JP2010509876A - 暗黙の証明書検証 - Google Patents
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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
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
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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
- H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
- H04L9/0841—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols
- H04L9/0844—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols with user authentication or key authentication, e.g. ElGamal, MTI, MQV-Menezes-Qu-Vanstone protocol or Diffie-Hellman protocols using implicitly-certified keys
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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
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
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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
- H04L9/3247—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
- H04L9/3252—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 using DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr 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
- H04L9/3263—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 certificates, e.g. public key certificate [PKC] or attribute certificate [AC]; Public key infrastructure [PKI] arrangements
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
- G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
- G06F7/724—Finite field arithmetic
- G06F7/725—Finite field arithmetic over elliptic curves
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Abstract
Description
(本発明の概要)
公開鍵暗号法は、一対の通信者の間の安全な通信を可能にし、一対の通信者のうちの一方の通信者が発するメッセージの認証を可能にするために用いられる。公開鍵暗号法において各通信者は、数学的関数による秘密鍵に関連した秘密鍵および公開鍵を利用する。その数学的関数は、関係者の秘密鍵が対応する公開鍵から獲得され得ないことを保証するために「困難な」数学的問題を提供する。そのような問題は、RSA暗号システムにおいて用いられる2つの大きな素数の積を因数分解する困難さ、およびデジタル署名アルゴリズム(DSA)において用いられる有限体上の離散対数問題の難しさ(intractabiliy)を含む。離散対数システムは、広く用いられ、そのようなシステムの特定の適用は、有限体上に定義された楕円曲線の点を使用する。楕円曲線暗号システム(ECC)として参照されるそのようなシステムは、他のシステムよりも小さい鍵の大きさで高いレベルの安全性を提供する。
・鍵のコントリビューション(key contribution):各関係者は、任意の整数である秘密鍵と、かつ一時的な公開鍵を表す点を提供するためのシード点とから、任意の短期の(一時的な)公開鍵を生成し、対応する一時的な公開鍵(しかし、秘密鍵ではない)をもう一方の関係者に伝える。加えて、鍵のコントリビューションは、その長期の固定的な公開鍵を伝え得る。
・鍵の設定:各関係者は、他方の関係者から受け取った固定的および一時的な鍵に基づいて、および自身で生成した秘密鍵に基づいて、共有される鍵を計算する。楕円曲線の特性に起因して、両方の関係者は、同一の共有される鍵に到達する。
・鍵の認証:各関係者は、共通の鍵を計算する能力があり得る唯一の関係者が、本当に、その受け取られた通信する関係者である証拠を獲得するために、他方の関係者の長期の固定的な鍵の信頼性を検証する。
・鍵の確認:各関係者は、いずれかの関係者によって伝えられた鍵のコントリビューションに対応するストリング(string)を介して通例ではメッセージの認証チェック値を伝えることによって、他方の関係者に対し共通の鍵の所有を実証する。このことは、各関係者に対して他方の関係者の真の識別を確認し、その関係者が首尾よく共通の鍵を計算したことを証明する。このステップは、鍵の合意プロトコルの一部として、またはその後に、共有される鍵の使用を介して行われ得る。
1.任意の整数
4.e=H(m)を計算する。ここでHは、出力がnのビット長さを超えないビット長さを有する、暗号ハッシュ関数を示す(この条件が満たされない場合には、Hの出力は切り捨て(truncate)られ得る)。
5.s=k−1(e+αr)mod nを計算する。ここでαは、署名者の長期の秘密鍵である。s=0の場合には、ステップ1に戻る。
6.対(r,s)をメッセージmのECDSA署名として出力する。
1.rおよびsが区間[1,n−1]にある整数であることを検証する。すべての検証が失敗する場合には、拒絶が返される。
2.e=H(m)を計算する。
3.w=s−1 mod nを計算する。
4.u1=ew mod nおよびu2=rw mod nを計算する。
5.R=u1G+u2Q=s−1(eG+rQ)を計算する。(上記の3および4から)
6.R=∞の場合には、署名は、拒絶される。
7.Rのx座標x1を整数
したがって、図1を参照すると、暗号通信システムが、数字10によって一般的に示されている。システム10は、通信チャネル16を介して互いに通信し得る第一の通信者12および第二の通信者14を有する。通信チャネル16は、安全であり得るか、または、安全でないこともあり得る。各通信者は、選ばれた体上で定義される楕円曲線E上で機能する暗号化操作を実行するために、暗号モジュール18および暗号モジュール20をそれぞれ有する。暗号モジュール18は、以下に説明されるもののような暗号化操作を実行するように構成されるハードウェア、コンピューター読み取り可能なソフトウェア命令または両者の組み合わせであり得る。
KA=abG+λ1(sB −1(eBG+rBQB)−RB)
この式で、
λ1は、任意の値である。
rB、sBは、証明書TBの署名成分である。
eBは、証明書におけるメッセージmのハッシュである。証明書は、通信者14の公開鍵Bを含む。そして、
RBは、rBから復元される値である。
K=cX+dB
の形式である。
ここで、
c=x+ag(x)(mod n)かつ
d=cg(Y)(mod n)。
ここで、gは、楕円曲線の点を適切な整数に写像する公知の表現関数である。
KA=s12(Y+g(y)B)+λΣ=(x+ag(x))(Y+g(y)B)+(λ1eBsB −1)G+(λ1rBsB −1)Q+λ1RB
として、かつ、通信者14によって、
KB=s14(Y+g(x)A)+λΣ=(y+bg(y))(X+g(x)A)+(λ2eAsA −1)G+(λ2rAsA −1)QA+λ2RA
として、計算される。
Claims (13)
- 暗号システムを介して互いに通信する一対の通信者の間で共有されるべき暗号鍵を計算する方法であって、該一対の通信者のうちの一方の通信者は、該鍵を生成するために該一方の通信者の秘密鍵情報と組み合わされるべき他方の通信者の公開鍵情報の証明書を受け取り、該方法は、
該公開鍵情報と該秘密鍵情報とを組み合わせることによって該鍵を計算するステップと、
該証明書の検証に失敗した結果として、該一方の通信者での鍵が該他方の通信者で計算された鍵とは異なるように、該証明書の検証に対応する成分を該計算に含めるステップと
を含む、方法。 - 前記検証は、前記証明書に含まれる署名を利用する、請求項1に記載の方法。
- 前記成分は、前記証明書が検証するときにゼロに等しい、請求項2に記載の方法。
- 前記証明書の検証を隠すために、任意の要素が前記成分に含まれる、請求項3に記載の方法。
- 前記任意の要素は、前記署名の検証において繰り返される反復を提供することにより、側面チャネル攻撃を禁止するように選ばれる、請求項4に記載の方法。
- 前記暗号システムは、楕円曲線暗号システムである、請求項1に記載の方法。
- 前記計算は、重複点の倍増を用いて実行される、請求項6に記載の方法。
- 前記証明書は、楕円曲線署名プロトコルによって実行される署名を含む、請求項6に記載の方法。
- 前記署名プロトコルは、ECDSAである、請求項8に記載の方法。
- 前記公開鍵情報は、楕円曲線の点を表し、公開鍵情報と前記秘密鍵情報との組み合わせが点の倍増を含む、請求項6に記載の方法。
- 前記署名の検証は、重複点の倍増を要求する、請求項10に記載の方法。
- 前記計算は、重複点の倍増を用いて実行される、請求項11に記載の方法。
- 前記一方の通信者によって生成された鍵が前記他方の通信者の鍵と一致することを確認するステップを含む、請求項1に記載の方法。
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US86601306P | 2006-11-15 | 2006-11-15 | |
US60/866,013 | 2006-11-15 | ||
PCT/CA2007/002049 WO2008058388A1 (en) | 2006-11-15 | 2007-11-15 | Implicit certificate verification |
Related Child Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP2012247137A Division JP2013034251A (ja) | 2006-11-15 | 2012-11-09 | 暗黙の証明書検証 |
Publications (2)
Publication Number | Publication Date |
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JP2010509876A true JP2010509876A (ja) | 2010-03-25 |
JP5174828B2 JP5174828B2 (ja) | 2013-04-03 |
Family
ID=39401282
Family Applications (2)
Application Number | Title | Priority Date | Filing Date |
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JP2009536569A Active JP5174828B2 (ja) | 2006-11-15 | 2007-11-15 | 暗黙の証明書検証 |
JP2012247137A Withdrawn JP2013034251A (ja) | 2006-11-15 | 2012-11-09 | 暗黙の証明書検証 |
Family Applications After (1)
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JP2012247137A Withdrawn JP2013034251A (ja) | 2006-11-15 | 2012-11-09 | 暗黙の証明書検証 |
Country Status (7)
Country | Link |
---|---|
US (2) | US8069346B2 (ja) |
EP (1) | EP2082524B1 (ja) |
JP (2) | JP5174828B2 (ja) |
CN (1) | CN101641905B (ja) |
CA (1) | CA2669145C (ja) |
SG (1) | SG174833A1 (ja) |
WO (1) | WO2008058388A1 (ja) |
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CA2669145C (en) | 2013-11-05 |
US20120047363A1 (en) | 2012-02-23 |
JP5174828B2 (ja) | 2013-04-03 |
US20100023771A1 (en) | 2010-01-28 |
CN101641905A (zh) | 2010-02-03 |
SG174833A1 (en) | 2011-10-28 |
CN101641905B (zh) | 2012-09-05 |
CA2669145A1 (en) | 2008-05-22 |
EP2082524A4 (en) | 2010-08-18 |
US8380984B2 (en) | 2013-02-19 |
WO2008058388A1 (en) | 2008-05-22 |
EP2082524A1 (en) | 2009-07-29 |
US8069346B2 (en) | 2011-11-29 |
EP2082524B1 (en) | 2013-08-07 |
JP2013034251A (ja) | 2013-02-14 |
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