Curve25519
外觀
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在密碼學中,Curve25519是一種橢圓曲線,被設計用於橢圓曲線迪菲-赫爾曼(ECDH)金鑰交換方法,可用作提供256位元的安全金鑰。它是不被任何已知專利覆蓋的最快ECC曲線之一。[1][2]
最初的Curve25519草稿將其定義成一個迪菲-赫爾曼(DH)函數。在那之後Daniel J. Bernstein提出Curve25519應被作為底層曲線的名稱,而將X25519作為其DH函數的名稱。[3]
數學屬性
[編輯]所用的曲線是y2 = x3 + 486662x2 + x,蒙哥馬利曲線,在由質數2255 − 19定義的質數場的二次擴展上,並且使用基點x = 9。這個基點的階數是[4].
該協定使用壓縮橢圓點(僅X座標),因此它允許在ECDH中高效地使用Montgomery梯子,僅使用XZ座標。[5]
Curve25519的構造使其避免了許多潛在的實現缺陷。[6] 根據設計,它不受定時攻擊的影響,並且它接受任何32位元組的字串作為有效的公鑰,並且不需要驗證。
該曲線在雙有理幾何上等同於Ed25519簽名方案中使用的扭曲Edwards曲線。[7]
普及
[編輯]庫
[編輯]協定
[編輯]- OMEMO, 一個對XMPP (Jabber)的建議性擴充[22]
- Secure Shell
- Signal Protocol
- Tox
- Zcash
- TLS
應用
[編輯]- Conversations Android application[b]
- Cryptocat[23][b]
- DNSCrypt[24]
- DNSCurve
- Dropbear[9][25]
- Facebook Messenger [c][d]
- Gajim via plugin[26][b]
- GNUnet[27]
- GnuPG
- Google Allo[e][d]
- I2P[28]
- IPFS[29]
- iOS[30]
- Monero[31]
- OpenBSD[f]
- OpenSSH[9][g]
- Peerio[36]
- PuTTY[37]
- Signal[d]
- Silent Phone
- SmartFTP[9]
- SSHJ[9]
- Threema Instant Messenger[38]
- TinySSH[9]
- TinyTERM[9]
- Tor[39]
- Viber[40]
- WhatsApp[d]
- Wire
- WireGuard
註腳
[編輯]- ^ 從Windows 10 (1607)及Windows Server 2016開始使用。
- ^ 2.0 2.1 2.2 Via the OMEMO protocol
- ^ Only in "secret conversations"
- ^ 4.0 4.1 4.2 4.3 Via the Signal Protocol
- ^ Only in "incognito mode"
- ^ Used to sign releases and packages[32][33]
- ^ Exclusive key exchange in OpenSSH 6.7 when compiled without OpenSSL.[34][35]
參見
[編輯]參照
[編輯]- ^ Bernstein. Irrelevant patents on elliptic-curve cryptography. cr.yp.to. [2016-02-08]. (原始內容存檔於2017-08-25).
- ^ A state-of-the-art Diffie-Hellman function (頁面存檔備份,存於互聯網檔案館) by Daniel J. Bernstein"My curve25519 library computes the Curve25519 function at very high speed. The library is in the public domain. "
- ^ [Cfrg] 25519 naming. [2016-02-25]. (原始內容存檔於2018-04-08).
- ^ Bernstein, Daniel J. Yung, Moti; Dodis, Yevgeniy; Kiayias, Aggelos; et al , 編. Curve25519: New Diffie-Hellman Speed Records (PDF). Public Key Cryptography. Lecture Notes in Computer Science 3958. New York: Springer: 207–228. 2006 [2019-10-22]. ISBN 978-3-540-33851-2. MR 2423191. doi:10.1007/11745853_14. (原始內容存檔 (PDF)於2020-01-22).
- ^ Lange, Tanja. EFD / Genus-1 large-characteristic / XZ coordinates for Montgomery curves. EFD / Explicit-Formulas Database. [8 February 2016]. (原始內容存檔於2017-03-09).
- ^ SafeCurves: Introduction. safecurves.cr.yp.to. [2016-02-08]. (原始內容存檔於2017-09-05).
- ^ Bernstein, Daniel J.; Lange, Tanja. Kurosawa, Kaoru , 編. Faster addition and doubling on elliptic curves. Advances in cryptology—ASIACRYPT. Lecture Notes in Computer Science 4833. Berlin: Springer: 29–50. 2007 [2018-12-10]. ISBN 978-3-540-76899-9. MR 2565722. doi:10.1007/978-3-540-76900-2_3. (原始內容存檔於2018-12-15).
- ^ Werner Koch. Libgcrypt 1.7.0 release announcement. 15 April 2016 [22 April 2016]. (原始內容存檔於2017-01-22).
- ^ 9.0 9.1 9.2 9.3 9.4 9.5 9.6 SSH implementation comparison. Comparison of key exchange methods. [2016-02-25]. (原始內容存檔於2017-09-24).
- ^ Introduction. yp.to. [11 December 2014]. (原始內容存檔於2017-10-07).
- ^ nettle: curve25519.h File Reference - doxygen documentation | Fossies Dox. fossies.org. [2015-05-19]. (原始內容存檔於2015-05-20).
- ^ Limited, ARM. PolarSSL 1.3.3 released - Tech Updates - mbed TLS (Previously PolarSSL). tls.mbed.org. [2015-05-19]. (原始內容存檔於2017-01-22).
- ^ wolfSSL Embedded SSL/TLS Library - wolfSSL Products. [2018-05-01]. (原始內容存檔於2017-09-08).
- ^ Botan: src/lib/pubkey/curve25519/curve25519.cpp Source File. botan.randombit.net. [2018-05-01]. (原始內容存檔於2017-12-10).
- ^ Justinha. TLS (Schannel SSP). docs.microsoft.com. [2017-09-15]. (原始內容存檔於2018-02-28) (美國英語).
- ^ Denis, Frank. Introduction · libsodium. libsodium.org. [2020-09-25]. (原始內容存檔於2019-09-24).
- ^ Inc., OpenSSL Foundation,. OpenSSL. www.openssl.org. [2016-06-24]. (原始內容存檔於2018-03-17).
- ^ Add support for ECDHE with X25519. · openbsd/src@0ad90c3. GitHub. [2018-05-01]. (原始內容存檔於2018-04-22).
- ^ Tclers Wiki - NaCl for Tcl. [2018-05-01]. (原始內容存檔於2017-12-09).
- ^ NSS 3.28 release notes. [25 July 2017]. (原始內容存檔於2017-12-09).
- ^ Monocypher Manual. [2017-08-03]. (原始內容存檔於2017-10-19).
- ^ Straub, Andreas. OMEMO Encryption. conversations.im. 25 October 2015 [2018-05-01]. (原始內容存檔於2017-03-13).
- ^ Cryptocat - Security. crypto.cat. [2016-05-24]. (原始內容存檔於2016-04-07).
- ^ Frank Denis. DNSCrypt version 2 protocol specification. [2016-03-03]. (原始內容存檔於2015-08-13).
- ^ Matt Johnston. Dropbear SSH - Changes. [2016-02-25]. (原始內容存檔於2018-03-23).
- ^ Bahtiar Gadimov; et al. Gajim plugin for OMEMO Multi-End Message and Object Encryption. [2016-10-01]. (原始內容存檔於2017-12-17).
- ^ GNUnet 0.10.0. gnunet.org. [11 December 2014]. (原始內容存檔於2017-12-09).
- ^ zzz. 0.9.15 Release - Blog. 2014-09-20 [20 December 2014]. (原始內容存檔於2017-06-28).
- ^ 存档副本. [2018-12-05]. (原始內容存檔於2019-02-15).
- ^ iOS Security Guide (PDF). [2018-05-01]. (原始內容存檔 (PDF)於2018-04-13).
- ^ MRL-0003 - Monero is Not That Mysterious (PDF). getmonero.com. [2018-12-05]. (原始內容 (PDF)存檔於2019-05-01).
- ^ Murenin, Constantine A. Soulskill , 編. OpenBSD Moving Towards Signed Packages — Based On D. J. Bernstein Crypto. Slashdot. 2014-01-19 [2014-12-27]. (原始內容存檔於2016-03-04).
- ^ Murenin, Constantine A. timothy , 編. OpenBSD 5.5 Released. Slashdot. 2014-05-01 [2014-12-27]. (原始內容存檔於2017-05-05).
- ^ Friedl, Markus. ssh/kex.c#kexalgs. BSD Cross Reference, OpenBSD src/usr.bin/. 2014-04-29 [2014-12-27]. (原始內容存檔於2017-12-09).
- ^ Murenin, Constantine A. Soulskill , 編. OpenSSH No Longer Has To Depend On OpenSSL. Slashdot. 2014-04-30 [2014-12-26]. (原始內容存檔於2016-06-24).
- ^ How does Peerio implement end-to-end encryption?. Peerio. [2018-05-01]. (原始內容存檔於2017-12-09).
- ^ PuTTY Change Log. www.chiark.greenend.org.uk. [2018-05-01]. (原始內容存檔於2018-02-02).
- ^ Threema Cryptography Whitepaper (PDF). [2018-05-01]. (原始內容 (PDF)存檔於2017-09-21).
- ^ Roger Dingledine & Nick Mathewson. Tor's Protocol Specifications - Blog. [20 December 2014]. (原始內容存檔於2018-11-15).
- ^ Viber Encryption Overview. Viber. 3 May 2016 [24 September 2016]. (原始內容存檔於2016-10-24).