JPH0621939A - User confirming system - Google Patents
User confirming systemInfo
- Publication number
- JPH0621939A JPH0621939A JP2409817A JP40981790A JPH0621939A JP H0621939 A JPH0621939 A JP H0621939A JP 2409817 A JP2409817 A JP 2409817A JP 40981790 A JP40981790 A JP 40981790A JP H0621939 A JPH0621939 A JP H0621939A
- Authority
- JP
- Japan
- Prior art keywords
- person
- random number
- authenticated
- key
- public
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Abstract
Description
【0001】[0001]
【産業上の利用分野】本発明は、送信者の身元を確認す
る方式に関し、特に、安全性が高く、かつ、通信量を削
減可能な、効率の良い利用者認証方式に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of confirming the identity of a sender, and more particularly to an efficient user authentication method which is highly secure and can reduce the amount of communication.
【0002】[0002]
【従来の技術】従来、提案されている方式としては、F
iatとShamirの方式がある。これは、以下の如きもので
ある。2. Description of the Related Art Conventionally, the proposed method is F
There are iat and Shamir methods. This is as follows.
【外1】 上記(mod N)における平方根の計算は、Nの素因数(P
とQ)が分かっているときのみ実行できる。その方法
は、例えば、Rabin M.O.により“DigitalizedSign
aturesand Public-key Functions as Intractable a
s Factorization"(Tech.Rep.MIT/LCS/TR-21
2 MIT Lab.Comput.Sci.1979)に示されている。
また、平方根の計算装置の具体的な構成例は、本出願人
による特許出願「公開鍵暗号システム」(特願昭61-169350
号 明細書参照)に示されている。送信者Aは、認証者B
に対して、Aが本物であることを次の手順で証明する。[Outer 1] Calculation of the square root in the above (mod N) is performed by calculating the prime factor (P
And Q) are known. The method is described, for example, by Rabin MO in "Digitalized Sign".
aturesand Public-key Functions as Intractable a
s Factorization "(Tech.Rep.MIT/LCS/TR-21
2 MIT Lab. Computer. Sci. 1979).
A concrete configuration example of the square root calculation device is described in the patent application “Public Key Cryptography System” by the applicant (Japanese Patent Application No. 61-169350).
No.). Sender A is authenticator B
On the other hand, the following procedure proves that A is genuine.
【外2】 上述の方式の詳細については、Fiat A. and Shamir
A:“How to proveyourself:Practical solution t
o identification and signature problems",Proceedi
ngs of Crypto 86,Santa Barbara,Aug.1986,pp.
18-1-18-7に記述されている。この方式については、計
算量理論的な手法で、安全性が証明されている。つま
り、この方式は、零知識証明となることが、前述のFia
tとShamirの論文で証明されている。利用者認証方式が
零知識証明であるならば、如何なる不正行為も困難であ
るが、計算量理論的観点から保証される。[Outside 2] For details of the above method, see Fiat A. and Shamir.
A: “How to proveyourself: Practical solution t
o identification and signature problems ", Proceedi
ngs of Crypto 86, Santa Barbara, Aug. 1986, pp.
It is described in 18-1-18-7. This method has been proved to be safe by a computational theory method. In other words, this method is a zero-knowledge proof.
Proven in the paper by T and Shamir. If the user authentication method is zero-knowledge proof, any fraudulent activity is difficult, but it is guaranteed from the viewpoint of computational complexity theory.
【0003】[0003]
【発明が解決しようとする課題】しかし、FiatとSham
irの方式では、通信文のビット数は(1000×t+k×t)
ビットであり、安全性を確保するにはある程度の大きさ
のkとtを選ぶ必要があるので、通信量が大きくなり、
転送情報量が大きいことが問題である。本発明は上記事
情に鑑みてなされたもので、その目的とするところは、
従来の技術における上述の如き問題を解消し、転送情報
量を少なくすることが可能な利用者認証方式を提供する
ことにある。[Problems to be Solved by the Invention] However, Fiat and Sham
In the ir method, the number of bits of the message is (1000 × t + k × t)
Since it is a bit and it is necessary to select k and t of a certain size to secure security, the amount of communication increases,
The problem is that the amount of transferred information is large. The present invention has been made in view of the above circumstances, and its object is to:
It is an object of the present invention to provide a user authentication method capable of solving the above-mentioned problems in the conventional technique and reducing the amount of transferred information.
【0004】[0004]
【課題を解決するための手段】本発明の上記目的は、利
用者の正当性を確認するための利用者認証を実現するシ
ステムであって、以下の各項を含むことを特徴とする利
用者認証方式によって達成される。 (1)システム加入時に利用者が一度だけ行う初期情報設
定段階において、 (a)システムに加入した前記利用者(被認証者)は、ディ
ジタル署名の公開鍵および秘密鍵を生成し、秘密鍵を秘
密に保持し、公開鍵を公開情報として被認証者の識別情
報(ID)と対にして、公開鍵管理簿もしくは認証者の管
理簿に登録する。 (2)初期情報設定段階以降の認証処理段階において、 (a)最初に、被認証者は自分のIDを認証者に送信す
る。 (b)前記IDを受信した認証者は、IDに基づいて前記
管理簿から公開鍵を検索した後、乱数Rを生成し、それ
を被認証者に送付する。 (c)前記乱数Rを受信した被認証者は、乱数Uを生成し
た後、公開の一方向性関数Fを用いて、M=F(R,U)
を計算し、Mに対するディジタル署名Sを被認証者の秘
密鍵を用いて生成し、S,Uを認証者に送信する。 (d)前記S,Uを受信した認証者は、前記公開の一方向
性関数Fを用いてM=F(R,U)を計算し、Mと前記デ
ィジタル署名Sの正当性を、被認証者の公開鍵を用いて
検証し、その検証に合格すれば被認証者の正当性を確認
する。The above-mentioned object of the present invention is a system for realizing user authentication for confirming the legitimacy of a user, characterized by including the following items: It is achieved by the authentication method. (1) In the initial information setting step that the user performs only once when joining the system, (a) the user (authenticatee) who has joined the system generates a public key and a secret key of a digital signature, and stores the secret key. It is kept secret, and the public key is paired with the identification information (ID) of the person to be authenticated as public information and registered in the public key management list or the certifier management list. (2) In the authentication processing stage after the initial information setting stage, (a) First, the person to be authenticated transmits his / her own ID to the authenticator. (b) The authenticator receiving the ID generates a random number R after searching the public key in the management list based on the ID, and sends the random number R to the authenticated person. (c) The authenticated person who receives the random number R generates a random number U and then uses the public one-way function F to obtain M = F (R, U).
Is calculated, a digital signature S for M is generated using the private key of the authenticatee, and S and U are transmitted to the certifier. (d) The authenticator receiving S and U calculates M = F (R, U) using the public one-way function F, and verifies the authenticity of M and the digital signature S as the authenticated Verification is performed using the public key of the authentication person, and if the verification is passed, the authenticity of the authenticated person is confirmed.
【0005】[0005]
【作用】前述のFiatとShamirの方式では、認証処理に
おいて、Yes/No(1ビット)の質問応答を繰り返した形
を基本に構成しているため、通信量が多くなるのに対し
て、本発明に係る利用者認証方式においては、数100ビ
ットの質問応答を 1回だけ行う形を基本に構成してい
るため、通信量を削減することができる。なお、前述の
FiatとShamirの方式がべき乗演算に限定された方式で
あるのに対して、本発明に係る方式は任意のディジタル
署名方式を基本として構成することができる点も有利な
点である。In the above-mentioned Fiat and Shamir method, since the authentication process is basically configured by repeating Yes / No (1 bit) question and answer, the communication amount increases, whereas Since the user authentication method according to the invention is basically configured to perform a query response of several 100 bits only once, it is possible to reduce the communication amount. It should be noted that, while the above-mentioned Fiat and Shamir method is a method limited to exponentiation, the method according to the present invention is also advantageous in that it can be configured based on an arbitrary digital signature method. .
【0006】[0006]
【実施例】以下、本発明の実施例を図面に基づいて詳細
に説明する。図2は、本発明の一実施例の全体構成を示
すブロック図である。図中、100は認証を受ける利用
者(または局)、200は認証を行う認証者(または局)を
示しており、これらが、安全でない通信路300を介し
て結合されているとする。まず、システムに加入した局
100は、システム加入時に、局が基本的に一度だけ行
う初期情報設定段階において、以下に示す手順で、公開
鍵と秘密鍵を生成し、公開鍵を、認証を受ける利用者の
識別情報(ID)と対にして、公開鍵管理簿もしくは認証
者200に登録する。図3は、図2におけるシステムに
加入した局100の初期情報設定段階の処理を示すブロ
ック図である。ここでは、処理に用いるディジタル署名
アルゴリズムを定め、暗号鍵生成器120を用いて、公
開鍵Aと秘密鍵Bを生成する。なお、後述する署名作成
器が用いる署名作成関数GB,署名検証器が用いる署名
検証関数VA,更に、一方向性関数演算器140が用い
る一方向性関数Fを定める。また、上で定めたもののう
ち、公開鍵Aと一方向性関数Fとを公開情報とし、秘密
鍵Bを秘密情報とする。なお、ディジタル署名方式とし
ては、本発明者による方式(“A Fast Signature Sc
heme Based on Congruetial PolynominalOperation
s”IEEE Transactions on Information Theory,
vol.36,No.1,pp.47-53,1990参照)等がある。上述の一
方向性関数とは、F(x)の計算は容易であるが、F(x)
からxを求めるのが困難な関数である。一方向性関数F
は、高速の慣用暗号化装置、例えば、DES暗号(例え
ば、Data Encryption Standard Federal Informat
ionProcessing Standards Publication 46,1977参
照),FEAL暗号(例えば、宮口等著「FEAL暗号の
拡張」,NTT R&D,vol.39,No.10,pp.1439-145
0,1990参照)およびハッシュ関数(例えば、宮口等著「1
28ビットハッシュ関数“N-Hash"」,NTT R&D,
vol.39,No.10,pp.1451-1458,1990参照)等を用いて構
成できる。この場合、F(x)の計算時間は殆んど無視で
きる。Embodiments of the present invention will now be described in detail with reference to the drawings. FIG. 2 is a block diagram showing the overall configuration of an embodiment of the present invention. In the figure, reference numeral 100 denotes a user (or station) to be authenticated, and 200 denotes an authenticator (or station) to perform authentication, and these are assumed to be coupled via an insecure communication path 300. First, the station 100 that has joined the system generates a public key and a private key and authenticates the public key according to the following procedure in the initial information setting stage that the station basically performs only once when joining the system. It is registered in the public key management book or the authenticator 200 in pairs with the user's identification information (ID). FIG. 3 is a block diagram showing the processing of the initial information setting stage of the station 100 that has joined the system in FIG. Here, the digital signature algorithm used for the process is determined, and the public key A and the secret key B are generated using the encryption key generator 120. A signature creation function GB used by the signature creation device, a signature verification function VA used by the signature verification device, and a one-way function F used by the one-way function calculator 140 are defined. In addition, among those defined above, the public key A and the one-way function F are the public information, and the secret key B is the secret information. As a digital signature method, a method ("A Fast Signature Sc
heme Based on Congruetial Polynominal Operation
s "IEEE Transactions on Information Theory,
vol.36, No.1, pp.47-53, 1990). With the above-mentioned one-way function, F (x) is easy to calculate, but F (x)
Is a function that is difficult to obtain from x. One-way function F
Is a high-speed conventional encryption device, for example, DES encryption (for example, Data Encryption Standard Federal Format).
ionProgressing Standards Publication 46, 1977), FEAL encryption (for example, Miyaguchi et al., "Extending FEAL encryption", NTT R & D, vol.39, No.10, pp.1439-145).
0, 1990) and hash functions (see, for example, Miyaguchi et al. “1.
28-bit hash function "N-Hash"", NTT R & D,
vol.39, No.10, pp.1451-1458, 1990) and the like. In this case, the calculation time of F (x) can be almost ignored.
【0007】次に、局100が局200に対して、自分
の正当性を証明する利用者認証手順について説明する。
以下の説明では、局100を被認証者、局200を認証
者と呼ぶことにする。もちろん、局200が被認証者、
局100が認証者として動作することも可能である。以
下、図4,図1(a)および(b)に基づいて、認証手順を
説明する。なお、図4は、被認証者と認証者の通信文の
交信の様子を示す図、図1(a)および同(b)は、図4に
示した交信に係る被認証者100および認証者200の
利用者認証処理を示すブロック図である。利用者認証手
順は、以下の通りである。 ステップ1:被認証者100は、自分のIDを認証者2
00に送信する。 ステップ2:認証者200は、受信したIDに基づき管
理簿270から前述の公開鍵Aを検索した後、乱数発生
器210を用いて乱数Rを生成して、これを被認証者1
00に送信する。 ステップ3:被認証者100は、乱数発生器110を用
いて乱数Uを生成し、更に、一方向性関数演算器140
により、受信した乱数Rと上述の乱数Uとから、前述の
一方向性関数Fを用いてM=F(R,U)を計算した後、
秘密鍵Bをメモリ150から取り出し、これを用いて、
署名作成器180により、前述の署名作成関数GBを用
いて、S=GB(M)を計算し、SとUを認証者200に
送信する。 ステップ4:認証者200は、一方向性関数演算器24
0により、前述の乱数Rと受信した乱数Uとから、一方
向性関数Fを用いてM=F(R,U)を計算し、MとSと
ステップ4で検索した公開鍵Aを署名検証器290に入
力し、前述の署名検証関数VA(M,S)=0を満足する
か否かを検査する。署名検証器290は、VA(M,S)
=0を満足する場合「合格」を、そうでなければ、「不合
格」を出力する。 なお、上述のステップ1でのIDの送信は、ステップ3
で行っても良く、ステップ2における公開鍵Aの検索
は、ステップ4で行っても良い。Next, a user authentication procedure in which the station 100 proves its validity to the station 200 will be described.
In the following description, the station 100 will be referred to as a person to be authenticated and the station 200 will be referred to as an authenticator. Of course, the station 200 is the authenticated person,
It is also possible for station 100 to act as an authenticator. The authentication procedure will be described below with reference to FIGS. 4, 1A and 1B. Note that FIG. 4 is a diagram showing a state of communication between a person to be authenticated and a communication text of the person to be authenticated, and FIGS. 1A and 1B show a person to be authenticated 100 and an authenticator involved in the communication shown in FIG. 3 is a block diagram showing a user authentication process of 200. FIG. The user authentication procedure is as follows. Step 1: The authenticated person 100 inputs his own ID to the authenticator 2.
To 00. Step 2: The authenticator 200 searches the management book 270 for the public key A based on the received ID, then generates a random number R using the random number generator 210, and generates this random number R as the authenticated person 1
To 00. Step 3: The authenticated person 100 generates a random number U using the random number generator 110, and further, the one-way function calculator 140
After calculating M = F (R, U) from the received random number R and the above-described random number U using the one-way function F described above,
The private key B is taken out from the memory 150, and using this,
The signature creator 180 calculates S = GB (M) using the signature creation function GB described above, and sends S and U to the authenticator 200. Step 4: The authenticator 200 uses the one-way function calculator 24.
From 0, the one-way function F is used to calculate M = F (R, U) from the above-mentioned random number R and the received random number U, and the public key A retrieved in step S and M and S is subjected to signature verification. It is input to the device 290, and it is checked whether the signature verification function VA (M, S) = 0 described above is satisfied. The signature verifier 290 is VA (M, S)
If = 0 is satisfied, "pass" is output, and if not, "fail" is output. In addition, the transmission of the ID in the above step 1 is performed in the step 3
Alternatively, the search for the public key A in step 2 may be performed in step 4.
【0008】上記実施例によれば、以下に説明する如
く、安全性および通信量削減の効果が得られる。すなわ
ち、 (1)安全性について: 完全性:正当な被認証者(Bを知っている)は、確率1で
合格する。 健全性:不正な被認証者(Bを知らない)は、任意の情報
Mに対して正しい署名を作成することが困難であるた
め、合格する確率は無視できるくらい低い。 機密性:認証者がどのようなRを選択・転送しても、正
しい被認証者がUをランダムに選べば、Mの値はランダ
ムに分布するため、特定の値に対する署名を認証者が得
ることはできず、認証者が被認証者の秘密情報に関する
有効な情報を得ることはできない。 (2)通信量について:According to the above-described embodiment, as will be described below, the effects of safety and reduction of communication amount can be obtained. That is, (1) Security: Completeness: A legitimate subject (who knows B) passes with probability 1. Soundness: An unauthorized subject (not knowing B) has a negligible probability of passing because it is difficult to create a correct signature for arbitrary information M. Confidentiality: No matter what R is selected and transferred by the certifier, if the correct subject randomly selects U, the value of M will be randomly distributed, so the certifier will get a signature for a specific value. The certifier cannot obtain valid information regarding the confidential information of the authenticatee. (2) Regarding communication volume:
【外3】 通信文のビット数を、Nが512ビットでk=4,t=
5(前述の論文中の推奨値)の場合で比較すると、 FiatとShamirの方式:5120+20+IDのビット
数 本実施例の場合:712+IDのビット数 となり、本実施例の場合、通信量は、前述のFiatとSh
amirの方式の場合の約1/7で済むことになる。これは
顕著な効果ということができる。なお、上記実施例は本
発明の一例を示すものであり、本発明はこれに限定され
るべきものではないことは言うまでもない。[Outside 3] The number of bits of the communication text is k = 4, t = when N is 512 bits
Comparing in the case of 5 (recommended value in the above-mentioned paper), the method of Fiat and Shamir: 5120 + 20 + ID bit number In this embodiment: 712 + ID bit number. In this embodiment, the communication amount is Fiat and Sh
It will be about 1/7 of the case of the amir method. This can be said to be a remarkable effect. It is needless to say that the above embodiment is an example of the present invention and the present invention should not be limited to this.
【0009】[0009]
【発明の効果】以上、詳細に説明した如く、本発明によ
れば、安全性を確保しながら、転送情報量を少なくする
ことが可能な利用者認証方式を実現できるという顕著な
効果を奏するものである。As described above in detail, according to the present invention, a remarkable effect that a user authentication method capable of reducing the amount of transferred information while ensuring security can be realized can be achieved. Is.
【0010】[0010]
【図1】本発明の一実施例における被認証者および認証
者の利用者認証処理を示すブロック図である。FIG. 1 is a block diagram showing user authentication processing of a person to be authenticated and an authenticator in an embodiment of the present invention.
【図2】実施例の全体構成を示すブロック図である。FIG. 2 is a block diagram showing the overall configuration of the embodiment.
【図3】システムに加入した局の初期情報設定段階の処
理を示すブロック図である。FIG. 3 is a block diagram showing a process of an initial information setting stage of a station that has joined the system.
【図4】被認証者と認証者の通信文の交信の様子を示す
図である。FIG. 4 is a diagram showing how communication is performed between the authenticated person and the authenticator.
100:被認証局、200:認証局、300:通信路、
110,210:乱数発生器、120:暗号鍵生成器、
140,240:一方向性関数演算器、150:メモ
リ、180:署名作成器、270:(公開)管理簿、29
0:署名検証器。100: authenticated station, 200: certificate authority, 300: communication path,
110, 210: random number generator, 120: encryption key generator,
140, 240: one-way function calculator, 150: memory, 180: signature generator, 270: (public) management book, 29
0: Signature verifier.
【手続補正書】[Procedure amendment]
【提出日】平成5年8月9日[Submission date] August 9, 1993
【手続補正1】[Procedure Amendment 1]
【補正対象書類名】図面[Document name to be corrected] Drawing
【補正対象項目名】全図[Correction target item name] All drawings
【補正方法】変更[Correction method] Change
【補正内容】[Correction content]
【図1】 [Figure 1]
【図2】 [Fig. 2]
【図4】 [Figure 4]
【図3】 [Figure 3]
Claims (1)
認証を実現するシステムであって、以下の各項を含むこ
とを特徴とする利用者認証方式。 (1)システム加入時に利用者が一度だけ行う初期情報設
定段階において、 (a)システムに加入した前記利用者(被認証者)は、ディ
ジタル署名の公開鍵および秘密鍵を生成し、秘密鍵を秘
密に保持し、公開鍵を公開情報として被認証者の識別情
報(ID)と対にして、公開鍵管理簿もしくは認証者の管
理簿に登録する。 (2)初期情報設定段階以降の認証処理段階において、 (a)最初に、被認証者は自分のIDを認証者に送信す
る。 (b)前記IDを受信した認証者は、IDに基づいて前記
管理簿から公開鍵を検索した後、乱数Rを生成し、それ
を被認証者に送付する。 (c)前記乱数Rを受信した被認証者は、乱数Uを生成し
た後、公開の一方向性関数Fを用いて、M=F(R,U)
を計算し、Mに対するディジタル署名Sを被認証者の秘
密鍵を用いて生成し、S,Uを認証者に送信する。 (d)前記S,Uを受信した認証者は、前記公開の一方向
性関数Fを用いてM=F(R,U)を計算し、Mと前記デ
ィジタル署名Sの正当性を、被認証者の公開鍵を用いて
検証し、その検証に合格すれば被認証者の正当性を確認
する。1. A system for realizing user authentication for confirming the legitimacy of a user, which includes the following items: (1) In the initial information setting step that the user performs only once when joining the system, (a) the user (authenticatee) who has joined the system generates a public key and a secret key of a digital signature, and stores the secret key. It is kept secret, and the public key is paired with the identification information (ID) of the person to be authenticated as public information and registered in the public key management list or the certifier management list. (2) In the authentication processing stage after the initial information setting stage, (a) First, the person to be authenticated transmits his / her own ID to the authenticator. (b) The authenticator receiving the ID generates a random number R after searching the public key in the management list based on the ID, and sends the random number R to the authenticated person. (c) The authenticated person who receives the random number R generates a random number U and then uses the public one-way function F to obtain M = F (R, U).
Is calculated, a digital signature S for M is generated using the private key of the authenticatee, and S and U are transmitted to the certifier. (d) The authenticator receiving S and U calculates M = F (R, U) using the public one-way function F, and verifies the authenticity of M and the digital signature S as the authenticated Verification is performed using the public key of the authentication person, and if the verification is passed, the authenticity of the authenticated person is confirmed.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2409817A JP2513170B2 (en) | 1990-12-10 | 1990-12-10 | User authentication method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2409817A JP2513170B2 (en) | 1990-12-10 | 1990-12-10 | User authentication method |
Publications (2)
Publication Number | Publication Date |
---|---|
JPH0621939A true JPH0621939A (en) | 1994-01-28 |
JP2513170B2 JP2513170B2 (en) | 1996-07-03 |
Family
ID=18519095
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP2409817A Expired - Lifetime JP2513170B2 (en) | 1990-12-10 | 1990-12-10 | User authentication method |
Country Status (1)
Country | Link |
---|---|
JP (1) | JP2513170B2 (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2013031151A (en) * | 2011-06-20 | 2013-02-07 | Renesas Electronics Corp | Encryption communication system and encryption communication method |
US10389913B2 (en) | 2017-03-29 | 2019-08-20 | Fuji Xerox Co., Ltd. | Information management control apparatus, image processing apparatus, and information management control system |
US11370220B2 (en) | 2020-03-23 | 2022-06-28 | Ricoh Company, Ltd. | Liquid discharge apparatus |
-
1990
- 1990-12-10 JP JP2409817A patent/JP2513170B2/en not_active Expired - Lifetime
Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2013031151A (en) * | 2011-06-20 | 2013-02-07 | Renesas Electronics Corp | Encryption communication system and encryption communication method |
US9363082B2 (en) | 2011-06-20 | 2016-06-07 | Renesas Electronics Corporation | Cryptographic communication system and cryptographic communication method |
US9608818B2 (en) | 2011-06-20 | 2017-03-28 | Renesas Electronics Corporation | Cryptographic communication system and cryptographic communication method |
US10469256B2 (en) | 2011-06-20 | 2019-11-05 | Renesas Electronics Corporation | Cryptographic communication system and cryptographic communication method |
US10389913B2 (en) | 2017-03-29 | 2019-08-20 | Fuji Xerox Co., Ltd. | Information management control apparatus, image processing apparatus, and information management control system |
US11370220B2 (en) | 2020-03-23 | 2022-06-28 | Ricoh Company, Ltd. | Liquid discharge apparatus |
Also Published As
Publication number | Publication date |
---|---|
JP2513170B2 (en) | 1996-07-03 |
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