This document provides a 3-sentence summary of an EdDSA cryptography document: 1. EdDSA is a digital signature algorithm that is based on Curve25519 and Curve448, which provide faster signatures than existing algorithms like RSA and DSA while maintaining high security. 2. It has been integrated into software libraries and protocols like OpenSSH, OpenSSL, and OpenPGP to provide more efficient and secure digital signature verification for public-key authentication and data integrity. 3. Resources linked in the document provide further details on the specifications, implementations, and advantages of EdDSA for applications requiring cryptographic signatures.

1. EdDSAͬͯͳΜͩʁ
by Hiromasa Takeda

2. Who?

3. ஛ా େক(λέμ ώϩϚα)
‫ؠ‬ख‫ཱݝ‬େֶɹM2
http://t-takeda.work

4. ୅දऔక໾ De
fi
os Lab ॴ௕
https://de
fi
os.jp
SecHack365 ༏लमྃ
ηΩϡϦςΟɾΩϟϯϓ मྃ
ηΩϡϦςΟɾωΫετΩϟϯϓߨࢣ …
ͳΜ͔৭ʑͯ͠·͢
IoTLT੝Ԭ ओ࠵
ηΩϡϦςΟؔ܎ɿ

5. ͦΕ͸ͱ΋͔͘

6. EdDSAͬͯͳΜͩʁ

7. &E%4"ͱ͔
͍͍Μ͡Όͳ͍
(16ͰͳΜ͔‫͍ͨ͠ࢉܭ‬

8. ͦͷ1
֓ཁͳΜ΋Θ͔ΒΜ

9. σδλϧॺ໊ΞϧΰϦζϜͷҰͭΒ͍͠ʁ
σδλϧॺ໊ɿ
σʔλͷૹ৴ऀΛূ໌͢Δɻσʔλ͕վ᜵͞ΕΔͱΘ͔Δɻ
EdDSAɿ
Τυϫʔζ‫ۂ‬ઢσδλϧॺ໊ΞϧΰϦζϜ͕ϑϧωʔϜʁ
Τυϫʔζ‫ۂ‬ઢΛ࢖͏͔Β͜ͷ໊લ
OpenSSH, OpenSSL,OpenPGPͱ͔Ͱ‫͑࢖ʹط‬ΔΒ͍͠
࢖͏ପԁ‫ۂ‬ઢʹΑͬͯΑΓࡉ໊͔͍લ͕͋Δ(IRTF: RFC7748)
Curve25519 - Ed25519
Curve448 - Ed448

10. σδλϧॺ໊ΞϧΰϦζϜͷҰͭΒ͍͠ʁ
σδλϧॺ໊ɿ
σʔλͷૹ৴ऀΛূ໌͢Δɻσʔλ͕վ᜵͞ΕΔͱΘ͔Δɻ
EdDSAɿ
Τυϫʔζ‫ۂ‬ઢσδλϧॺ໊ΞϧΰϦζϜ͕ϑϧωʔϜʁ
Τυϫʔζ‫ۂ‬ઢΛ࢖͏͔Β͜ͷ໊લ
OpenSSH, OpenSSL,OpenPGPͱ͔Ͱ‫͑࢖ʹط‬ΔΒ͍͠
࢖͏ପԁ‫ۂ‬ઢʹΑͬͯΑΓࡉ໊͔͍લ͕͋Δ(IRTF: RFC7748)
Curve25519 - Ed25519
Curve448 - Ed448
͜ΕͰ‫ʹ͡ײ͍͍͕͏΄ͨ͠ࡧݕ‬ग़Δ

11. ͦͷ2
EdDSAͳΜ΋Θ͔ΒΜ

12. ࢖ΘΕͯΔͷʁ
ʮEdDSA͸ൺֱత৽͍͠҉߸Ͱ͋ΔͨΊɺ
ɹRSA΍DSAʹൺ΂Δͱ࣮૷΍‫׵ޓ‬ੑͷ໘ͰྼΓ·͕͢ɺ
ɹߴ͍ύϑΥʔϚϯε΍ηΩϡϦςΟΛ͓࣋ͬͯΓɺ
ɹެ։伴‫ج‬൫‫ۀ‬ք͸ঃʑʹEdDSAʹҠߦͭͭ͋͠Δʯ
ʮύϑΥʔϚϯε΍ηΩϡϦςΟΛॏࢹ͢Δ৔߹͸EdDSAΛਪ঑ʯ
by ιϑτ΢ΣΞ‫ۀا‬ʮGravitationalʯͷVirag Modyࢯ (2020೥08݄)
Ҿ༻ɿ
SSHͷެ։伴҉߸ʹ͸ʮRSAʯʮDSAʯʮECDSAʯʮEdDSAʯͷͲΕΛ࢖͑͹Α͍ͷ͔ʁ - GIGAZINE
https://gigazine.net/news/20200828-ssh-encryption-algorithm/

13. ࢖ΘΕͯΔͷʁ
ʮEdDSA͸ൺֱత৽͍͠҉߸Ͱ͋ΔͨΊɺ
ɹRSA΍DSAʹൺ΂Δͱ࣮૷΍‫׵ޓ‬ੑͷ໘ͰྼΓ·͕͢ɺ
ɹߴ͍ύϑΥʔϚϯε΍ηΩϡϦςΟΛ͓࣋ͬͯΓɺ
ɹެ։伴‫ج‬൫‫ۀ‬ք͸ঃʑʹEdDSAʹҠߦͭͭ͋͠Δʯ
ʮύϑΥʔϚϯε΍ηΩϡϦςΟΛॏࢹ͢Δ৔߹͸EdDSAΛਪ঑ʯ
by ιϑτ΢ΣΞ‫ۀا‬ʮGravitationalʯͷVirag Modyࢯ (2020೥08݄)
Ҿ༻ɿ
SSHͷެ։伴҉߸ʹ͸ʮRSAʯʮDSAʯʮECDSAʯʮEdDSAʯͷͲΕΛ࢖͑͹Α͍ͷ͔ʁ - GIGAZINE
https://gigazine.net/news/20200828-ssh-encryption-algorithm/
ී‫్ٴ‬தͬͯ‫͡ײ‬ɾɾɾʁ

14. ͱΓ͋͑ͣԿΛࢀরͨ͠Β͍͍͔
EdDSAͷ‫ݪ‬ஶ࿦จ(2011೥)
http://ed25519.cr.yp.to/ed25519-20110926.pdf
RFC 8032(2017೥)
‫ݪ‬ஶ͔Βগ͠վྑ͞Ε͍ͯΔ….?
https://www.rfc-editor.org/rfc/rfc8032.html
Ed25519 home page(͜͜ʹؔ࿈࿦จ·ͱ·ͬͯΔΑ)
http://ed25519.cr.yp.to

15. ͪΐͬͱಡΜͰΈΑ͏

16. ͳʹ͕ಛ௃ͳͷʁ
1. EdDSA ͸༷ʑͳϓϥοτϑΥʔϜͰߴ͍ύϑΥʔϚϯεΛఏ‫͢ڙ‬Δɻ
2. ॺ໊͝ͱʹϢχʔΫͳཚ਺Λ࢖༻͢Δඞཁ͕ͳ͍ɻ
3. αΠυνϟωϧ߈ܸʹରͯ͠ΑΓճ෮ྗ͕͋Δɻ
4. EdDSA ͸ Ed25519 ͱ Ed448 ͷ྆ํͰ
খ͞ͳެ։伴 (32 ·ͨ͸ 57 όΠτ) ͱॺ໊ (64 ·ͨ͸ 114 όΠτ) Λ࢖༻͢Δɻ
5. ਺͕ࣜ ‫׬‬શ Ͱ͋Δɻͭ·Γ‫ۂ‬ઢ্ͷ͢΂ͯͷ఺Ͱ༗ޮͰ͋Γྫ֎͸ͳ͍ɻ
͜ΕʹΑΓ EdDSA ͕৴པͰ͖ͳ͍ެͷ஋ʹରͯ͠ߴՁͳ఺‫ূݕ‬Λ࣮ߦ͢Δඞཁ͕ͳ͍ɻ
6. EdDSA ͸িಥ଱ੑΛ࣋ͭɻ
͜Ε͸ϋογϡؔ਺ͷিಥ͕͜ͷγεςϜΛഁյ͠ͳ͍͜ͱΛҙຯ͍ͯ͠Δɻ
(PureEdDSA ͷΈʹ౰ͯ͸·Δ)

17. ͳʹ͕ಛ௃ͳͷʁ
1.EdDSA ͸༷ʑͳϓϥοτϑΥʔϜͰߴ͍ύϑΥʔϚϯεΛఏ‫͢ڙ‬Δɻ
2.ॺ໊͝ͱʹϢχʔΫͳཚ਺Λ࢖༻͢Δඞཁ͕ͳ͍ɻ
3. αΠυνϟωϧ߈ܸʹରͯ͠ΑΓճ෮ྗ͕͋Δɻ
4. EdDSA ͸ Ed25519 ͱ Ed448 ͷ྆ํͰ
খ͞ͳެ։伴 (32 ·ͨ͸ 57 όΠτ) ͱॺ໊ (64 ·ͨ͸ 114 όΠτ) Λ࢖༻͢Δɻ
5. ਺͕ࣜ ‫׬‬શ Ͱ͋Δɻͭ·Γ‫ۂ‬ઢ্ͷ͢΂ͯͷ఺Ͱ༗ޮͰ͋Γྫ֎͸ͳ͍ɻ
͜ΕʹΑΓ EdDSA ͕৴པͰ͖ͳ͍ެͷ஋ʹରͯ͠ߴՁͳ఺‫ূݕ‬Λ࣮ߦ͢Δඞཁ͕ͳ͍ɻ
6. EdDSA ͸িಥ଱ੑΛ࣋ͭɻ
͜Ε͸ϋογϡؔ਺ͷিಥ͕͜ͷγεςϜΛഁյ͠ͳ͍͜ͱΛҙຯ͍ͯ͠Δɻ
(PureEdDSA ͷΈʹ౰ͯ͸·Δ)

18. ͳʹ͕ಛ௃ͳͷʁ
1.EdDSA ͸༷ʑͳϓϥοτϑΥʔϜͰߴ͍ύϑΥʔϚϯεΛఏ‫͢ڙ‬Δɻ
2.ॺ໊͝ͱʹϢχʔΫͳཚ਺Λ࢖༻͢Δඞཁ͕ͳ͍ɻ
→ ൿີ伴͸୯७ʹϥϯμϜͳόΠτྻΛੜ੒͢Ε͹ͦΕͰϤγʂ
΍ͬͺΓ଎͍ͷͱɺָͳͷ͸͍͍ΑͶʂ

19. ͦͷ3
ཧ࿦͸͍͍͔Β࣮૷͡Όʂ

20. ࣮૷ͷࢀߟ
ͳΜͱʂ
RFC 8032ʹPythonͷϥΠϒϥϦ࣮૷͕ࡌͬͯΔʂ
https://www.rfc-editor.org/rfc/rfc8032.html
͞Βʹʂ
Ed25519 home pageʹPythonͰͷ؆қ࣮૷͕͋Δʂ
ʮඇৗʹ஗͍͕ඇৗʹ؆ܿͳPython࣮૷Ͱ͢ʯ(ҙ༁Ҿ༻)
https://ed25519.cr.yp.to/software.html

21. Ed25519 home pageͷPython࣮૷
ɾ100ߦ͘Β͍͔͠ແ͍
ɹˠ ษ‫͠ڧ‬΍ͦ͢͏ͩͶ
‫ج‬ຊతʹҎԼͷ‫ػ‬ೳ͕͋Δ
ɾެ։伴ͷੜ੒ɿ publickey(sk)
ɾॺ໊ɿsignature(m,sk,pk)
ɾॺ໊֬ೝɿcheckvalid(s,m,pk)

22. ެ։伴ͷੜ੒
1. ൿີ伴͔Βsha512Λ‫ࢉܭ‬
64όΠτฦͬͯ͘Δ͕࢖͏ͷ͸্Ґ32όΠτͷΈ

23. ެ։伴ͷੜ੒
1. ൿີ伴͔Βsha512Λ‫ࢉܭ‬
64όΠτฦͬͯ͘Δ͕࢖͏ͷ͸্Ґ32όΠτͷΈ
2. ࠷্ҐόΠτͱ࠷ԼҐόΠτʹ
ҎԼͷΑ͏ʹܾΊଧͪͰϏοτΛॻ͖ࠐΉ
#ZUF #ZUF
99999 ɾɾɾ 999999

24. ެ։伴ͷੜ੒
1. ൿີ伴͔Βsha512Λ‫ࢉܭ‬
64όΠτฦͬͯ͘Δ͕࢖͏ͷ͸্Ґ32όΠτͷΈ
2. ࠷্ҐόΠτͱ࠷ԼҐόΠτʹ
ҎԼͷΑ͏ʹܾΊଧͪͰϏοτΛॻ͖ࠐΉ
3. LittleEndianͷਖ਼ͷ੔਺ͱͯ͠aʹ‫ه‬Ա
#ZUF #ZUF
99999 ɾɾɾ 999999

25. ެ։伴ͷੜ੒
1. ൿີ伴͔Βsha512Λ‫ࢉܭ‬
64όΠτฦͬͯ͘Δ͕࢖͏ͷ͸্Ґ32όΠτͷΈ
2. ࠷্ҐόΠτͱ࠷ԼҐόΠτʹ
ҎԼͷΑ͏ʹܾΊଧͪͰϏοτΛॻ͖ࠐΉ
3. LittleEndianͷਖ਼ͷ੔਺ͱͯ͠aʹ‫ه‬Ա
4. BΛεΧϥʔaഒͯ͠(ପԁ‫ۂ‬ઢ্ʁ)఺AΛ‫ࢉܭ‬
5. ఺Aͷ఺࠲ඪΛ࢖ͬͯͳΜ͔‫͢ࢉܭ‬Δ
#ZUF #ZUF
99999 ɾɾɾ 999999
}΋͏Θ͔ΒΜ

26. ͜ͷઌ͸ษ‫ڧ‬த~
αϯϓϧίʔυΛඥղ͘ͷʹҎԼͷϒϩά‫ͳʹߟࢀ͕͘͢͝ࣄه‬Γ·͢ʂ‫ँײ‬ʂ
ʮed25519ͷpython࣮૷Λඥղ͘ ͦͷ̎ ҉߸ฤΩʔϖΞੜ੒͔ΒϕϦϑΝΠ·Ͱʯ
https://pebble8888.hatenablog.com/entry/2017/10/07/231342

27. ͦͷ4
ͱΓ͋͑ͣಈ͚͹Ϥγʂ

29. ެ։伴Λ࡞ͬͯॺ໊͢Δ
ൿີ伴͸ϚδͰద౰ͳ32ByteྻͰྑ͍….? ͨͿΜ…
ൿີ伴Λ‫ެʹݩ‬։伴Λ࡞ͬͯɺ
ద౰ͳϝοηʔδʹॺ໊͢Δ

30. ॺ໊֬ೝͱվ᜵

31. ॺ໊֬ೝͱվ᜵
վ͟Μ͞Εͯͳ͚Ε͹Success!!

32. ॺ໊֬ೝͱվ᜵
్தͰΘ͟ͱϝοηʔδΛվ᜵ͯ͠ΈΔ
վ͟Μ͞Εͯͳ͚Ε͹Success!!

33. Ϥγʂ

34. Gistʹςετίʔυ্͛ͯ·͢
https://gist.github.com/TakedaHiromasa/ed5a3b69dc2ba2af2cab018087bb0956