WO2021144974A1 - 秘密最大値計算装置、方法及びプログラム - Google Patents
秘密最大値計算装置、方法及びプログラム Download PDFInfo
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- 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
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
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- 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
- H04L9/3218—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 using proof of knowledge, e.g. Fiat-Shamir, GQ, Schnorr, ornon-interactive zero-knowledge proofs
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/46—Secure multiparty computation, e.g. millionaire problem
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- the present invention relates to a cryptographic application technique, and particularly to a method of calculating a maximum value and a flag of a maximum value without revealing an input or an output.
- Non-Patent Document 1 There is a method called secret calculation as a method of obtaining a specific calculation result without restoring the encrypted numerical value (see, for example, Non-Patent Document 1).
- the encryption is performed by distributing the numerical value fragments among the three secret computing devices, and the three secret computing devices perform the cooperative calculation, so that the numerical values are added or subtracted without being restored.
- the state where the results of constant addition, multiplication, constant multiplication, logical operation (negative, logical product, logical sum, exclusive logical sum), and data format conversion (integer, binary number) are distributed to three secret arithmetic units, that is, It can be kept encrypted.
- Non-Patent Document 2 When calculating the maximum value and maximum value flag of n values encrypted by secret calculation, keep the current maximum value and the number of the element that is the maximum value as a ciphertext, and n ciphertexts There is a method of performing comparison in order, updating the number of the maximum value and the element which is the maximum value, and finally calculating the flag from the number (see, for example, Non-Patent Document 2).
- the total number of comparisons when calculating the maximum value is ⁇ (n), but the number of comparison stages is as large as ⁇ (n).
- An object of the present invention is to provide a secret maximum value calculation device, method and program with reduced processing time.
- Initialization part to create one or more pairs so that none of the elements in X'from X'are included in two or more pairs, and one or more created pair creation parts.
- a determination unit that determines the concealed value of a large value with respect to the sequence R in [[x i ]], [[x j ]] contained in each of one or more pairs by secret calculation, and If there is a concealed value that is not included in one or more pairs of X', the concealed value that is not included in one or more pairs of X'and the concealed value determined by the determination unit are included. Control is performed so that the processing of the set update unit in which the set is a new X', the pair creation unit in which the new X'is X', the determination unit, and the set update unit is repeated until
- 1.
- the processing time can be reduced.
- FIG. 1 is a diagram showing an example of a functional configuration of a secret maximum value calculation device.
- FIG. 2 is a diagram showing an example of a processing procedure of the secret maximum value calculation method.
- FIG. 3 is a diagram showing an example of a functional configuration of a computer.
- a certain value a is called a secret value of a value a that is hidden by encryption or secret sharing, and is written as [[a]].
- [[a]] refers to the set of secret sharing fragments possessed by each secret computing unit.
- the selection operation is performed by inputting the secret value [[c]] of the boolean value c ⁇ ⁇ 0,1 ⁇ and the secret value [[a]], [[b]] of the two values a and b.
- the secret maximum value calculation device includes, for example, an initialization unit 1, a pair creation unit 2, a determination unit 3, a set update unit 4, a control unit 5, and a flag determination unit 6.
- the secret maximum value calculation method is realized, for example, by each component of the secret maximum value calculation device performing the processes of steps S1 to S6 described below and shown in FIG.
- X ⁇ [[x 1 ]], [[x 2 ]], ..., [[x n ]] ⁇ is input to the initialization unit 1.
- n is a predetermined positive integer of 2 or more. For example, n ⁇ 4.
- the initialized X' is output to the pair creation unit 2.
- ⁇ Pair creation unit 2> X'initialized by the initialization unit 1 is input to the pair creation unit 2. In the second and subsequent processes of the pair creation unit 2, X'updated by the set update unit 4 is input.
- the pair creation unit 2 creates one or more pairs from the input X'so that no element in X'is included in the two or more pairs (step S2).
- the created one or more pairs are output to the determination unit 3. If there is a secret value that is not included in one or more pairs of X', the secret value that is not included in one or more pairs of X'is output to the set update unit 4. NS.
- the pair creation unit 2 creates two or more pairs at least once.
- n ⁇ 4 this makes it possible to perform the calculation by comparing the number of stages n-2 or less.
- ⁇ Decision part 3> One or more pairs created by the pair creation unit 2 are input to the determination unit 3.
- the determination unit 3 For each of the created one or more pairs, the determination unit 3 has a large value with respect to the order R in [[x i ]], [[x j]] included in each of the one or more pairs.
- the secret value is determined by secret calculation (step S3).
- the determined large hidden value is output to the set update unit 4.
- ⁇ Set update unit 4> A large secret value determined by the determination unit 3 is input to the set update unit 4. If there is a secret value that is not included in one or more pairs of X', the secret value that is not included in one or more pairs of X'is input to the set update unit 4. NS.
- the set update unit 4 determines the secret value not included in one or more pairs of X'and the determination unit 3. Let the set including the concealed value be a new X'(step S4).
- Control unit 5 repeats the processes of the pair creation unit 2, the determination unit 3, and the set update unit 4 in which the new X'generated by the set update unit 4 is X'until
- 1. (Step S5).
- the flag determination unit 6 sets the concealed value, which is the only element of X'with
- the flag determination unit 6 sets the flag [[z (x i )]] by performing the following processes (a) and (b) on [x i] contained in X'even once. decide.
- the calculation of the flag [[z (x i )]] is performed in the reverse order of the calculation order of the pair creation unit 2, the determination unit 3, the set update unit 4, and the control unit 5.
- [[x k ]] is calculated by comparing [[x i ]] and [[x j ]], and [[z (x k )]] is already calculated.
- the larger of [[x i ]] and [[x j ]] was used.
- the maximum value was updated in order from the set of hidden values while holding the maximum value, so the number of comparison stages was ⁇ (n).
- the number of stages of comparison can be reduced by recursively calculating the maximum value while reducing the problem exponentially.
- the number of comparison stages is ⁇ (n) in the conventional method.
- the number of stages of comparison can be reduced while keeping the total number of comparisons ⁇ (n).
- data may be exchanged directly between the constituent units of the secret maximum value calculation device, or may be performed via a storage unit (not shown).
- the program that describes this processing content can be recorded on a computer-readable recording medium.
- the computer-readable recording medium may be, for example, a magnetic recording device, an optical disk, a photomagnetic recording medium, a semiconductor memory, or the like.
- the distribution of this program is carried out, for example, by selling, transferring, or renting a portable recording medium such as a DVD or CD-ROM on which the program is recorded.
- the program may be stored in the storage device of the server computer, and the program may be distributed by transferring the program from the server computer to another computer via a network.
- a computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. Then, when the process is executed, the computer reads the program stored in its own storage device and executes the process according to the read program. Further, as another execution form of this program, a computer may read the program directly from a portable recording medium and execute processing according to the program, and further, the program is transferred from the server computer to this computer. Each time, the processing according to the received program may be executed sequentially. In addition, the above processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition without transferring the program from the server computer to this computer. May be.
- the program in this embodiment includes information to be used for processing by a computer and equivalent to the program (data that is not a direct command to the computer but has a property of defining the processing of the computer, etc.).
- the present device is configured by executing a predetermined program on the computer, but at least a part of these processing contents may be realized by hardware.
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Abstract
Description
ある値aを暗号化や秘密分散などにより秘匿化した値aの秘匿値と呼び、[[a]]と書く。秘匿化が秘密分散である場合は,[[a]]により各秘密計算装置が持つ秘密分散の断片の集合を参照する。
aの秘匿値[[a]]を入力とし,c=aとなる値cを計算する処理を
c←Open([[a]])
と記述する。
加算、減算、乗算の各演算は2個の値a,bの秘匿値[[a]],[[b]]を入力とし、それぞれa+b,a-b,abの計算結果c1,c2,c3の秘匿値[[c1]],[[c2]],[[c3]]を計算する。これらの演算の実行をそれぞれ、
[[c1]]←Add([[a]],[[b]])
[[c2]]←Sub([[a]],[[b]])
[[c3]]←Mul([[a]],[[b]])
と記述する。誤解を招く恐れのない場合は、Add([[a]],[[b]]),Sub([[a]],[[b]]),Mul([[a]],[[b]])をそれぞれ[[a]]+[[b]],[[a]]-[[b]],[[a]]×[[b]]と略記する。
比較の演算は2個の値a,bの秘匿値[[a]],[[b]]を入力とし,a=b,a≦b,a<bの真偽値c∈{0,1}の秘匿値[[c1]],[[c2]],[[c3]]を計算する。真偽値は真のとき1、偽のとき0とする。この演算の実行を
[[c0]]←EQ([[a]],[[b]])
[[c1]]←LE([[a]],[[b]])
[[c2]]←LT([[a]],[[b]])
と記述する。
選択の演算は、真偽値c∈{0,1}の秘匿値[[c]]と2個の値a,bの秘匿値[[a]],[[b]]を入力とし、
[[d]]←IfElse([[c]],[[a]],[[b]])
と記述する。この演算は
[[d]]←[[c]]×([[a]]-[[b]])+[[b]]
により実現できる。
秘密最大値計算装置は、図1に示すように、初期化部1、ペア作成部2、決定部3、集合更新部4、制御部5及びフラグ決定部6を例えば備えている。
初期化部1には、X={[[x1]],[[x2]],...,[[xn]]}が入力される。nは、2以上の所定の正の整数である。例えば、n≧4である。
ペア作成部2には、初期化部1により初期化されたX′が入力される。なお、ペア作成部2の2回目以降の処理においては、集合更新部4により更新されたX′が入力される。
決定部3には、ペア作成部2により作成された1個以上のペアが入力される。
集合更新部4には、決定部3により決定された大きい値の秘匿値が入力される。また、X′のうち1個以上のペアに含まれなかった秘匿値がある場合には、X′のうち前記1個以上のペアに含まれなかった秘匿値が、集合更新部4に入力される。
制御部5は、集合更新部4により生成された新たなX′をX′とするペア作成部2、決定部3及び集合更新部4の処理を、|X′|=1になるまで繰り返すように制御する(ステップS5)。
フラグ決定部6には、|X′|=1となったX′が入力される。
以下、上記の秘密最大値計算装置及び方法により実現されるアルゴリズムの例について説明する。このアルゴリズムでは、ペアを作成する際に、└|X′|/2┘対のペアが作成される。なお、└|X′|/2┘は、|X′|/2以下の最大の整数である。このアルゴリズムにより、nに対して比較の段数が漸近的にO(log n)とすることができる。
出力:[[y]],[[z(x1)]],...,[[z(xn)]]
記法:[[y]],[[z(x1)]],...,[[z(xn)]]←f([[x1]],...,[[xn]])
(1) もしn=1であれば、[[y]]=[[x1]],[[z(x1)]]=[[1]]を返して終了。
(2) nが2の倍数であれば以下の(2-a)から(2-f)を実行。
(2-a) h←n/2
(2-b) [[fi]]←LE([[xi]],[[xi+h]])(i∈[1,h])
(2-c) [[mi]]←IfElse([[fi]],[[xi+h]],[[xi]])(i∈[1,h])
(2-d) [[y]],[[z(m1)]],...,[[z(mh)]]←f([[m1]],...,[[mh]])
(2-e) [[z(xi)]]←[[z(mi)]]×(1-[[fi]])(i∈[1,h])
(2-f) [[z(xi+h)]]←[[z(mi)]]×[[fi]](i∈[1,h])
(3) nが2の倍数でないならば以下を実行。
(3-a) h←(n-1)/2
(3-b) [[fi]]←LE([[xi]],[[xi+h]])(i∈[1,h])
(3-c) [[mi]]←IfElse([[fi]],[[xi+h]],[[xi]])(i∈[1,h])
(3-d) [[mh+1]]←[[xn]]
(3-e) [[y]],[[z(m1)]],...,[[z(mh)]],[[z(mh+1)]]←f([[m1]],...,[[mh+1]])
(3-f) [[z(xi)]]←[[z(mi)]]×(1-[[fi]])(i∈[1,h])
(3-g) [[z(xi+h)]]←[[z(mi)]]×[[fi]](i∈[1,h])
(3-h) [[z(xn)]]←[[z(mh+1)]]
(2-b),(2-c),(3-b),(3-c)で、[[xi]],[[xi+h]]のペアが用いられている。上記のアルゴリズムでは明記されていないが、このペアの作成がペア作成部2の処理に対応している。
以上、本発明の実施の形態について説明したが、具体的な構成は、これらの実施の形態に限られるものではなく、本発明の趣旨を逸脱しない範囲で適宜設計の変更等があっても、本発明に含まれることはいうまでもない。
上記説明した各装置における各種の処理機能をコンピュータによって実現する場合、各装置が有すべき機能の処理内容はプログラムによって記述される。そして、このプログラムをコンピュータで実行することにより、上記各装置における各種の処理機能がコンピュータ上で実現される。例えば、上述の各種の処理は、図3に示すコンピュータの記録部2020に、実行させるプログラムを読み込ませ、制御部2010、入力部2030、出力部2040などに動作させることで実施できる。
2 ペア作成部
3 決定部
4 集合更新部
5 制御部
6 フラグ決定部
Claims (3)
- X={[[x1]],[[x2]],...,[[xn]]}であるとして、X′=Xとする初期化部と、
X′の中からX′の中のどの要素も2個以上のペアに含まれないように1個以上のペアを作成するペア作成部と、
前記作成された1個以上のペアのそれぞれについて、前記1個以上のペアのそれぞれに含まれる[[xi]],[[xj]]の中の、順序Rに関して大きい値の秘匿値を秘密計算により決定する決定部と、
X′のうち前記1個以上のペアに含まれなかった秘匿値がある場合には、前記X′のうち前記1個以上のペアに含まれなかった秘匿値と前記決定部で決定された秘匿値とを含む集合を新たなX′とする集合更新部と、
前記新たなX′をX′とする前記ペア作成部、前記決定部及び前記集合更新部の処理を、|X′|=1になるまで繰り返すように制御する制御部と、
|X′|=1であるX′の唯一の要素である秘匿値を最大値として、[[xg]](g∈[1,n])が最大値であるときは[[z(xg)]]=[[1]]であり、i≠gであるときは[[z(xi)]]=[[0]]であるようにフラグ[[z(xi)]](i=1,…,n)を決定するフラグ決定部と、
を含む秘密最大値計算装置。 - 初期化部が、X={[[x1]],[[x2]],...,[[xn]]}であるとして、X′=Xとする初期化ステップと、
ペア作成部が、X′の中からX′の中のどの要素も2個以上のペアに含まれないように1個以上のペアを作成するペア作成ステップと、
決定部が、前記作成された1個以上のペアのそれぞれについて、前記1個以上のペアのそれぞれに含まれる[[xi]],[[xj]]の中の、順序Rに関して大きい値の秘匿値を秘密計算により決定する決定ステップと、
集合更新部が、X′のうち前記1個以上のペアに含まれなかった秘匿値がある場合には、前記X′のうち前記1個以上のペアに含まれなかった秘匿値と前記決定部で決定された秘匿値とを含む集合を新たなX′とする集合更新ステップと、
制御部が、前記新たなX′をX′とする前記ペア作成部、前記決定部及び前記集合更新部の処理を、|X′|=1になるまで繰り返すように制御する制御ステップと、
フラグ決定部が、|X′|=1であるX′の唯一の要素である秘匿値を最大値として、[[xg]](g∈[1,n])が最大値であるときは[[z(xg)]]=[[1]]であり、i≠gであるときは[[z(xi)]]=[[0]]であるようにフラグ[[z(xi)]](i=1,…,n)を決定するフラグ決定ステップと、
を含む秘密最大値計算方法。 - 請求項1の秘密最大値計算装置の各部としてコンピュータを機能させるためのプログラム。
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See also references of EP4092654A4 |
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AU2020422786A1 (en) | 2022-07-14 |
US20230029772A1 (en) | 2023-02-02 |
CN114930431A (zh) | 2022-08-19 |
JP7322976B2 (ja) | 2023-08-08 |
EP4092654A1 (en) | 2022-11-23 |
EP4092654A4 (en) | 2023-10-11 |
JPWO2021144974A1 (ja) | 2021-07-22 |
AU2020422786B2 (en) | 2023-04-27 |
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