed as a key exchange technique that can conceal metadata. The technique of Non-patent Literature 1 implements a key exchange between two parties using probabilistic public key encryption in the communication channel. This makes it possible to conceal metadata (for instance, a telephone number, a destination, a source, communication time, a communication path, an attached file name, and the number of transmissions) on communication at the time of a key exchange between two parties.
However, in the technique of Non-patent Literature 1, users who can exchange a common key are limited to two parties. This makes it impossible to implement a key exchange with metadata being concealed in communication among N (≥3) parties.
An object of the present invention is accordingly to provide a key exchange technique of performing a key exchange among N (≥2) parties, which can conceal metadata on communication.
An aspect of the present invention is an anonymous broadcast method in which N is assumed to be an integer greater than or equal to 2, L is assumed to be an integer greater than or equal to 1, and the anonymous broadcast method allows communication devices of N communication devices U1, . . . , UN, the communication devices included in a set R of communication devices={U1, . . . , Un} (2≤n≤N), to share messages M1, . . . , Mn. IDi (1≤i≤N) is assumed to be an identifier of a communication device Ui, MPKj (1≤j≤L) is assumed to be a master public key of an anonymous ID-based broadcast encryption scheme, SMPKj (1≤j≤L) is assumed to be a master public key of an ID-based signature scheme, dki(j) (1≤i≤N, 1≤j≤L) is assumed to be a decryption key of the anonymous ID-based broadcast encryption scheme, and ski(j) (1≤i≤N 1≤j≤L) is assumed to be a signature key of the ID-based signature scheme. The anonymous broadcast method includes: a cipher text generation step in which, for i∈{1, . . . , n}, the communication device Ui generates a signature ωi←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lski(j), (IDi, Mi)) from a master public key Σj=1, . . . , LSMPKj, a signature key Σj=1, . . . , Lski(j), and a message (IDi, Mi) which is a tuple of the identifier IDi and a message Mi and generates cipher text Ci←(Σj=1, . . . , LMPKj, (IDi, ωi, Mi), (R-{Ui})) from a master public key Σj=1, . . . , LMPKj, plaintext (IDi, ωi, Mi) which is a tuple of the identifier IDi, the signature ωi, and the message Mi, and a set R-{Ui} and, for i∈{n+1, . . . , N}, the communication device Ui generates cipher text Ci which is a dummy message; a cipher text obtaining step in which, for i∈{1, . . . , N}, the communication device Ui obtains cipher text {C1, . . . , CN} obtained by a shuffle performed by a mix-net; and a message reconstruction step in which, for i∈{1, . . . , N}, the communication device Ui generates a message (IDk, ωk, Mk)←(Σj=1, . . . , Ldki(j), Ck) from a decryption key Σj=1, . . . , Ldki(j) and cipher text Ck (1≤k≤N) and, if Ui∈R-{Uk}, generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, Mk, ωk) from the master public key Σj=1, . . . , LSMPKj and the message (IDk, ωk, Mk), and, if a signature ωk is successfully verified, regards a message Mk as a message transmitted from a communication device Uk with an identifier IDk and the communication device Ui∈R obtains the messages M1, . . . , Mn.
An aspect of the present invention is a key exchange method in which N is assumed to be an integer greater than or equal to 2, L is assumed to be an integer greater than or equal to 1, and the key exchange method allows communication devices of N communication devices U1, . . . , UN, the communication devices included in a set R of communication devices={U1, . . . , Un} (2≤n≤N), to share a session key SK. IDi (1≤i≤N) is assumed to be an identifier of a communication device Ui, MPKj(1≤j≤L) is assumed to be a master public key of an anonymous ID-based broadcast encryption scheme, SMPKj (1≤j≤L) is assumed to be a master public key of an ID-based signature scheme, dki(j) (1≤i≤N, 1≤j≤L) is assumed to be a decryption key of the anonymous ID-based broadcast encryption scheme, ski(j) (1≤i≤N, 1≤j≤L) is assumed to be a signature key of the ID-based signature scheme, G is assumed to be a finite cyclic group of prime number order p with generators g and h, ∥ is assumed to be a concatenation operator, and secret strings sti and st′i are recorded on a recording unit of the communication device Ui (1≤i≤N). The key exchange method includes: a first key generation step in which, for i∈{1, . . . , n}, the communication device Ui calculates ri, ki, and si using the secret strings sti and st′i by a twisted pseudo-random function and generates a first key (Ri, ci) by calculating Ri=gr_i and ci=gk_ihs_i and, for i∈{n+1, . . . , N}, the communication device Ui randomly selects Ri, ci∈RG and generates a first key (Ri, ci); a first anonymous broadcast step in which, for i∈{1, . . . , n}, the communication device Ui anonymously broadcasts the first key (Ri, ci) with a set R-{Ui} being designated and, for i∈{n+1, . . . , N}, the communication device Ui anonymously broadcasts the first key (Ri, ci) with φ, which means no recipient, being designated; a second key generation step in which, for i∈{2, . . . , n}, the communication device Ui calculates a session ID sid using ck (1≤k≤n) by a target-collision resistant hash function, calculates Ki(l) using (sid, Ri−1r_i) by a pseudo-random function, calculates Ki(r) using (sid, Ri+1r_i) by a pseudo-random function, calculates Ti by an exclusive OR of Ki(l) and Ki(r), randomly selects T′i∈RZp2, generates a signature σi←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lski(j), (R, Ri, ci, ki, si, Ti, T′i)) from a master public key Σj=1, . . . , LSMPKj, a signature key Σj=1, . . . , Lski(j), and a message (R, Ri, ci, ki, si, Ti, T′i), and generates a second key (ki, si, Ti, T′i, σi), for i=1, a communication device U1 calculates a session ID sid from ck (1≤k≤n) by a target-collision resistant hash function, calculates K1(l) using (sid, Rnr_1) by a pseudo-random function, calculates K1(r) using (sid, R2r_1) by a pseudo-random function, calculates T1 by an exclusive OR of K1(l) and K1(r), calculates T′ by an exclusive OR of K1(l) and k1∥s1, randomly selects k″1, s″1∈RZp, generates a signature σ1←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lsk1(j), (R, R1, ci, k″1, s″1, T1, T′)) from the master public key Σj=1, . . . , LSMPKj, a signature key Σj=1, . . . , Lsk1(j), and a message (R, R1, c1, k″1, s″1, T1, T′), and generates a second key (k″1, s″1, T1, T′, σ1), and, for i∈{n+1, . . . , N}, the communication device Ui randomly selects ki, si∈RZp, Ti, T′i∈RZp2, and σi∈RΣ (where Σ is a signature space) and generates a second key (ki, si, Ti, T′i, σi); a second anonymous broadcast step in which, for i∈{2, . . . , n}, the communication device Ui anonymously broadcasts the second key (ki, si, Ti, T′i, σi) with the set R-{Ui} being designated, for i=1, the communication device U1 anonymously broadcasts the second key (k″1, s″1, T1, T′, σ1) with a set R-{U1} being designated, and, for i∈{n+1, . . . , N}, the communication device Ui anonymously broadcasts the second key (ki, si, Ti, T′i, σi) with the φ being designated; and a session key generation step in which, for i∈{2, . . . , n}, when the communication device Ui obtains the second key (k″1, s″1, T1, T′, σ1) and a second key (kk, sk, Tk, T′k, σk) (2≤k≤n, k≠i), the communication device Ui generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, (R, Rk, ck, kk, sk, Tk, T′k), σk) from the master public key Σj=1, . . . , LSMPKj, a message (R, Rk, ck, kk, sk, Tk, T′k), and a signature σk, if the signature σk is successfully verified, calculates K1(l) by an exclusive OR of Ki(l) and an exclusive OR of Tj(1≤j≤i−1), calculates k1∥s1 by an exclusive OR of T′ and K1(l), and, if ck=gk_khs_k holds for k that satisfies 1≤k≤n, generates the session key SK using the sid and an exclusive OR of the ki (1≤i≤n) by a pseudo-random function and, for i=1, when the communication device U1 obtains a second key (kk, sk, Tk, T′k, σk) (2≤k≤n), the communication device U1 generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, (R, Rk, ck, kk, sk, Tk, T′k), σk) from the master public key Σj=1, . . . , LSMPKj, a message (R, Rk, ck, kk, sk, Tk, T′k), and a signature σk and, if the signature σk is successfully verified and ck=gk_khs_k holds for k that satisfies 1≤k≤n, generates the session key SK using the sid and an exclusive OR of the ki (1≤i≤n) by a pseudo-random function.
According to the present invention, a plurality of users can share a common key with metadata being concealed. Furthermore, in the more general sense, a plurality of users can share messages with metadata being concealed.
Hereinafter, an embodiment of the present invention will be described in detail. It is to be noted that component units having the same function will be identified with the same reference character and overlapping explanations will be omitted.
<Notation System>
Prior to explanations of the embodiment, a notation system which is used in this specification will be explained.
An underscore (_) represents a subscript. For example, xy_z denotes that yz is a superscript attached to x and xy_z denotes that yz is a subscript attached to x.
Randomly selecting an element in from a given set Set is written as m∈RSet.
When a given algorithm ALG outputs y for input x and a random number r, this output is written as y←ALG(x;r). It is to be noted that, if ALG is a deterministic algorithm, the random number r is a null.
κ is assumed to be a security parameter.
[Pseudo-Random Function (PRF)]
F={Fκ:Domκ×FSκ→Rngκ}κ is assumed to be a family of functions with a domain of definition {Domκ}κ, a key space {FSκ}κ, and a range {Rngκ}κ. In this case, if it is impossible for a discriminator D in arbitrary polynomial time to discriminate between a function Fκ and a true random function RFκ:Domκ→Rngκ, F={Fκ}κ is referred to as a family of pseudo-random functions. A specific example of a pseudo-random function is described in, for example, Reference Non-patent Literature 1 below.
[Target-Collision Resistant Hash Function]
H={Hκ:Domκ→Rngk}k is assumed to be a family of hash functions with a domain of definition {Domk}k and a range {Rngκ}k. In this case, if it is impossible for an attacker A, who is provided with x∈RDomκ, in arbitrary polynomial time to find x′ (≠x) which makes Hκ(x)=Hκ(x′) hold, H={Hκ}κ is referred to as a family of target-collision resistant hash functions. A specific example of a target-collision resistant hash function is described in, for example, Reference Non-patent Literature 2 below.
[Twisted Pseudo-Random Function (Twisted PRF)]
A function tPRF: {0, 1}κ×FSκ×FSκ×{0, 1}κ→Rngκ is referred to as a twisted pseudo-random function and is defined as follows using a pseudo-random function Fκ.
tPRF(a,a′,b,b′):=Fκ(a,b)⊕Fκ(b′,a′)
Here, a, b′∈{0, 1}κ and a′, b∈FSκ hold. A specific example of a twisted pseudo-random function is described in, for example, Reference Non-patent Literature 3 below.
[Mix-Net]
A mix-net system includes M (M is an integer greater than or equal to 2) mix-net servers S1, . . . , SM. The mix-net server S1, which is the first server, receives n (n is an integer greater than or equal to 2) input messages to be processed in one round (that is, a series of processing which is performed by S1, . . . , SM). Then, the mix-net servers shuffle the messages in the order of m=1, . . . , M. The mix-net server SM, which is the last server, outputs N (N is an integer greater than or equal to 2) output messages. Even if an arbitrary outside attacker colludes with an M−1 mix-net server, the attacker cannot know the relationship between the input messages and the output messages. A specific example of a secure mix-net protocol is described in, for example, Reference Non-patent Literature 4 below.
[Anonymous ID-Based Broadcast Encryption (AIBBE) Scheme]
An anonymous ID-based broadcast encryption scheme consists of the following four algorithms.
A master key generation algorithm (1κ) outputs a master secret key MSK and a master public key MPK using the security parameter κ as input. A key generation center KGC is provided with the master secret key MSK. Moreover, the master public key MPK is made public.
A decryption key generation algorithm (MSK, IDi) outputs a decryption key dki using the master secret key MSK and an identifier IDi of a user i (1≤i≤N) as input. The decryption key dki is securely transmitted to the user i.
An encryption algorithm (MPK, M, R) outputs cipher text CT using the master public key MPK, plaintext M, and a set R of recipients as input. Here, the set R of recipients is a set of identifiers of users who are the recipients of the plaintext M.
A decryption algorithm (dki, CT) outputs, if the identifier IDi of the user i is included in the set R of recipients, the plaintext M using the decryption key dki and the cipher text CT as input.
A specific example of a secure AIBBE scheme is described in, for example, Reference Non-patent Literature 5 below.
An anytrust anonymous ID-based broadcast encryption (anytrust-AIBBE: AT-AIBBE) scheme is defined by using the anonymous ID-based broadcast encryption scheme. To distribute credibility, the AT-AIBBE scheme includes a plurality of key generation centers (KGC1, . . . , KGCL) (L is an integer greater than or equal to 1). A key generation center KGCj (1≤j≤L) makes a master public key MPKj public. Moreover, the key generation center KGCj (1≤j≤L) generates a decryption key dki(j) for a user i (1≤i≤N). The user i (1≤i≤N) encrypts plaintext M and obtains cipher text CT←(Σj=1, . . . , LMPKj, M, R). Furthermore, the user i (1≤i≤N) decrypts the cipher text CT and obtains the plaintext M←(Σj=1, . . . , Ldki(j), CT) (only if an identifier IDi of the user i is included in a set R of recipients). Even if an L−1 key generation center of the key generation center KGCj (1≤j≤L) has a malicious intention, the L−1 key generation center cannot decrypt the cipher text CT.
[ID-Based Signature Scheme]
An ID-based signature scheme consists of the following four algorithms.
A master key generation algorithm (1κ) outputs a master secret key SMSK and a master public key SMPK using the security parameter κ as input. A key generation center KGC is provided with the master secret key SMSK. Moreover, the master public key SMPK is made public.
A signature key generation algorithm (SMSK, IDi) outputs a signature key ski using the master secret key SMSK and an identifier IDi of a user i (1≤i≤N) as input. The signature key ski is securely transmitted to the user i.
A signature generation algorithm (SMPK, ski, M) outputs a signature σ using the master public key SMPK, the signature key ski, and a message M as input.
A signature verifying algorithm (SMPK, IDi, M, σ) outputs a verification result Ver (for example, 0 or 1 as a binary indicating the verification result) using the master public key SMPK, the identifier IDi of the user i, the message M, and the signature σ as input.
An anytrust ID-based signature (anytrust-IBS: AT-IBS) scheme is defined by using the ID-based signature scheme. To distribute credibility, the AT-TBS scheme includes a plurality of key generation centers (KGC1, . . . , KGCL) (L is an integer greater than or equal to 1). A key generation center KGCj (1≤j≤L) makes a master public key SMPKj public. Moreover, the key generation center KGCj (1≤j≤L) generates a signature key ski(j) for a user i (1≤i≤N). The user i (1≤i≤N) obtains a signature σ←(Σj=1, . . . , LSMPKj, Σ=1, . . . , Lski(j), M) as a signature for a message M. Furthermore, the user i (1≤i≤N) verifies the signature σ and obtains a verification result Ver←(Σj=1, . . . , LSMPKj, IDi, M, σ). Even if an L−1 key generation center of the key generation center KGCj (1≤j≤L) has a malicious intention, the L−1 key generation center cannot forge the signature σ.
<System Configuration>
As illustrated in
As illustrated in
Here, the first anonymous broadcast unit 410-1 and the second anonymous broadcast unit 410-2 each provide a function for sharing a message between communication devices belonging to a designated set of communication devices. That is, the first anonymous broadcast unit 410-1 and the second anonymous broadcast unit 410-2 provide the same function. Therefore, the first anonymous broadcast unit 410-1 and the second anonymous broadcast unit 410-2 will be explained as an anonymous broadcast unit 410 in the following description. As illustrated in
A key exchange method of the embodiment is implemented as a result of these key generation servers 1001, . . . , 100L, the release server 200, the mix-net servers 3001, . . . , 300M, and the communication devices 4001, . . . 400N performing processing in steps illustrated in
The key generation servers 1001, . . . , 100L, the release server 200, the mix-net servers 3001, . . . , 300M, and the communication devices 4001, . . . 400N are each a special device configured as a result of a special program being read into a publicly known or dedicated computer including, for example, a central processing unit (CPU), a main storage unit (random access memory: RAM), and so forth. Each device executes each processing under the control of the central processing unit, for example. The data input to each device and the data obtained by each processing are stored in the main storage unit, for instance, and the data stored in the main storage unit is read into the central processing unit when necessary and used for other processing. At least part of each processing unit of each device may be configured with hardware such as an integrated circuit.
Each of the recording units of the key generation servers 1001, . . . , 100L, the release server 200, the mix-net servers 3001, . . . , 300M, and the communication devices 4001, . . . , 400N can be configured with, for example, a main storage unit such as random access memory (RAM), an auxiliary storage unit configured with a hard disk, an optical disk, or a semiconductor memory device such as flash memory, or middleware such as a relational database or a key-value store. When the recording unit stores secret information, it is desirable that the recording unit is a tamper-resistant storage unit (for example, a SIM card).
In the following explanation, symbols are defined as follows. Ui (i∈{1, . . . , N}) is assumed to denote N communication devices 4001, . . . , 400N. Likewise, Sm (m∈{1, . . . , M}) is assumed to denote M mix-net servers 3001, . . . , 300M.
Moreover, p is assumed to be a K-bit prime number and G is assumed to be a finite cyclic group of order p with generators g and h. TCR:{0, 1}*→{0, 1}κ is assumed to be a target-collision resistant hash function. tPRF:{0, 1}κ×FSκ×FSκ×{0, 1}κ→Zp and tPRF′:{0, 1}κ×FSκ×FSκ×{0, 1}κ→FSκ are assumed to be twisted pseudo-random functions. F:{0, 1}κ×G→Zp2, F′:{0, 1}κ×Zp→FSκ, F″:{0, 1}κ×FSκ→{0, 1}κ, and F′″:{0, 1}κ×FSκ→Zp are assumed to be pseudo-random functions.
<System Setup>
A processing procedure of system setup in the key exchange method of the embodiment will be described with reference to
The operation of a key generation server 100j (1≤j≤L) will be described with reference to
Next, in Step S102, the decryption key and signature key generation unit 102 of the key generation server 100j (1≤j≤L) generates a decryption key dki(j)←(MSKj, IDi) from the master secret key MSKj and an identifier IDi of a communication device Ui (1≤i≤N) by the decryption key generation algorithm of the anonymous ID-based broadcast encryption scheme and generates a signature key ski(j)←(SMSKj, IDi) from the master secret key SMSKj and the identifier IDi of the communication device Ui (1≤i≤N) by the signature key generation algorithm of the ID-based signature scheme. The key generation server 100j (1≤j≤L) transmits the decryption key dki(j) and the signature key ski(j) to the communication device Ui (1≤i≤N) using the transmitting and receiving unit 198. The communication device Ui records the received decryption key dki(j) and signature key ski(j) (1≤j≤L) on the recording unit 499. Moreover, the communication device Ui obtains the master public keys (MPKj, SMPKj) (1≤j≤L) and records the master public keys (MPKj, SMPKj) on the recording unit 499.
It is to be noted that the master secret keys (MSKj, SMSKj) which are generated by the key generation server 100j are periodically updated to ensure the forward confidentiality of metadata. The period of this update can be set so that an update is performed once per day, for example.
The operation of the release server 200 will be described with reference to
The operation of the communication device Ui (1≤i≤N) will be described with reference to
<Anonymous Broadcast>
A processing procedure of anonymous broadcast in the key exchange method of the embodiment will be described with reference to
A set of communication devices is assumed to be R={Ui_1, . . . , Ui_n} (where {i1, . . . , in}⊆{1, . . . , N}), and a communication device Ui_k (1≤k≤n) performs anonymous broadcast so as to share a message Mi_k with each communication device belonging to the set R with the message Mi_k being concealed. That is, each communication device belonging to the set R can receive messages Mi_1, . . . , Mi_n, but each communication device which does not belong to the set R cannot receive the messages Mi_1, . . . , Mi_n.
Hereinafter, for the sake of simplification, an explanation will be given on the assumption that the set R={Ui_1, . . . , Ui_n}={U1, . . . , Un}. This does not lead to loss of generality.
In anonymous broadcast in one round (one unit of processing), the following three procedures are executed.
(1) Signature and Encryption
This procedure is executed separately in two cases: a case where the communication device Ui is included in the set R and a case where the communication device Ui is not included in the set R.
In Step S411, if Ui∈R, the cipher text generation unit 411 of the communication device Ui generates, from a master public key Σj=1, . . . , LSMPKj, a signature key Σj=1, . . . , Lski(j), and a message (IDi, Mi) (that is, a tuple of the identifier IDi of the communication device Ui, which is a source, and an original message Mi to be shared), a signature ωi←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lski(j), (IDi, Mi)) for the message (IDi, Mi) by the signature generation algorithm of the ID-based signature scheme. The cipher text generation unit 411 of the communication device Ui generates cipher text Ci←(Σj=1, . . . , LMPKj, (IDi, ωi, Mi), (R-{Ui})) from a master public key Σj=1, . . . , LMPKj, plaintext (IDi, ωi, Mi) (that is, a tuple of the identifier IDi of the communication device Ui, the signature ωi, and the original message Mi) and a set R-{Ui} of recipients by the encryption algorithm of the anonymous ID-based broadcast encryption scheme.
If Ui∈{U1, . . . , UN}-R, the cipher text generation unit 411 of the communication device Ui generates cipher text Ci which is a dummy message. For example, the dummy message Ci is the cipher text Ci obtained by encrypting an appropriate message Mi by the master public key Σi=1, . . . , LMPKj with φ, which means no recipient, being designated. By doing so, decryption of the cipher text in Step S415, which will be described later, fails without exception.
(2) Mix-Net
The communication device Ui∈{U1, . . . , UN} transmits the cipher text Ci generated in S411 to the mix-net server S1 using the transmitting and receiving unit 498. The mix-net servers S1, . . . , SM sequentially shuffle the cipher text (C1, . . . , CN) received by the mix-net server S1. The mix-net server SM posts the shuffled cipher text (˜C1, . . . , ˜CN) obtained by shuffling the cipher text (C1, . . . , CN), which is an output message, on a release bulletin board. Here, (C1, . . . , CN) and (˜C1, . . . , ˜CN) are equal as a set. That is, {˜C1, . . . , ˜CN}={C1, . . . , CN}. For instance, the mix-net server SM only has to upload the shuffled cipher text (˜C1, . . . , ˜CN) to the release server 200 to post the shuffled cipher text (˜C1, . . . , ˜CN). This allows the communication device Ui (1≤i≤N) to obtain the shuffled cipher text (˜C1, . . . , ˜CN).
(3) Downloading and Check
In Step S414, the cipher text obtaining unit 414 of the communication device Ui∈{U1, . . . , UN} obtains the cipher text {C1, . . . , CN} by downloading the shuffled cipher text (˜C1, . . . , ˜CN) from the bulletin board.
In Step S415, the message reconstruction unit 415 of the communication device Ui∈{U1, . . . , UN} generates plaintext (IDk, ωk, Mk)←(Σj=1, . . . , Ldki(j), Ck) from a decryption key Σj=1, . . . , Ldki(i) and cipher text Ck(1≤k≤N) by the decryption algorithm of the anonymous ID-based broadcast encryption scheme (only if Ui∈R-{Uk}). If the cipher text Ck is successfully decrypted, the message reconstruction unit 415 of the communication device Ui generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, Mk, ωk) from the master public key Σi=1, . . . , LSMPKj and a message (IDk, ωk, Mk) by the signature verifying algorithm of the ID-based signature scheme and verifies a signature ωk. If the signature ωk is successfully verified, the message reconstruction unit 415 of the communication device Ui regards a message Mk as a message transmitted from a communication device Uk with an identifier IDk. As a result, the communication device Ui∈R obtains messages M1, . . . , Mn (including the message Mi which the communication device Ui itself has transmitted). On the other hand, the communication device Ui∈{U1, . . . , UN}-R cannot obtain the messages M1, . . . , Mn.
As described above, the communication device Ui does not need to use a public key infrastructure because the communication device Ui encrypts the information on destinations (the set R-{Ui} of recipients) along with the original message by the encryption algorithm of the anonymous ID-based broadcast encryption scheme. This makes it possible to conceal the information on destinations, which is one of metadata. Moreover, since each communication device receives the cipher text via a mix-net and reconstructs the original message, it is possible to conceal the information on a source (the sender Ui), which is one of metadata. That is, a plurality of users can share messages with metadata being concealed.
<Session Key Generation>
A processing procedure of session key generation in the key exchange method of the embodiment will be described with reference to
A new session is started between the communication devices of the set R of communication devices={Ui_1, . . . , Ui_n} (where {i1, . . . , in}⊆{1, . . . , N}) and a session key is shared among the communication devices.
Hereinafter, for the sake of simplification, an explanation will be given on the assumption that the set R={Ui_1, . . . , Ui_n}={U1, . . . , Un} and a communication device Ui_1=U1 in the same fashion as described above. This does not lead to loss of generality.
A communication device U1 which desires to share the session key with each communication device belonging to the set R with the session key being concealed is referred to as a representative communication device. Moreover, communication devices of a set R-{U1} are referred to as general communication devices.
(1) Round 1: First Broadcast
This procedure is executed separately in two cases: a case where the communication device Ui is included in the set R and a case where the communication device Ui is not included in the set R.
In Step S421, if Ui∈R, the first key generation unit 421 of the communication device Ui generates ˜ri∈R{0, 1}κ, ˜r′i∈RFSκ, ˜ki∈R{0, 1}κ, ˜k′i∈RFSκ, ˜si∈R{0, 1}, and ˜s′i∈RFSκ and calculates ri=tPRF(˜ri, ˜r′i, sti, st′i), ki=tPRF(˜ki, ˜k′i, sti, st′i), and si=tPRF(˜si, ˜s′i, sti, st′i). Furthermore, the first key generation unit 421 of the communication device Ui calculates Ri=gr_i and ci=gk_ihs_i and generates a first key (Ri, ci).
If Ui∈{U1, . . . , UN}-R, the first key generation unit 421 of the communication device Ui randomly selects Ri, ci∈RG and generates a first key (Ri, ci).
In Step S410-1, if Ui∈R, the first anonymous broadcast unit 410-1 of the communication device Ui anonymously broadcasts the first key (Ri, ci) with the set R-{Ui} being designated.
If Ui∈{U1, . . . , UN}-R, the first anonymous broadcast unit 410-1 of the communication device Ui anonymously broadcasts the first key (Ri, ci) with φ, which means no recipient, being designated.
(2) Round 2: Second Broadcast
This procedure is executed separately in three cases: a case where the communication device Ui is included in the set R-{U1}, a case where the communication device Ui is U1, and a case where the communication device Ui is not included in the set R.
In Step S423, if Ui∈R-{U1}, when the communication device Ui receives a first key (Rk, ck) from each communication device Uk (1≤k≤n, k≠i) belonging to the set R-{Ui}, the second key generation unit 423 of the communication device Ui calculates sid=TCR(c1, . . . , cn). Here, sid is referred to as a session ID. Next, the second key generation unit 423 of the communication device Ui calculates Ki(l), Ki(r), and Ti by the following formulae and randomly selects T′i∈RZp2.
Ki(l)=F(sid,Ri−1r
Ki(r)=F(sid,Ri+1r
Ti=Ki(l)⊕Ki(r)
That is, Ti is the exclusive OR of Ki(l) and Ki(r).
The second key generation unit 423 of the communication device Ui generates, from the master public key Σ=j=1, . . . , LSMPKj, the signature key Σj=1, . . . , Lski(j), and a message (R, Ri, ci, ki, si, Ti, T′i) (that is, a tuple of the set R of recipients, Ri, ci, ki, and si generated in S421, and Ti and T′i just generated), a signature σi←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lski(j), (R, Ri, ci, ki, si, Ti, T′i)) for the message (R, Ri, ci, ki, si, Ti, T′i) by the signature generation algorithm of the ID-based signature scheme. The second key generation unit 423 of the communication device Ui generates (ki, si, Ti, T′i, σi) as a second key.
If Ui=U1, when the communication device U1 receives a first key (Rk, ck) from each communication device Uk (2≤k≤n) belonging to the set R-{U1}, the second key generation unit 423 of the communication device Ui calculates sid=TCR(c1, . . . , cn). Next, the second key generation unit 423 of the communication device Ui calculates K1(l), K1(r), T1, and T′ by the following formulae and randomly selects k″1, s″1∈RZp.
K1(l)=F(sid,Rnr
K1(r)=F(sid,R2r
T1=K1(l)⊕K1(r)
T′=K1(l)⊕(k1∥s1)
Here, ∥ is a concatenation operator.
The second key generation unit 423 of the communication device Ui generates, from the master public key Σj=1, . . . , LSMPKj, a signature key Σj=1, . . . , Lsk1(j), and a message (R, R1, c1, k″1, s″1, T1, T′) (that is, a tuple of the set R of recipients, R1 and c1 generated in S421, and k″1, s″1, T1, and T′ just generated), a signature σ1←(Σj=1, . . . , LSMPKj, Σj=1, . . . , Lsk1(j), (R, R1, c1, k″1, s″1, T1, T′)) for the message (R, R1, c1, k″1, s″1, T1, T′) by the signature generation algorithm of the ID-based signature scheme. The second key generation unit 423 of the communication device Ui generates (k″1, s″1, T1, T′, σ1) as a second key.
If Ui∈{U1, . . . , UN}-R, the second key generation unit 423 of the communication device Ui randomly selects ki, si∈RZp, Ti, T′i∈RZp2, and a signature σi which is an element of a signature space Σ. The second key generation unit 423 of the communication device Ui generates (ki, si, Ti, T′i, σi) as a second key.
In Step S410-2, if Ui∈R-{U1}, the second anonymous broadcast unit 410-2 of the communication device Ui anonymously broadcasts the second key (ki, si, Ti, T′i, σi) with the set R-{Ui} being designated.
If Ui=U1, the second anonymous broadcast unit 410-2 of the communication device Ui anonymously broadcasts the second key (k″1, s″1, T1, T′, σi) with the set R-{U1} being designated.
If Ui∈{U1, . . . , UN}-R, the second anonymous broadcast unit 410-2 of the communication device Ui anonymously broadcasts the second key (ki, si, Ti, T′i, σi) with φ, which means no recipient, being designated.
(3) Session Key Generation
This procedure is executed separately in three cases: a case where the communication device Ui is included in the set R-{U1}, a case where the communication device Ui is U1, and a case where the communication device Ui is not included in the set R.
It is to be noted that, if the communication device Ui is not included in the set R, the communication device Ui executes no processing. That is, the communication device Ui which is not included in the set R performs no processing.
In Step S427, if Ui∈R-{U1}, when the communication device Ui receives the second key (k″1, s″1, T1, T′, σ1) and a second key (kk, sk, Tk, T′k, σk) (2≤k≤n, k≠i) from each communication device Uk (1≤k≤n, k≠i) belonging to the set R-{Ui}, the session key generation unit 427 of the communication device Ui generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, (R, Rk, ck, kk, sk, Tk, T′k), σk) from the master public key Σj=1, . . . , LSMPKj, an identifier IDk, a message (R, Rk, ck, kk, sk, Tk, T′k) (that is, a tuple of the set R of recipients, Rk and ck received in S423, and kk, sk, Tk, and T′k received at the start of S427), and a signature σk received at the start of S427 by the signature verifying algorithm of the ID-based signature scheme and verifies the signature σk. If the signature σk is not successfully verified, the session key generation unit 427 of the communication device Ui stops the processing. The session key generation unit 427 of the communication device Ui calculates K1(l) and k1∥s1 by the following formulae and checks whether ck=gk_khs_k holds for k that satisfies 1≤k≤n.
K1(l)=Ki(l)⊕(⊕1≤j≤i−1Tj)
k1∥s1=T′⊕K1(l)
If ck=gk_khs_k does not hold for at least one of k that satisfies 1≤k≤n, the session key generation unit 427 of the communication device Ui stops the processing. The session key generation unit 427 of the communication device Ui calculates a session key SK by the following formula.
SK=F′(sid,⊕1≤i≤nki)
If Ui=U1, when the communication device U1 receives a second key (kk, sk, Tk, T′k, σk) from each communication device Uk (2≤k≤n) belonging to the set R-{U1}, the session key generation unit 427 of the communication device U1 generates a verification result Verk←(Σj=1, . . . , LSMPKj, IDk, (R, Rk, ck, kk, sk, Tk, T′k), σk) from the master public key Σj=1, . . . , LSMPKj, an identifier IDk, a message (R, Rk, ck, kk, sk, Tk, T′k) (that is, a tuple of the set R of recipients, Rk and ck received in S423, and kk, sk, Tk, and T′k received at the start of S427), and a signature σk received at the start of S427 by the signature verifying algorithm of the ID-based signature scheme and verifies the signature σk. If the signature σk is not successfully verified, the session key generation unit 427 of the communication device U1 stops the processing. Moreover, the session key generation unit 427 of the communication device U1 checks whether ck=gk_khs_k holds for k that satisfies 1≤k≤n. If ck=gk_khs_k does not hold for at least one of k that satisfies 1≤k≤n, the session key generation unit 427 of the communication device U1 stops the processing. The session key generation unit 427 of the communication device U1 generates a session key SK by the following formula.
SK=F′(sid,⊕1≤i≤nki)
If Ui∈{U1, . . . , UN}-R, as described earlier, the session key generation unit 427 of the communication device Ui does not generate a session key SK.
With the above-described configuration, a key exchange technique of this invention makes it possible for a plurality of communication devices to share a session key with metadata being concealed.
Anonymous broadcast establishes a concealed communication channel, by which messages can be exchanged at regular intervals, by using the mix-net. By implementing a key exchange by the session key generation procedure using this concealed communication channel, concealment of metadata is implemented. Furthermore, by performing communication using the shared session key, concealed communication is implemented. In this way, leak of metadata from a key exchange protocol can be prevented, which makes it possible to conceal the metadata completely.
The use of this key exchange protocol provides a global company and a company using satellite communications with a network such as The Onion Router (Tor) that makes a connection path in TCP/IP anonymous, for example, which makes it possible to ensure confidentiality including metadata in communication.
It goes without saying that this invention is not limited to the above embodiment but modifications may be made within the scope of this invention. Also, the various processes described in the embodiment may be executed not only in a chronological sequence in accordance with the order of their description but may be executed in parallel or separately according to the processing capability of the device executing the processing or any necessity.
[Program and Recording Medium]
When various types of processing functions in the devices described in the above embodiment are implemented on a computer, the contents of processing function to be contained in each device is written by a program. With this program executed on the computer, various types of processing functions in the above-described devices are implemented on the computer.
This program in which the contents of processing are written can be recorded in a computer-readable recording medium. The computer-readable recording medium may be any medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory.
Distribution of this program is implemented by sales, transfer, rental, and other transactions of a portable recording medium such as a DVD and a CD-ROM on which the program is recorded, for example. Furthermore, this program may be stored in a storage unit of a server computer and transferred from the server computer to other computers via a network so as to be distributed.
A computer which executes such program first stores the program recorded in a portable recording medium or transferred from a server computer once in a storage unit thereof, for example. When the processing is performed, the computer reads out the program stored in the storage unit thereof and performs processing in accordance with the program thus read out. As another execution form of this program, the computer may directly read out the program from a portable recording medium and perform processing in accordance with the program. Furthermore, each time the program is transferred to the computer from the server computer, the computer may sequentially perform processing in accordance with the received program. Alternatively, a configuration may be adopted in which the transfer of a program to the computer from the server computer is not performed and the above-described processing is executed by so-called application service provider (ASP)-type service by which the processing functions are implemented only by an instruction for execution thereof and result acquisition. It should be noted that a program in this form includes information which is provided for processing performed by electronic calculation equipment and which is equivalent to a program (such as data which is not a direct instruction to the computer but has a property specifying the processing performed by the computer).
In this form, the present device is configured with a predetermined program executed on a computer. However, the present device may be configured with at least part of these processing contents realized in a hardware manner.
The foregoing description of the embodiment of the invention has been presented for the purpose of illustration and description. It is not intended to be exhaustive and to limit the invention to the precise form disclosed. Modifications or variations are possible in light of the above teaching. The embodiment was chosen and described to provide the best illustration of the principles of the invention and its practical application, and to enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.
Number | Date | Country | Kind |
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2017-170072 | Sep 2017 | JP | national |
This application is a division of and claims the benefit of priority under 35 U.S.C. § 120 from U.S. application Ser. No. 16/641,716 filed Feb. 25, 2020, there entire contents of which are incorporated herein by reference. U.S. application Ser. No. 16/641,716 is a National Stage of PCT/JP2018/030281 filed Aug. 14, 2018, which claims the benefit for priority under 35 U.S.C. § 119 from Japan Application No. 2017-170072 filed Sep. 5, 2017.
Number | Date | Country |
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WO 2016016656 | Feb 2016 | WO |
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Number | Date | Country | |
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20220337428 A1 | Oct 2022 | US |
Number | Date | Country | |
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Parent | 16641716 | US | |
Child | 17852745 | US |