비대칭키 만들기 (P-256)
KeyGen : 𝔹³² → [1, n−1] × E(𝔽ₚ), d ↦ (d, [d]G) · 이 키로: 전자서명 · Curve25519로는: 키 합의
KeyGen 전체
무작위 32바이트32바이트
c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721KeyGen
𝔹³² → [1, n−1] × E(𝔽ₚ)
개인 키 d32바이트
c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721공개 키 (비압축)65바이트
0460fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb67903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299KeyGen 안에서
- 1
바이트열을 정수로: 𝔹³² → ℤ
무작위 32바이트32바이트c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721d = Σ bᵢ · 256³¹⁻ⁱ정수 d77자리 십진수91225253027397101270059260515990221874496108017261222445699397644687913215777 - 2
정의역 확인: d ∈ [1, n−1]
n (위수)32바이트ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551정수 d↑ 1단계 결과c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721아니면 다시 뽑음개인 키 d32바이트c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721 - 3
이진 전개: d = Σ dᵢ2ⁱ (i = 255 … 0)
개인 키 d32바이트↑ 2단계 결과c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721ℤ → {0,1}ᵏ이진 전개256비트1100100110101111101010011101100001000101101110100111010100010110011010110101110000100001010101110110011110110001110101101001001101001110010100001100001111011011001101101110100010011011000100100111101110001010011000100010101100010010000011110110011100100001 - 4
스칼라 곱: [d]G, 호너 규칙 Rⱼ₊₁ = 2Rⱼ + dᵢ·G
기준점 G (x, y)x, y 각 32바이트6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5이진 전개256비트↑ 3단계 결과1100100110101111101010011101100001000101101110100111010100010110011010110101110000100001010101110110011110110001110101101001001101001110010100001100001111011011001101101110100010011011000100100111101110001010011000100010101100010010000011110110011100100001ℤₙ × E(𝔽ₚ) → E(𝔽ₚ)Q = [d]G (x, y)60fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb67903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299 - 5
곡선 위의 점인지: y² ≡ x³ − 3x + b (mod p)
Q (x, y)↑ 4단계 결과60fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb67903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299E(𝔽ₚ) → {참, 거짓}좌변 · 우변e44a854fa5290000166da076d336607c0e2d938bab1ea14b412a0e6da28aea8ae44a854fa5290000166da076d336607c0e2d938bab1ea14b412a0e6da28aea8a✓ 좌변 = 우변 - 6
직렬화: 04 ‖ I2OSP(x, 32) ‖ I2OSP(y, 32)
형식 표시 041바이트04Q (x, y)↑ 4단계 결과60fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb67903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299E(𝔽ₚ) → 𝔹⁶⁵공개 키 (비압축)65바이트0460fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb67903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299
호너 규칙 256단계 전부: R₀ = O, Rⱼ₊₁ = 2Rⱼ + dᵢ·G
접기 / 펼치기
| j | dᵢ | 연산 | Rⱼ₊₁.x | Rⱼ₊₁.y |
|---|---|---|---|---|
| 0 | 1 | O + G | 6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 | 4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 |
| 1 | 1 | 2P → + G | 5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c | 8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032 |
| 2 | 0 | 2P | b01a172a76a4602c92d3242cb897dde3024c740debb215b4c6b0aae93c2291a9 | e85c10743237dad56fec0e2dfba703791c00f7701c7e16bdfd7c48538fc77fe2 |
| 3 | 0 | 2P | 741dd5bda817d95e4626537320e5d55179983028b2f82c99d500c5ee8624e3c4 | 0770b46a9c385fdc567383554887b1548eeb912c35ba5ca71995ff22cd4481d3 |
| 4 | 1 | 2P → + G | 3a67e2554b0c0bb685f4f52d8c07fa8441652fc5b76f1b2484a4dc45f200d687 | 27d0f1872f1fcf4326daf267163afb0d8c188af735a7618aa9ed16b302f79324 |
| 5 | 0 | 2P | ba6821cba9bab3ba57a98127482a5de00c108a6ac3241ebb508c58a24d9edba2 | 8841c5de60c4af3b87375ec78cbd21e7e70a85292d77eb4f8f218b036784e120 |
| 6 | 0 | 2P | 490a19531f168d5c3a5ae6100839bb2d1d920d78e6aeac3f7da81966c0f72170 | bbcd2f21db581bd5150313a57cfa2d9debe20d9f460117b588fcf9b0f4377794 |
| 7 | 1 | 2P → + G | f7120a01ae3d274253718f6f38336046965793cbea40661f7bbfa0421cd4c0c7 | bfb7e83e496595804f07b0985bc52625f4dd90e654efde43c4454d3a2b176ba6 |
| 8 | 1 | 2P → + G | 42184307a30b94158f6c5fa62bda46ffccc7e5ca6f4a3eaa80aa28e5ff1db101 | 86664ae7978294223c75da487cd348e347cc1f5ff1c0a5d498ac0112965ee748 |
| 9 | 0 | 2P | 71cce02a8d8797c264e0530db9172b4234c0c16dc02d142f298eb53dfe81ffec | a2aafd168369d58fc6fad1360516e8dbdfcce965210c20a72b9d83a4a75b7b66 |
| 10 | 1 | 2P → + G | ea392785644e88015a5589b6a8bf699bfad3354db9e643624a7bbd06a4e7a7b9 | f9bf8ef318c6c7e0cdecc5611722fa9f8a674ecd11b05a14c92f40fb2a6fd6ef |
| 11 | 0 | 2P | 52d380b464089706d830ce7d6d0a00da5c843b6a5b7ef8f8af7c640e5e10613c | 5553cae4df8b2204a7c5a9db87f95986ab6cc0a15376d92de00470db6948599c |
| 12 | 1 | 2P → + G | 35b9eeca93fd9ab8aed193432630141919f8b3e1a65768643019f72f1df52452 | bb2426b62ef871dd5994ad4c071a53753b33fcc81311dd64a235826563b30927 |
| 13 | 1 | 2P → + G | ae20509a243a1e623c7b1511cb7e3b736f2e88d4f36eb39cf5d073f28188a560 | 5139e126044d12a5d7d18b29a3ea2693765e40b7a31e8193a5e0fa3f2bba4c24 |
| 14 | 1 | 2P → + G | e1f1911ed16704a3acc2eda642c562f587633c6c5634b457701ed32f9d17ca32 | b421b6c0cac2987a81d1635ae4bd1b502a4529f8c647947bd6e3bb70c2fc1a49 |
| 15 | 1 | 2P → + G | 44e7bb7a8fabad5136fd8f397b94084d569c083ba207e65635ca7143960336cd | 2d4e0ed15f6311f2526d098aefdcf568a397bdaf47204cce27f08d7464197415 |
| 16 | 1 | 2P → + G | 90ca3e8143c57f2082071e31337fc9a604e2cdd0e794dfb80d10349895abf742 | 0a432928e524b7f11686587b09a243b0bd1d6fa30e21553ebb9ade932036b299 |
| 17 | 0 | 2P | e400bf60d57be72fae0afbe5a17efa7e3edda6ff5d3c2df83ec0ae7f00f28da5 | a2a71af158968ff9be16be8df606237c131632d889efeb1172968c73fd097fc7 |
| 18 | 1 | 2P → + G | bc03e60dfd7a967e630175ad49fac1d82f910731e50182d60127efc4d0415f2b | e622fb9a978285ee3fde6af09ff5fd991a6e34b45483d6923da99ea8fbf2d145 |
| 19 | 0 | 2P | 5feea2be07c0380a184df5ee36083a10983b10e31454fe1a293ca5bfb95ff30d | b5dce6a80f691f2fa0a96f4ca9639e22878de8e9c6028c9b5b4a1edc3e8093d9 |
| 20 | 1 | 2P → + G | 517793a86f7aaeadac8fd10fb817eabb53ecc5f253c642118fa697edb4065780 | 29609d760a0636e2e6def639f692ed6f4bbfc4e52f6c0d8172738178fa50c194 |
| 21 | 0 | 2P | cf629852a90d1a69af33b682650977976515ccf9dcec0b0aa78aa45ada82441f | 28050c2124b8a8ec5550590e6ce16add59f50d2ba104ba4f3e82b14095655c44 |
| 22 | 0 | 2P | 0d873304a101c85f467a7623f51cee392fe73c93a67f770e9e9f72ba2a0fa340 | 2fccb2857599cc314ce48b216da01b828985f963de21f143cd8e16a80c597405 |
| 23 | 1 | 2P → + G | 6f0721ef7abe64fd252128278bb55cdcd0801b74b4cf957ffeaf843d8cb32c3e | 58c64279f1761791afa294008cec723a8c6bbfb69b26fae5c9b60868671f8574 |
| 24 | 1 | 2P → + G | 78aac008b7b97279589ff9e3c3a6ca114a0fda4c471261bcb337ad8e4348fa1b | 8f7d1536e9a86611c83ccff591533ceed61ed224eac4b0d713e321893788ca48 |
| 25 | 1 | 2P → + G | 05a1067ce1202f4dafca397c25f1a9f5e600999598baa07344ba00d1c5e28762 | e7808fadc3d5d47d1f540175f949900b31cc8cdcff3cbf12fe0f5a289764c610 |
| 26 | 0 | 2P | b5585ba1d61f23968b293f76d3866a37ba07fc2ef2dc8a69bba4103336b5f081 | 54faa346d95f4600cdcb87d65f35322e00a84fbebc1b2181df4c5106f543863d |
| 27 | 1 | 2P → + G | b097207f8ca37de0d78600561f440563b9445442afbaaa5b0a9ae5977a5b2607 | 591be8d489b603f5f64f076387455419003119994f9398067e30fb9cac44cce6 |
| 28 | 1 | 2P → + G | 82ace147b7ac5dee5963886a49a550747420f6e2453c3798d84b8a509dc11fb3 | f895367e94d998d0d32b854007bc0e62d269efc0365c824bebb3be3cc5c66ca6 |
| 29 | 0 | 2P | dfc8e9c1b0d645917a03903f509140bc855353eda553efef79936b4af3d730a1 | eabf2ce1aa988e15619df83c2583797ee0e2ba939570992372cb2d04e704be16 |
| 30 | 0 | 2P | 00025b2da8c97c032bd1dbbffe19c86ca6f0da3291518c5a7d08a78e4581cced | 2f2b7c9884dd03fd02066564a55c96e92af16341fbe4e22645e8e1e0598a5e0c |
| 31 | 0 | 2P | 7e99ffc2a617a781320b7851483551a228c6087959d44f8864166ff209c88643 | 2c72912c2b4ea7a6d13ac35dd3385d4f8eea7a737bcfd0df3de2051bb421485d |
| 32 | 0 | 2P | 4861b6e5f004642ebc260529ef639f80a349c6eb1e98ae0ae6a31d32939d07c0 | 5aa0eb6a4c514e3d4619858d36d6f21c6bcc6a10902dd8d5707c84e27ffeb200 |
| 33 | 1 | 2P → + G | cd9f137e27160e6003e0dfb5dfb79dec783d506dc4e0be7c54d2716544b542fc | 53440a17fc044e8e12b8319e59b204b578601e6bc4eb6d1efcbaf3a4bd63cd57 |
| 34 | 0 | 2P | ba0d880e597da16dc40341f82bb8b0e87b875bed2e3394d2bfa41ffcdba796e0 | ab00e12ceb06af8db0ea24ca25af0a7c03851ec3c8be2d4d2d0d184996ac7d91 |
| 35 | 0 | 2P | 255b5e01d9d67173106de48975bbb5a094651b3907d82499db5886569611276c | 183118f45a968eaba9c0dbecc5d30d8870961780daaff2df60e5b99023b00f28 |
| 36 | 0 | 2P | 7792f0724efe3e0dcc8fe43465e4643ec84633f0f6b44f5c11f1ad0f568802cf | bd0f189dd13ac9fdca55777d818b9906a8c5de1c6730c602053cc5f3d0c30474 |
| 37 | 1 | 2P → + G | c9a7c9a85c875db08a7889fcf2d42dbfeb0e9a52c3bd427819f7587739f0e457 | 94d560f28f09ddd680f3d2105326a35f70decde767b2ff6c77930f0cc94fb285 |
| 38 | 0 | 2P | de017a01441dd4708e0ac1100984348b94b8f75db84121ed3a500f2839c588e2 | dd302a0967d8503711f5ab54484554b5944ecdde30e5d32c89a3db9857288264 |
| 39 | 1 | 2P → + G | 6a46b6052a77dfa66707b9bfd07f65f107cc90c8368237d1a027fe0037540de3 | 54042558321a65c169b70ce49b40be450c2c583bf31168c58792fd553328b870 |
| 40 | 1 | 2P → + G | 7dc1bfd9b99bf5ee9f9f1d4b98f0a4358daa55a3bc57d033c9259471bbf5baba | c20b98f6948cecd9018a5b925515eb2bf56a054e79409316d23d0042b125fd9d |
| 41 | 0 | 2P | 1f6168e5dc1833f9124137fd162c663dab9cf9bf81b3df294162ac27b0c58e4b | f82ae9edada23b790f1a26cc0da2037346cccd9688b2098d637f2ff142f971a9 |
| 42 | 1 | 2P → + G | 0669d83aa289f1d059341bf85cf1b1097bf489b53eeb2ed9c9657adf04242f2c | f7db47b638ba5814d340d28c2b4086ddaf18167d226b1d651ea1af1b8c4d58fb |
| 43 | 1 | 2P → + G | 8356fade70e2b2119802ccce4072944f97ca1f0c1edb940b218720f445ce3477 | 10518900af91bc2d9397872ab35e031166f4f65273d682a3943fe2da866832c0 |
| 44 | 1 | 2P → + G | 6607447fe04ea81bf673c58fe39117be683fc5cdc8a8b7d8f6aba29ab8aa100b | 3f4b7ce61b9ddec11d9d267ed0c98919112b8250e91fe2e5a1e26a3a271308aa |
| 45 | 0 | 2P | 58b3a9473467c097aed3f42cb4d79111b29f8650bdaa706b2dd6bb0c872c2567 | 7dab7cba15e8e73c074e7c82b1a3ddd762908f7adf3df276d4a8e9af3f6f2e5e |
| 46 | 1 | 2P → + G | 54586168debbc8dd1633d84ede7acc0fdb004e430a0aa619ffc2736786bf582c | df633a52fcb7f7c6f3abf15ebccb9672eb9de29761b65397648bddc0c99c6b48 |
| 47 | 0 | 2P | 861b45551140fb972291a0faa427176aba43063da41461b442dd7515a741fd6a | f5edbf1b1880e56b52de4d39be489ff95125a0eb22ac250c13c1c81e516b631d |
| 48 | 0 | 2P | 652c6ac7c2c63277f3a595a1e9b5e386dadf82b1518b05bba2758d8a7988a728 | d953ed61229b5efe5d2ddc749f2162e0cd35de32251eb4a6c1ef42c06e14624f |
| 49 | 1 | 2P → + G | be05a95a8412413fcef72226c66321cab67fd391b5dd84630c84f3c4fcf930d1 | a13ad1cbae7bf9548fa10e048e82e367e23080a66e3fce91091ee34e65c2f9f4 |
| 50 | 1 | 2P → + G | 8f75b24e0cc57709a7fd75eda30c7bffe145d358b22f7c2363f23fbdc72dc917 | f9d7050b1dd34793e0da9e478f9b37501d6779d03e54c6d5fde14941cdd755f0 |
| 51 | 1 | 2P → + G | 262a8f3bdc9396a7583ab23cefe9463e4b17df5c25d5de702c5828e82e4a68f4 | 465c9fd82ed88b9539551382991f2b84cc74d3a3863718393564a848455bfa12 |
| 52 | 0 | 2P | 19ad3646d3201ed2ffb8e0d0bddbefa29f0aab549a00397a70a930847a80222e | 1a2087d315398c2e32762e742f61dcf98692d2e9b6baaa13ba18ca1b7a79f160 |
| 53 | 1 | 2P → + G | f612a56772475b2b9369109c0d1e95df6886647505aa6f203351cd9536358257 | e606a1a4d61813e97b4157faf16264c2a25a9007268fd13a1b6308b643da0aaa |
| 54 | 0 | 2P | 3b940f88eaebab58e97e86c85b92dc04e9f6c10587bf3a137baeac6e4cbbe2f4 | e1b1ca9db77cc0841d9b81b5bdb1dd8a3a513bd2e098937afee6d5f1edc4c844 |
| 55 | 1 | 2P → + G | 4791f92385ab1ddc70f4049f815c5b5a14af35ab76aa741c07b47ff82d73899f | e7e7a504cff42d2b4e73b40b5f2d149f6680fb67080dfb2b9e0eccac1cd2fbdd |
| 56 | 0 | 2P | c8cde396acb5e0b7f0e5226e51dc9d2320c0108733bb52616e07c7dc649483f9 | 5567daf999a40b3fd8783207521b8b43f423d004e7ccfd0a7c6d0346a02072be |
| 57 | 0 | 2P | ae96ce6ed3872726bc5a1a4b2aa731f0e8e548d68a5643db0fc0d0ecdb1fa264 | e2291fb165db6bb21448b6c6b69f1123d6d3047b0c69ae52fd73113ea451ee9c |
| 58 | 0 | 2P | 787a1e0b2cf3756a28337459bb7b8b4856681abf6d434df9fd4afe3e7459dc6f | 56357aea4d21f6ed9ca44f155d58a91ab7593af5dee3222d112682f80f242a4f |
| 59 | 1 | 2P → + G | 4f028ac6e62c3fc3bcdeae12075cf758ec117599c7fab605061fb71d2031cbb2 | f35ddb3154c4a764ca03b63fb1d9709d50feaa6cb91c9ddde9e42f1856bd0786 |
| 60 | 0 | 2P | 454de65302e553fedb06b2c0a7c5a5c29f875c7fafdb2d3a516a2cbf9a35b09b | 045aa1341cc526c2eb9ba44c7715c5c3af197a0c2caa2c625b53d8be79bb50f1 |
| 61 | 1 | 2P → + G | 4f0b8f04287a360736fb046690661f054094be18fd54582f0a0797407f5dec1c | fdecb434138a5082d657a470879c3a83dffb989569b6101c1b338bc92d059228 |
| 62 | 1 | 2P → + G | f3d19fa587a99cadce1eb84c76e9e545af9cfc36bc62d138a6d7fb8ce5a460f0 | 6c192852116cf8eb1e8f036541e22b1ac8c656832206b1673314f9cd82b792c8 |
| 63 | 0 | 2P | a6d3161d761d59ee91db963c2ee3d19f8e419bb387d0d835d2670b50de78983d | 186ab4f272a25c4b6ac5af30bd7f2fc360f7f629a0b69f18abdb00ca8d2a4e2b |
| 64 | 0 | 2P | 8c03dc501fb670b4ab281a78c0cc83ee5ac09ca844160abb83b8bac93c08e81e | 7c5509ba5e4aa21a1b420a0369c527436c5ef656ea3f850c338ea15f8511eb48 |
| 65 | 1 | 2P → + G | f4fbb870007b47de7c9d9def73525ff65d1e65c105a4e3abd580761cd62f1f88 | d36401aa07c6de60f6a848296091ef6fdb70876bfb93b9feff5dfa636c409e5c |
| 66 | 1 | 2P → + G | 0e956a0d10788090d110ecabf6ab2ef57c8f895d2bccd4f8bd2861585f7b8097 | 8219f3cd4dd4d2a04ba952c025c5d425b812d89bb60aa1b97b126edb4112c9ff |
| 67 | 0 | 2P | 155ed3a8b424b4b339326b817ee4e80721ebc8a46982cec5d48b2181065cf792 | b16633b3f03fb9e11a26b6f55041cf5fbcf64eaaab3fd71d949d98adcdcaa595 |
| 68 | 1 | 2P → + G | 726bdc8b75d450ed4c0ced27bb8ea8c1fa9aeb90619650cd4c81371ea62ff776 | c7b4789cff7b06c23acfcd3c7dff94a2c3d65c02e714cc6352bca4d87e345625 |
| 69 | 0 | 2P | f15a0456bdb64ebdb2af88de574f4609be8baeb555f14c59278c8ec9db2e4f86 | f5a24543f655e9b929e4885c639c1a260eb9575512d5c267abe6d8c1705c8b56 |
| 70 | 1 | 2P → + G | 8a1ef9318231e5fe214534a9dd380f1de48db8144e96ce874835a2d5e306c873 | b1a84d18a4bd4fdc1989af20a512c663e3dde0a88e3bd9311c9cb6f471d249b7 |
| 71 | 1 | 2P → + G | 2613662ac4df0bcbfe3daa30a1194fca1e7591f88a3ecc9bf261f01384b4b534 | 19b27432f1b9cdc851f63128323bbb5a0055c13c65df61865fd7532ada81900d |
| 72 | 0 | 2P | cb37dde97c4bec723cf2433097a59719ff1b87341ad1f987038d18bd8f76bda0 | d28c287a88b11e0d93b0b4d7fb0e2dc25b01ad002037cd149b8dfdc182556be7 |
| 73 | 1 | 2P → + G | 4074fdfe030f98bb0ddc6e4720534ac5982737bee278d2580dde7eb57e1cb473 | 4a5f14c25f37a552c71c55c6fae02158fcb22ac9d1d07a69c44535caa5f7cb41 |
| 74 | 0 | 2P | 8addd56aad143365cc3b681656d5e349cbbbc9494bcc23ec7e951b9d7bae86df | dff4515db729ab705384fd880fd919f7e0975dd9890501f0b97c1781cf07e286 |
| 75 | 1 | 2P → + G | 962a3f7b22ccb5865df476b59ef435f95c09ae5b713ab1e0fcadad9151da0711 | 3f1f440269742434e96f0fbc9e2ff9b6de750b17a5479fe6cd39f1cc12e3b7bb |
| 76 | 1 | 2P → + G | 8e7c9b2fd664a6d74e84b36b9e32fba2cea0ef6c67b6673a330454d6710fbaf8 | 0f277a9ab2bd2b7e4b19a79c57d54998db5234ca4a10ea97ad731057c784d1a4 |
| 77 | 1 | 2P → + G | 2fb0032da883ded19edce469a509c0294e959ea296967fad77486091ea544d24 | ffae5a3f96f4039d147a1280d584ddd01110e15716c88a76b0a4d7269390c4cb |
| 78 | 0 | 2P | 5dd887d1845c12f35b4a6172de886b2a1d382ddc493881ba3f6ebdc48a7a351a | 5e4f9271ada8000ea73ba28643b9c8945a18fa022e3636d5f781c48f7a0d1086 |
| 79 | 0 | 2P | 45ae68144aa5420fa3b24b096de49b100ab915aba058a7defcb2030e4606e526 | 76bf45d979ef827d2b331786d8b4a585c9089b060e88740adfa1f68a3cde7c25 |
| 80 | 0 | 2P | 8e812f886f11c128eda127d40b882f0c799c6f886aa793170c82d63dfd4443a9 | 3d6aa092210e6bafccc86d60d7b34cd067fac6d85151e952901b14a0483cea06 |
| 81 | 0 | 2P | cce7277a062688800d354dac18eb71f819eea7e933675817108d32e98bbe0c25 | 8403a73952eb17b7acf3da1d8084686881bb4b0f15ecc671b880ad69236ed754 |
| 82 | 1 | 2P → + G | e70289c9a03434111ed8dd9d40dde696e9e335ebcdfc4f95b8eb67192d029860 | bccde9c0dcfd19ca787df20d1a130784b61d88c718b61cdef03c3f98c4880c0f |
| 83 | 0 | 2P | 25dba9ce06b71912afd317b05a235b4320417056d18be57d18e722f472275408 | 94bc64a06813e9ef73bc9b259124d420f8bb8141375d1fde04cd18d4dbb87d68 |
| 84 | 0 | 2P | c7c11b6a25509b1ab3b43f962a194942ef1d76f8033d3d7666551d05c9785056 | 079e47af7844f6a3b9881ad03b4efd63b73aed1881652b28ceb5c99f8f271948 |
| 85 | 0 | 2P | 6935178bb00610bb7ba85707cf1949e964c4e27be2a9f6425daadae57b6fc72e | dc1624b9eee518eed1ebf7bc77d56cb126aa1468a8ca66a5ae1c549eabfefe4a |
| 86 | 0 | 2P | db456dbf963a7edb8507dbcf3104a73b4b997fcc0747746a653fca1d0ec311b6 | e007d965b9e8d1d33236557d0f2ebb0f346f0a7c4d2ff7fc2b873cf26ce4a39c |
| 87 | 1 | 2P → + G | ccb1783e78ca0de284e0c56d84666056cf5ef7c400cf2d629081c3cd0895d56f | 82429fc12ff99171bc1f396625ce27cdeccacc2c5c1a085dcabd4ebd6d325602 |
| 88 | 0 | 2P | 6d43cd080daca70cc9fd0b5a7ba45410ae251edf0056b57c31da9f961adfa320 | 39562bca141b81bf5b80770c8a686952c162c67241795de68ed7969e586636d7 |
| 89 | 1 | 2P → + G | 42ef4909bd8dc0507ff1c071d8ad579e2156a347244f4e356142bfbae8ef78fe | 6482956cf377aa35970959c183746790257710d9388febd39688803f1d9774d9 |
| 90 | 0 | 2P | b9201f7b73a36215f53bb00728bd0dcc923beb083055cbc8b3ebfacf884ae074 | d91db02d7c2985cc0aff10771ecb3c86e21eede2de34ab238dc95e3ccbc725a6 |
| 91 | 1 | 2P → + G | c3b1db041c32d4314aa0274d9bb7cf3b25532f962c94ed4ca246a7139231d326 | 96fe97068f66e069fc8f9c11767c608e09807279816e99c705934db065abd546 |
| 92 | 0 | 2P | e0aa4bc4029e33bacbe9ed41a79070f84fd8b484fba0f666accbf1dd2f482e5c | 7515d46e4278307c79670f991c8b384ccc53e6cada7c5d80b7ed198aa2c7f848 |
| 93 | 1 | 2P → + G | 847d30edea010871247724e190e1ea40a4e61927e2cabf876ca3886bf00fed7b | 6528f9140d3ed844e9b5e4904f883fd2f96b11d61e6eea26a709f669a9f364df |
| 94 | 1 | 2P → + G | e4d2e7ea02d78cae37602a819813d405bf49f653a0917540a7d09092b9528f1c | c4090decb9ecfb7c8bc076d869b4920b20c0e1e306bbedf5dbe1a8ceb8a816a5 |
| 95 | 1 | 2P → + G | 04bf4dec70ac26d6ccfe3193589603f83025d4dbb027ec4236edfdd90d9cc163 | 1b78be14a29c597ac09b868596844de967838249ba3d4b0260d9dfa246396a58 |
| 96 | 0 | 2P | 27b46440c271bce79311c203b7bb34c6c9a1852cbaff39ea1b3414e6b1692780 | fbfe62c6634e428d39b7dc3605647b0645a82c1f263d9cb46d565c2df62ece28 |
| 97 | 1 | 2P → + G | cedb652f03682a15ed68cbc3c5b6c2d691a9682da51dae2fb144c2bfab15e1fb | f097ed0438ae5e111e4ab4151af8a26e8b2a545b79012533a2fda74ff584d0c3 |
| 98 | 1 | 2P → + G | e85055dc2d6b844d18a2cc98a6a8bc76199cb9adff4f394970f2154a7919a711 | ce6d6dc43667961100651b1b9aaff4dc5762bbf4fceae1964432cc69fb343057 |
| 99 | 0 | 2P | 27b9184f9e681f4bd36120c8719c23c22930922cacd05f79c3be4f519de97915 | 59ce6101f325d4d63eb46007f8aff5fae13978ee5915720b4d133951945c4469 |
| 100 | 0 | 2P | 5e858a1f8713888d08f8c8d460b0fa78f8b83af0c31aa5bf7be7724a6146c287 | 13cf4332ce09ed3a51a609192f8c6ae184412624de8076cbd1f0af9b0776944b |
| 101 | 1 | 2P → + G | d6638405aa0ce1341c47a3a9657a16caed8b55ab218fedeb88c744470bf4825f | f6122b59b7439a2d07dd31eef7dbf4ea245466084a529610589a95da209dbcb4 |
| 102 | 1 | 2P → + G | e7fb160d86fed12c0da6b798689ffc307f10891a7695e70af858eebbae22ad31 | 5ec896d49e5a6a179aa89609be9148ce2ed085feb9ddeebb7ba7ed4298cfd12b |
| 103 | 1 | 2P → + G | e2332868a63ee7bcabd941c9f035aa088864ac0588dc635848d91f108e821bbf | 8c4a3da89ddbf29dc46d42fd62306a65d7be7f7167180a4da8a0e614cb47af04 |
| 104 | 1 | 2P → + G | 21f4493305667c99d3dfe56fefa9354935d417fbdd642cfe315296c0a17ac771 | b9ff1a8f47c8e94bee92815663da08bf9ac35f840c284575747ca7162b39c4a2 |
| 105 | 0 | 2P | d8480ea7d53c156aec80beafaf84f5a693024d7b473fb3f1b30121f8d0599f82 | e5263275a933f0996d277b4c01f092355611421599d397fb13ba61540b07520d |
| 106 | 1 | 2P → + G | 1d85800006c3276e28f8b3d007c426e342896caa222d95e4eb9351b1ec6b5ce6 | 1e43682a93ef04541d6fe37bebbc469e53997c01f360d3ad8a677ed67daa8e4a |
| 107 | 1 | 2P → + G | cdc188479f2e479cdad4bdddfebd3aac33c903cef0fde9e8a6f71bf741d22fd2 | c86758b98805a57e6050a6a26053630ee7bee85819cce2ab4a43e1b1701f6ff9 |
| 108 | 0 | 2P | c9b88b5b81fe201c7f1d563434ae14fa10ac1564b779169dcbda761b8e84b653 | 5327bc24fd547e309d9891040070758a40aca4ea4964c1cfa6c1da20e581abf0 |
| 109 | 0 | 2P | 333ab52bc71c0299e21b86df02f5e23810794d3b584126b732938b9762d391b0 | 4c595a511f97c1991a5cc0db4d9a88d8045f3338763ae76c5edbd800ae68b35b |
| 110 | 0 | 2P | 818458b34fc3bddc15b4e9099b985501dab83467047c1e00d72e4ab716e107f6 | 9dafb65734f360df8f0d8981a206205136ef5df2776b0201e92bb721dc98743e |
| 111 | 1 | 2P → + G | fea6aabedecd1c50a13bcab66685d2b82728025d98d0b5979c3d8f2bb536b5ba | e03dc84027c13f04c4cae227d9b27fd9a21cdfd469d543c1024ed2b520c3860a |
| 112 | 1 | 2P → + G | d7daa4147ff91a108a32a77a2ddd25b36bb7d30cfc558b98ac081f079cf86fae | d2f61563a5c463945ddd4f4a742950aa33b7b880fea8f36adb0da55fa36aecd7 |
| 113 | 1 | 2P → + G | 3a343ee381d379f453488054e00f71e65d0e198d3dc02054124484e2c0729b6c | eb6c258e8a162384e1d9b44508c012bc434b41de86acec215a5e7cd2b5c8d89e |
| 114 | 0 | 2P | e6d233aafbe83788c7372576524427903efe583418db10a247bf00200d7b5f73 | 2a922bf9714eaf51bc883442d6777821a38ff2012d497d4f44af74f594fb9e9d |
| 115 | 1 | 2P → + G | 90fb391b5bf74b23b5a09a2f658f957fc29a6335aff5904dbcf78533989bbf8c | 787845e91fec6814bb663fae20b80adc846fa8542b2198913a21ec057909bc1e |
| 116 | 0 | 2P | 66d155b5a8e2b14f77e9ff72c6cd20116062b36499d74386c8617d0e015afe1f | a8cbf2d862695eafd6f2d8bd24083f0dd4bb41efac44bff0410ad646ee481388 |
| 117 | 1 | 2P → + G | 4b087ce439fe117a0284cf9372ab4cd313c92b908c7c5bd2db56141204a8ae17 | 3e0ab5f69727b7979208436b529ecf93e9478f4d93179d05c144f717504110ca |
| 118 | 1 | 2P → + G | fb18f82d7170e6e19cc6efffe8ba877996cca50b6166a7484e86f08901f33e79 | bdf32c0102f7b205b3c843a29ad3219dd83ac3423d3f4c6425e050c9557229a8 |
| 119 | 0 | 2P | fb2002900c292f703fcc75c90206509b37d86c7ccfbd84f7bfb19e1cd2b95a46 | de9b9408e6fca3f4b2afe2009b36e46126a05e34969c4db074bc42522ed2fc5f |
| 120 | 1 | 2P → + G | 2dd7ec2b5e279f70f739e99ce8a4f26d7fe388e0bb322245588b55a258a41d42 | b01de4bc5eadbdac2b204a094f806671a2ad6f6d7cf2ec89d6b13ce15b465130 |
| 121 | 0 | 2P | 94fd504786737c5aa0e2e207fed3472b6e337fcb1cca6fa16163d41c99cd3b9f | ba450a695cb41410c7ad76de3e7dbd83f51e279048d30b709505021214f6bbd1 |
| 122 | 0 | 2P | b92c21e20efa48089e2b04aa24c72f715a2d4c34a033c08411033ef4c68a3633 | 594c5d9a55178990fe5e85346fb5c01d4d06766301aea3e958806dd17b03a1ae |
| 123 | 1 | 2P → + G | dc22b9c7acb790d003fcd3cd6e883c63982817f0a0b179d04e0d722bd541e05c | 91e888598543edc90b13ddb208bf51846d6785f682db140eafc2324f67b297e5 |
| 124 | 0 | 2P | b01a0a559868448e224238d95c6c4154ca8772dd8436a8fcd0259088b0bf12ed | 0c1e465ff2506c512c362e55ef88fba6369eaca96c811150f143a68a9bbc7eab |
| 125 | 0 | 2P | 5e8f71af9921f7adc7c661556887ff43cb9177f2e3256981030f900829e13f20 | 471415ec564065fba8d6922700224664e9dfd76b40d4157561186988592312f1 |
| 126 | 1 | 2P → + G | 5168bedfcb9b4b80b8bc3892b98ce94254f59b7481f648fb08da6d5d460777bc | d0f138d85ff14a9e4231200034b9a05cb2f74b71d363448178e02cc4dfd37912 |
| 127 | 1 | 2P → + G | cb996a390b707820d346cd1d350b6fc59278049bbe8a19cec59b0feb8218d76f | 0b6b2df57556f5f26df9359df887eca6ff1ba63bf47c0116921816c94d87eaa5 |
| 128 | 0 | 2P | 3d633fb1f559d636ff0c3ec3231d272ed4ba41bb75cdc5586d7573cc92a3b6a0 | 8a9f9645653391d47693123bc650afe226d1769519ac6535cc3d5f5fb7c8e46c |
| 129 | 1 | 2P → + G | e53909a3ac8b67c1f8a79154b726a0a019676d3e620509eb825ecbf390d73c69 | c505c34b618645cc47a8e4cf7ff7008f6549ee1923cda08156db3db69c1878a2 |
| 130 | 0 | 2P | c28d54724056c8fa3ade37b6a2e42d8f01bba1714bdf9a8e21deb565ad367172 | f460dd4c89976945fb2fd13ebfe383f022d929ba6b6c66de7143afbaa74b80b1 |
| 131 | 0 | 2P | e605cb78f2b0dd8e04a09fe5ac620eeebf27fbb9310d4bf1cb1b3aa9ed3bfdd5 | b555c63aa164e0c14f5cb35fd6357de00bd8acfcf2d5b34e1d46df344871085c |
| 132 | 1 | 2P → + G | d7b578f5748768323e007eb91a0e9bb1d497a3051a44b18d2574e945deed1fcb | 9064f7f90892e0325da81da7135070ee731b133555ec8bc07a3347782e75842d |
| 133 | 1 | 2P → + G | 224fe229c01973cf6fc464a07538559fa1c303150b626e2e6e80831f8f636c95 | b4f7bb63b67d50dd871f09ead54295511abcafd29ea29eee8fb0f8c4685af20b |
| 134 | 1 | 2P → + G | 2a6e83ba07bd07d7f480a76eb3f63e830d19fba7abfab3ccfe1c4192fbfa6e62 | 21e3ab7ebe83e6ed4db3ce985b74b5ffde36d2297303b13d969eb4c82cc417a9 |
| 135 | 0 | 2P | 9afa29662db1fb2f1b9d16a7f480a5a6c0426a8d8e341fff247710c247fb3bb3 | 328a764745408315a9399f135634d03ac187a39ff10faacbcc6886a1e6e47859 |
| 136 | 0 | 2P | bc0311162d0be5f0fec59b511538cf04142a9e1186d222ceb28f4c3cfdf2ac7d | eb2cf5b411022ec9a5a4477922d1ccbcc4613b6b0267aa4036859b2861af468f |
| 137 | 1 | 2P → + G | 69355c869ec6b6645796d75eae858123e3ee6255846cdf780ed0587e494fe8f4 | 0ff51c6b05884b746680245fff12115bf443894c3230adcb34a1bd0611d2b7aa |
| 138 | 0 | 2P | 7203e8fb774e3f5b35218869081236d8aaa58d6825825d3e83f58d0d21fb9eca | dd1999668b7cb8b4a9ea36e0111c547f6ef893a32b05b17d63bf984240bd741b |
| 139 | 1 | 2P → + G | 92ae4ed8356285839648fa7a8db6bae1de4a429abc9a7c7cabf2a01084596638 | 03d1fe51d9fd9f6b7df3f6690b3ad2fb001caa67311bfd976a82edfa80ec6267 |
| 140 | 0 | 2P | 6798c1293ad258da139220cbe420b6333b4a430f4ee21143e42f8da3975d78fa | 9f762f95aef1f0901bf0b393f17fb62b068255b70ec0ad9a02f5e3baa95c2fee |
| 141 | 0 | 2P | a7ee7f1f28ba6781147d115ff2fbcf5db58ef85a2ac17d69a632a7a2ae09fdd0 | 0449687c6a4996bd49604b360f88f7f8f16b1af1a0a19a0bfa83c42ff9848e1c |
| 142 | 0 | 2P | 0b83074ba2f02db91ecd2d98f4e429d612068101518e6022d59cfae47eebcd2b | 7fe0b44a9f403421f90e191adaeee6e7beedddae96446f878b41c1893d090a63 |
| 143 | 0 | 2P | b38cd9d5e48cbc33231b45fb8a571d37aaf325945cc425ac8dfc3c961282dbc7 | 41667cfa97767c5782f7166f0b6522ba79cd5513cab0ae62f8d8c304fdb09f6a |
| 144 | 1 | 2P → + G | 3ac8df4ecd9430b9c122e39b22d510df696e684ec3b7f03adcd478ccdb1bfc5d | 2660e56d782a1e514d1656625fb934b33e57bbaae1ec320e042c81576d1a5e1f |
| 145 | 1 | 2P → + G | 3bf202017bf0c3f65173a3a73d4fa67892baa1e9455b29a76ef61b28e2ff3b7c | 27cac65d31d42f316c5cfcb18c8e2193805ad01e72a744c42711663df8e0683e |
| 146 | 0 | 2P | 04f40584d99f014f6b8c1c5da8019e96047512da27fe05640b843941e0fe8f73 | 58b2a2628161424fe5b6d8706f4d14113be98db5144e8cfeeb3a7918496adabd |
| 147 | 0 | 2P | 1eacde96324bd10407b930d8132984b5beda8488e9918772a1d015eb4d59d534 | 6faebb0f3b742328cecd7003037517804c291c4477c8866ae2ed24cbfdd2b278 |
| 148 | 0 | 2P | ce75b0838932f774a3cdbb0394b13218f27df310b5fd4da6d8caad012589f663 | 549a916b2744fb94238b4e3c42fe82fe8ca75dca2f41503f27d51f45a06fe5d8 |
| 149 | 0 | 2P | 90aad15b625cd94403cbecbec2e0c1253e031a096369b0fd01043ac1cdbd5b6d | 74cdeb97b4c1145b866f39a93bcabb9a6c662f85f1149c88911262793ac6854b |
| 150 | 1 | 2P → + G | baf29ed5cc7fac531dfe005b8d4c5a675b10d8b26912033c29e3070a7bc4496d | d5cc6b30f7eb016dadefbbffa79f5c5f0cd7c2f01326b012930b0fb78b10646e |
| 151 | 1 | 2P → + G | fe27671609ea4272652ecf891fcd2dfd47d31d2c82e463b548f3e88c7dc22d80 | e15e711e48493b199f196c7d26e4ae818afdb048d1146dfb340c7ea172eefecc |
| 152 | 1 | 2P → + G | 334f136fc09ac488852769ea86155915c3cb62995b536c193f07d30ce05dd839 | 15c46765af91c165769b69fc4bc1d61d3e59ad4ea9b1fc4ee5d3d1d00a29537b |
| 153 | 1 | 2P → + G | 5e89dfd4536ce360cd27690d605f5659bde581aa033bb9547f9dd3c33911e672 | e07cc8d9fa54dc47d34287960564d8db5abbde183a015cffa52a843e936fff21 |
| 154 | 0 | 2P | 59acbeca8049cab1c22f858751e1f5afc35aa257f574dae5c399ac8f90323b18 | 4199de36b78558ea4462e0847154498772187513d6bff17f1000db34fb8c0beb |
| 155 | 1 | 2P → + G | 78ec7a9266d75c4df97709fc542210331055b4f2807a4cb8c13490764f07b484 | 7d50eb73974a44e13d3aaa5f39ed0f7729d06fa934f6881c7b8e81f866f89fcd |
| 156 | 1 | 2P → + G | f58de20790be1927b2ca87bdd8977b0288c4562052ed7bd28794c5cd7a92b701 | 98d36647cc418255a9302b0cc7b4e49d81a69bcd3137b4d23f852204ea753c16 |
| 157 | 0 | 2P | dbbf7acfbc688e14dec3c96d618bb2aeea06765d30ef32283f1c09bb92b2b6a2 | 685d8c7bed8f1066ce67220dbc5782a92371a9ed0444929f5576d2f93af61977 |
| 158 | 1 | 2P → + G | 8e483409559339a8199922cfcc79f31e7809ffa71d20a20c1ef36fb56e87789f | fbd1787645c3d23690de948da434b06115b87d9bbac50db619146ec2995172d4 |
| 159 | 1 | 2P → + G | 8c9881833911871acbe9ca52fd6c7872d4e7b4cab919263929860bfbcf982a5f | 8f1beecae91fd9f3b2b717f72c2e0d9213121ce06611fe5bc772a1893085c9bb |
| 160 | 0 | 2P | 5e45ba4871ebf72c3959f6e7a660f2f5e90c684880e3bca570e7ed8efd8a61ff | b974059101c2b03e7ceca895eb7e18e1fa1e0adcffa028c526c125cff655b474 |
| 161 | 0 | 2P | c25367fa766e9870403894cd9fee79fd26b65e4c4f62aa3a8d354e21945cd069 | b0e6114bcd3c8afa137cdf4067fd4bd7d3b644af199b6571a15255456751a9b5 |
| 162 | 1 | 2P → + G | 1d99edb5e751573c828c44b36f4dca0898925f098a045d05b1d1faddf4dc1f09 | 4e8b7ac7b060162fafdfd80d47e2b6ff4d35109753a0b55b891d8e75573a1be3 |
| 163 | 1 | 2P → + G | f2dba534d03a020b76c8bd34c2fabb07b67b43ad0bc106a49097fb34178b5aaf | a2b6842f91878239d320c520e649916c09ff0859fea6b387f69a44134e84fea1 |
| 164 | 0 | 2P | b23998bcc207ff65528c3b370b83f9ad9a60cb103a70e6ffb7252cd702369e56 | 95fc148343313ea07cd153bc59963d3d709315935588d31a9fcb632a6b2eeebf |
| 165 | 1 | 2P → + G | 925b051e1bcd06cb5f235063119e44b453dc2b644d8c4efdffe4149dc6f30a72 | 3d3101f4ba6faf02e3ec8054b9f74f0554853bcf59d93710d1c0e3aeac49daed |
| 166 | 1 | 2P → + G | 1c91b58ece888fbbf52f588f29e066a0f5afe293a70b1a96982529c51456320e | 323f4d374054487bf38b747021c199fed23e7cec8523d7c73dbdedd7e7996558 |
| 167 | 0 | 2P | 3bff94446a4ef76c85b0ebde7711d30705d02149109a0f00643be7da75bec103 | 868978729466e07a2fb2f53eec74ca7e6f7be6cdb0ac5e9631572eb0a4fbc234 |
| 168 | 1 | 2P → + G | bfb57f935fc67f6e670ba27f525a3e644b38d16b934f993c6dcec213cdd67ea0 | 01f246aeb67cb3e12b2e9f8c2e4abbc0d382696e43864491c59cf38d154857e2 |
| 169 | 1 | 2P → + G | 699e9192628e4f5bc7821d3fa83265f216b28f296a085a03c2be02344da5dcef | b3d503f4d885180ce8857c9423e135388f68da2aa072c1c78245ffb730d0a2c3 |
| 170 | 1 | 2P → + G | 94fd47b9e5a767f1be157d11be8ae789e94c3e1015f1fa6d5bd2138f76ab3a4d | 340f06b9b07c0e9d8d69c151576f67fc1c02954035da1d9e8d3ca1a7f5f82296 |
| 171 | 0 | 2P | f0d37c9b8d6ab3b274883a4373a59cb65ef5fe9c78f6d7e2e3048d09886aee87 | 3e27391686900c2b974a56a4ac3e80e8928cf2e03c12fae252709b92e8361dd7 |
| 172 | 1 | 2P → + G | 74b1c60372174ba6e1d38647366defee29a01931f98a565bda7045225eb7da28 | eabbf226935cccee0ae77881344cd8a96e68a7fe0fb5445d6620d5c6325e67e5 |
| 173 | 0 | 2P | 85751a255815523d51f750657dcc62b86f4179b677b8a9e1770bf4d17115faaf | 0275407dfcd35a5ee92f98b3dd1a83794afa14a2dc4873da79d65406a93d5d3a |
| 174 | 0 | 2P | 4d5959208145563abcf74c74f8be8bd0c70f39b8ae8cef48a54a94e259a3fa80 | 69b8c4d9599f451b50652380c46d967a5ace4037d3288870e85e8f92d320b9c6 |
| 175 | 0 | 2P | e47408136e4cb93acfb8d4b6a076e824f368f3901ab104259de0bde5d1880aed | 33f8992582600e090d37e29749f82dcde80f70712dcea2734142fe1fce1e71c7 |
| 176 | 1 | 2P → + G | 157ef94b577339b47f46d1379672c7fbc9f5fdf98a92e02e58b2f37559dbf101 | 9009dc9c85bff608dfbe42b944af2e25e7c9d4bf3e5826a3019c31fb9238b6b1 |
| 177 | 0 | 2P | 9666bc8d44273a178e404ef2cbf370b85708794a690ef14c4cb1c668dfdc53b5 | 9dd67be86f81788b9550171d1dcb14216c1a424e2ae1628d58649e7d38b803dd |
| 178 | 0 | 2P | 51008f58ca37696a9e1e2b66a7a6e7a7669db70dbf6fc945428183d96a342a9f | 648b4870df74f95043ced8506d2ec8932141be78a9b11b3a803b626a2594b2c7 |
| 179 | 1 | 2P → + G | 234831301e6e548d5d8c991bdad40782eb51095950edc410c7562754e5d54d32 | 947c960ae537913cca9d661b21e2deefb08fe6f15510f605597fbc49dfcaa3f1 |
| 180 | 1 | 2P → + G | 83c1a298aa60c53bbfe2f11e990d2d76f78c25d6c7e42ab7913e47cdabf77b8a | 16c78784abe4fa620f77b19f90b25fb1ec29c1b1a2d94e8574775b5879252e70 |
| 181 | 0 | 2P | e94d0c75e93d6b9e8eaa54b1f506d7ade5c96e55f42257491142b099764e40eb | c86cb6c324faa7b0900c65a9938607c6f455f080e0c25b2144facb04f68e54c4 |
| 182 | 1 | 2P → + G | dfa80e574a1bf8b4b26ff0b2a6ed6450ee704f3572a1a31697667d7d14b4bba1 | e55feb750aed7285761e7e6c4965b597b3dfa3f55513c31b351e9674dd975958 |
| 183 | 1 | 2P → + G | 5f8ef2f7ec0156247330e3e9da0f541a482190e2446b4d478c2e794d52e44bb1 | f7d3681277e9febffdda305dd9f36db361d3259fecbe19c4051e3777cbf2a02f |
| 184 | 0 | 2P | 8aefc39aa47254d3650610bad0f0d329733ff3b52a69d3e44d3dc5374985f231 | 586049f7844ba7c69591e0127c8476fbeef68f181f0e923aab1f69eb5fc9c614 |
| 185 | 0 | 2P | 93f6e48b3f216adc51f8544d69f623c002278ac743a772b742de91a829261ec0 | 190e03d274c45281f892f0f77e56cef5dc34047a4bf0e5f1a3d0ad00b1f6e3e1 |
| 186 | 0 | 2P | 740ee7eb11a2d9c09002939b02c3bf747899446b9a8b4212a744ffeb23310734 | 0caf9091163b3a040947c2f66d8e031f366900c6d1b88fc19721abc426fd3810 |
| 187 | 1 | 2P → + G | 8be37f10e89e6adf177c365c09fd6778e24e33d6bb7caf745e7dac71a6ee8a52 | 87c9f52a2d4911a8ec4bf6da07bed2303a608283cbb4a0ef50983c12cc5e3d5d |
| 188 | 0 | 2P | d52eda00da71e81df98328892b2e574987f78d83814b2affad66f0980a902812 | d8d86feee1044babd82ccf9ddb687bb3c677fccb69fe8fb6a1589f0cfc97c0f1 |
| 189 | 0 | 2P | a40f2caabb47ff917757072b9bb341316ecc90e26b800eb6888bb892e005c7f2 | 8785fbb3f0ba485547aadd35fa8fb7fca1bd20cbbe56f8efc92afd18c954de51 |
| 190 | 1 | 2P → + G | 3f62ddcff9afd3793302f09f9520a33cc1cc3d85f07391c3aee5c2aad70c4dc2 | ba46a0ef04889c6a74ebb4dd5ac489e49405755805ce3fe2be8168671329cc80 |
| 191 | 0 | 2P | bf36c92b345dcad08125e8a9d0bcc5df21dbcb7161ed14f43b979a9fc39968b9 | 29e504e614c0412e1385b24cc79abb037b1fef1dd5aa173221e20ba9b55871fd |
| 192 | 0 | 2P | 9e922c900940461a06be5fe4db48c03bfe3bfae84e89b1d07d1be2edf411c94a | 83be05f236df67d99ad7a1871efb43bf9271d90e599eab5768decfdd8d466c3f |
| 193 | 1 | 2P → + G | e79e9f5081a579049a9e2f3a16f5282289c23b3bd4b871aaf450fa294e8403a0 | 42be8811360a62fe09ea22e19b575227a530438e9a286d6469dc58ae49ed8493 |
| 194 | 1 | 2P → + G | 09c04ddfadb6c25cd783e58a5ab75ecc7d1dadc54ee8689aa04f7d5a01d98ef3 | e651d3e153fbbd80b5817bc6180d2ff0580ae14017562c28ca0df3f106befdb9 |
| 195 | 1 | 2P → + G | 45fade36356876458ea03a3522dabccb932ef12eeb9cd024284efc2b295ba205 | ca20c4193496306ebdeef0022dd1ab71e7388b38943c561680bdc914cd1717f3 |
| 196 | 1 | 2P → + G | 2c224114252ccd00e6889c5daf66f059e8763083377233278e241772d8d8cec2 | 8df3f2f0d345b75c4fd70348d96d872699fa57bd5885a14e3c3bf28a587ed5f6 |
| 197 | 0 | 2P | e44f9552080133ae844b2695de497c5e7b255c13a2a85e1039d2fe6126ebd853 | 74040e3ea89d0a77a12afbb69b62e664f82014c3dcbd0a1bcd2d3b3acbc39efb |
| 198 | 1 | 2P → + G | f3125667ee3a7c4083b675ec3580578a868b08fab58f9e6aa16849280b00cbb2 | 74c4808723b4a75737ce9252cc78e64a8d0dbcf567fbf7a1ca01117ba5b99071 |
| 199 | 1 | 2P → + G | 23d7fff630a439552e89e1e16f2f0a20a01164f7a4313c506ba89988c396094e | 551e13224de9059e1f6f4b10f80cd5effd546f141e556841da798926571ccb3f |
| 200 | 1 | 2P → + G | 6a1116ff23030ea80ef5c3d09bbb9f8f3f2db972d8e3952e6e7a1ed9a0d1fef5 | 92441874059a76789c9518ae69bfbacee4370add16d9a38dd8e2ce8d05fc5496 |
| 201 | 0 | 2P | df22589d69faf82985c7a8ba605b05c10940c3c63f27d7e06fee274efd3d4bca | f2f684f88588ad57403481e315fa26f115849e35b157e0528bbf97d9800bee93 |
| 202 | 0 | 2P | a858f58efd3fcf5eb217b368d25a55ad24c532dae1801e8fcb52e2d97517946e | 5b3f9d7f1d0b8e505082007b97480f7dddd50490c5e10c31847508f6a984404e |
| 203 | 0 | 2P | cd9a1847254583402e2ca23f3a26d35f2690c10d5acf4f9c3fe611187c898582 | 85c2e193db089aafa65203471d245278e9b17061f96a1137d94a6ec9d4162bdf |
| 204 | 1 | 2P → + G | 604bb54bd1121eb1a218aed7b23afccfe930adcae4c8b3d49ad5c396704b6ee5 | 8ef345474bdeeaa148771fe148e1c9cefefb46a1d0f59baeb17e84456fa9d903 |
| 205 | 0 | 2P | a3a41f3ad8f6c43aa945ae96008ea711e5cfaa743bfff2782fac853b78ff924e | d6cfb10da4deaeb7d25130f2c31b2455ccbed73629aa554c7039f54315125ed5 |
| 206 | 1 | 2P → + G | b728f7c311309be938f5b2aceafb91de0274a64c49d1393e20cfd98e3f9b278f | a0937d946d38714c7f6c0f3cf1652010d1b9393437b187eda93eac5379437aaf |
| 207 | 0 | 2P | 4f9e3459eb24b51f050f2dddd74b83c034139c551bd112daa2357e7867c4ab3d | 67f8e39804db84890666f1f6a71edc886803c3716ec5fad13c8c9bc3ce4bc73b |
| 208 | 0 | 2P | b597f0dd18605bbc2e149fab70ef3e09fb9f137cddee0741b19cb2e38b90de7f | 460ad9bc501afe66db634b709039e9817812d7365693278d08ec3d8bd418510b |
| 209 | 1 | 2P → + G | af13c9bcd14fac8ac0243baec6dfeb8c79fc231f55ec5a3444dc941c27231f93 | a529f5f8285a354489968786f953a9fba34826e82c46373ceed52f412c44aa0d |
| 210 | 1 | 2P → + G | e8f1e61761e2063b86309d692fbc979231b5b600c4d40f9f629b3de90b85e175 | 35a3803fcd0c29080efc746056054578397c6a13665cd43a2422a0d17a93c3af |
| 211 | 0 | 2P | c6e712afe139424e0b15e738548850ff7779f8cb400c5374cbb11c95cb053bb5 | 8447f24375f9e73e6dafb8348561521386b8fa8049fba9567fe548fd726d691e |
| 212 | 0 | 2P | 828099fc728c19f1d992d25d675bc19e060e29d20e6150d1aef239af034f3892 | 84981faa7c171da86f7398db9c6f349995c7a9bb1cf54147cd1fcfa7e3492a5d |
| 213 | 0 | 2P | 0537e745b09515da8670467e17e45c56d0e23812522170b18b635b651e017a2c | ec54efa76b053aa89ffe13c172b20dbf3d3828042462e74f937efa8590879047 |
| 214 | 1 | 2P → + G | e4f604b380d732df6f90b0027264b1b57c1ea7ccc8a6ce7ad12b6b603093700d | 6d1bc84050c5d2fcdc862aa6538b52d17bb254e0c5c23f876764bbc1d5b0aae7 |
| 215 | 0 | 2P | 993b49db2b28a96c6ff8791c84c4005872b91e7b76db03ea1c1d32b4bcf53115 | 59d7b056cca1321f88efc997d3ca3a7ba7a8737cd65a03c1cf10b3978f627203 |
| 216 | 0 | 2P | 61c90c5bf084206a7c03fb37262855a300d900a4a7d02557c8e91c54911b1877 | 9dd99c36c1d942228d70cb26c069df16bd812c08079c1df9acec35b846eafabb |
| 217 | 0 | 2P | 0b506bacfd6bf03430dbd935700c9900cabc2124ab225740dd1dc2722549bd6e | 3c841169801b418f3ba8c947a1a27c7cb60c74766b009fe86c6c055e158f4fba |
| 218 | 1 | 2P → + G | b3be8997010679a2592b5c8955747f64d06ccf430131d3427de1232e63478fc0 | 08d8dabd1fec11d90811680b0337fd27c9d4fa343d54ba2a17a39ca6e4e0102e |
| 219 | 0 | 2P | a0784ca873d1440309fce7ef029dd92d858bd16713b4fd1b1251672a4ab47ca7 | ebedc03feea9e2d97f5f6c585e07f7f156e670b976be0b36dddee4ece13352e4 |
| 220 | 1 | 2P → + G | c1ba27cbad1a44469771cbafa7b2d9f52c8e881b7bd45f1ba7f3c0b0e5c29bad | c663b93a71bc59d6c35141ac50062b09a0b3b941e52de35fa74d22c67d78e7bf |
| 221 | 0 | 2P | 08cd2ee9c9e35acc607f30cecf0b527a780a08c366d7f355569d7ba111c3f3df | cb991e565ee2490c8980b6609428468f3fd2172212da463528b2478cb97a7a7a |
| 222 | 1 | 2P → + G | c6b8d24b7782da58502d8e1b630748af5df1420174357e978f8a404cfc427542 | 9cb1da3d9e30224915e2f7dcd800980757ce403f626861952126c15e6cf940c2 |
| 223 | 1 | 2P → + G | ea14ba701904016a456d27776ae917dc47a98ab50fe24e560729f3dbc89a76ea | d64aa764cfd65afbe60cf326984025e8a8f866f6ea0100c4b83335b1d4d8357c |
| 224 | 0 | 2P | 56c306c4f26057c9186e0213dc25ab72fc66f0ae2bdc3203290ec791f37812b7 | 82daaedf0e63f02609917481c49425fcb73ab4e4d0c5e1f16d2f0473b0929237 |
| 225 | 0 | 2P | c503a61cacb8e7d22eb1a1f57c06f4d6840dfa9582e0751bb2f9eceb0186229b | 4cb83056abff42bde819acedec7ae3b6f692ccbb891e241fe8996773901e07ba |
| 226 | 0 | 2P | c1b09a2f650a116f5da9dbd12d02766242db8d27ddb7f484f7008921e321e1fa | 010fa5a23ea0aeb7369275ba4497a6cb45495870ebde52f44967346d1b6207de |
| 227 | 1 | 2P → + G | 456ac7415d194b4771670dfcdf15b9fdcf5cc76fd4ce26f9f12c2f3b2c29f5d9 | 0901673067d12bafac28396cadb605d0d2e7cb244d0f14b08a7708832e42778a |
| 228 | 0 | 2P | e4ac0a2c876af775e166b014a241e8928dc206e9f2c6e68030f2921f48d77f96 | 64f5d889a7e484b90b60677cdc654d67b2d30148985a5e0eabbec9aaabbc86b4 |
| 229 | 0 | 2P | 60ff94c0f7be96e03ca17e6cd65233c7b5fa01fb8da3265a653eb7f3401b2758 | 2d8c19cb58593a6e8cb7f750c7cb8d62926cee3c1c098bd2ad127f8c088f14e0 |
| 230 | 1 | 2P → + G | 114a775163eb5fcde457225a0b720a94825a9d3718696ea226884e16cfaae388 | 4a2473ff35721065befbccb817d3dfc659a75aeade081f7241aef0ae0892c186 |
| 231 | 0 | 2P | 12549cdf9eeb83c6df6e67369898708e93c5da6c0e29554be1473b610731644d | 32391f64668086f9bd76bdc6d4e067e90bb2b57a978d7fea1465ae1a9fd82c42 |
| 232 | 0 | 2P | a2c06ba549378bafbe580da12680186ecaf638585b5b69ecc227d138b027c6cf | 175a2391f8925e49cf28b5a92e3bc67c9a91e58269e6147f9ee262c16389fd6b |
| 233 | 0 | 2P | 75d5377241e0d8e05e0f70c6678de42af8e0e2ec1d8b7395f8aeea19b6f41ed5 | d75ceb7f909efd67fab38ea5ba283687afa50b060995f95db807abe3596f0174 |
| 234 | 0 | 2P | 59732845bd08426825f96fb50b6e799860b763fb1534ab496432e0ce6178431a | 29cd2a896d4dff72791cd463bf3ab8d3e65006727e41121a6f91b06d082a234e |
| 235 | 0 | 2P | ff5665fcf8dbb2b00ee29bb87c2c9c646b4cc8d1cd4813d59da23d329bc1f6d0 | 19c5a58267d7bc4b9ae048bc5b3d8839d0eb0ae11a6b372e329a87d78c84673c |
| 236 | 1 | 2P → + G | 44680ef51f8b9fc74a88f12d1911be89cf496c86bff93c47b2e4d158258542e6 | 2289a02a0a60f27114e6b05d431947e499722acee11f70d8467ce3f4b94f00f0 |
| 237 | 1 | 2P → + G | df29d92643723474fb60770b3e8629112ce4161572b1e2dfa9399b47723491ff | 85d017a9550a5c893c45f7a797738c338f41afae4be48d849183a266cc011000 |
| 238 | 1 | 2P → + G | 17333828bd1b46a7c0ad49a2142a26c8ff8f9db91ecc3a9e9db223e9504557bf | ffde8468b3ec5f4a189fa34be008b5a5055032e5fab3f24663bbcdd4e2281436 |
| 239 | 1 | 2P → + G | cd20a2429ba5f19914cd2f8052b7b245ce90dc402945e9eaf9065d2568bbc245 | cd76980a2d500fd797979ddbcffc6e2722a9a8c095cf7e4446f486708478cb3b |
| 240 | 0 | 2P | c5613b750f3758a4161755d4d466786aff6e98ea0c440acd435db798286c6d80 | 914df32812d8672d0d1f5ba3681b478faf366e2dc33f79c65670bdb3f0b231db |
| 241 | 1 | 2P → + G | 40af64a6f2c438dfa4947f4f8a762699d10967eae29b496252ad9e65f70662c3 | 52abdd8d6e9da43ea47b2e3687aba52fedf4db3e745f11ceaf39749634f3f353 |
| 242 | 1 | 2P → + G | 836c051f6519c0ae4970882aa518b74ebdc0553faccc246dd91f86bc73fe18b3 | 9de129252bb3339a90ba7dae5e68f74422a5285231daf9cf524a775726499a2f |
| 243 | 0 | 2P | a3adbe77ae1ccdfbbf428118129a0549918fd21c4881cc7c61ee6b2540c425ee | 267d2ef9ff90ffa03ffc70948491d29e6def8fca171ca25d0bde9b34ef7c2e68 |
| 244 | 0 | 2P | 24cabb3e2f5bcea103d6ce64d202a02d4ec2af2198a00299a3e417bc0237dda0 | e663ee31a71096a68aa3c0bd2414b29c368e8268666f9830f0d18107199d3953 |
| 245 | 1 | 2P → + G | d550ab44946106864d21093c6c647838e3ea3a1ee86bd5248d0e926df0f02a11 | e4b366fed94bea8e954a4864df5873508a59da842a2567bf4b5eef50eb27a2e7 |
| 246 | 1 | 2P → + G | f1e48e0bf703aeae7d31f57372aa88f4c2c415a2b5d85d303656bcc31e7c3f9b | cc978a4df12913fcebb7f3676dbcc361e745e1561de8286f270149a00a70c105 |
| 247 | 1 | 2P → + G | 686896ddb46ec3bc8579acf40094d683975fcd3271e948d4769dfd34f4ec22c8 | 68edc94466c7f23c821ed580baeaef86de6467fad273cb5cb896318e26e28477 |
| 248 | 0 | 2P | 2b37a1a3142b7846677104f2d321a38a10afa4f7d55b1d9dc15b73f2058d76cf | eba4241b59f14c3b275f5e09e665891664324f6f520e7f416bceb6ad542fc6a8 |
| 249 | 0 | 2P | 7a2bf6fc5fe6dadd047e3594a9b2a4fbd8968fc635775534e9d0ea7d0522a90e | 521f9bcded72fa03bf46cfe15c7570b89179960cc8ad19a363eb72ce7bd80d9b |
| 250 | 1 | 2P → + G | 03da14e9d15bbbc81ed72ec795caf21c705fec1332534f93269ddb7f48ce51b4 | d1575d118c8bfafe1a30d14773e341326d56411d3c5b527219fb388b2f5e2fc6 |
| 251 | 0 | 2P | 439ed13599d6e4f6ce33118b0421d0630e57c6919f6e0a8068c3c85a0c2412bf | 432d079a174b0c2f453fd6cf1d45078f30fe3dd1df73564340371be7dd545fb3 |
| 252 | 0 | 2P | c0f8d0a51ded9b30693cac04c84491218c4fcb0515578a9a7831d0d33b104d6d | afa75251fdb73bdc93a29244a53a04a554378e5a39d95aec7ef9856604ef8f39 |
| 253 | 0 | 2P | 087bb14958fee12c78ccc70fc1e7de5a4e289d38a0250334521c192b8ef71d02 | 88b2a67c411a9e043176a5259cb1bcd48b737eb55fa930cfa27f707e835cd6a8 |
| 254 | 0 | 2P | 35a86005fd023ed1b77e7a149746952aca0c4941942fca4d7b4ae3b53176e732 | 40788de45d362b2752c92bb8a73fbaba13e2ed530518d1612be7d29c1b67c688 |
| 255 | 1 | 2P → + G | 60fed4ba255a9d31c961eb74c6356d68c049b8923b61fa6ce669622e60f29fb6 | 7903fe1008b8bc99a41ae9e95628bc64f2f1b20c2d7e9f5177a3c294d4462299 |
단위 연산 ① 점 두 배: 2P (예: P = G)
P = G
6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
E(𝔽ₚ) → E(𝔽ₚ)
2P = 2G
7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc4766997807775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1
| 분자 | = 3x₁² + a mod p | cae428e87d3cd8168484cf1a2aa3b2889b23cbdb183be9730080b044c741bea2 |
| 분모 | = 2y₁ mod p | 9fc685c5fc34ff371dcfd694f81f3c2c579c66aed662bd9d976c80d06f7ea3ea |
| 분모⁻¹ | = 분모^(p−2) mod p | 7d13d1ed160030c54147c66b2e0d48cf7fe33dfb45a6dd82dded53bae22ea01a |
| λ | = 분자 · 분모⁻¹ mod p | a249bcb3191802d3cb56fc75a8731f848e7b2caf080f3477a4e4d904a671af9d |
| x₃ | = λ² − 2x₁ mod p | 7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978 |
| y₃ | = λ(x₁ − x₃) − y₁ mod p | 07775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1 |
단위 연산 ② 점 덧셈: P + Q, P ≠ ±Q (예: 2G + G)
P = 2G
7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc4766997807775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1
Q = G
6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
E(𝔽ₚ) → E(𝔽ₚ)
P + Q = 3G
5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032
| 분자 | = y₂ − y₁ mod p | 486bedd2228baf5b65aa5083dc9b6d3a715085712e47dca52db188cb1546de24 |
| 분모 | = x₂ − x₁ mod p | ee2556d95428f2ca6e6aaee25eef262eb67a139fb5f9186b4e95f0499132291d |
| 분모⁻¹ | = 분모^(p−2) mod p | fa32eb074f24c51be3b4757c84d0a102aa15ad5fa0b7fd8bd2cdb73cf951ad28 |
| λ | = 분자 · 분모⁻¹ mod p | 28cdb0fe6681d140c59fb73f85f16459ca4cee083742bada762de4ca226a8086 |
| x₃ | = λ² − x₁ − x₂ mod p | 5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c |
| y₃ | = λ(x₁ − x₃) − y₁ mod p | 8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032 |
단위 연산 ③ 역원: x⁻¹ mod p (예: 2G의 분모 2y)
지수 p − 2
ffffffff00000001000000000000000000000000fffffffffffffffffffffffdx = 2Gy mod p
9fc685c5fc34ff371dcfd694f81f3c2c579c66aed662bd9d976c80d06f7ea3eax^(p−2) mod p
역원 x⁻¹
7d13d1ed160030c54147c66b2e0d48cf7fe33dfb45a6dd82dded53bae22ea01a| 검산 | = x · x⁻¹ mod p | 1 ✓ |
한 방향으로만 쉬움
- d → [d]G
- 단위 연산 382번 (두 배 + 덧셈)
- [d]G → d
- 알려진 가장 빠른 방법으로도 약 2¹²⁸번 (타원곡선 이산로그 문제)
P-256과 Curve25519 · 둘 다 키 합의와 서명에 쓰임
| P-256 | Curve25519 | |
|---|---|---|
| 곡선 | y² = x³ − 3x + b (mod p) | v² = u³ + 486662u² + u (mod 2²⁵⁵ − 19) |
| 개인 키 처리 | d ∈ [1, n−1]인지 확인 | 비트 몇 개를 고정 (클램핑) |
| 공개 키 | 04 ‖ x ‖ y (65바이트) | u 좌표만 (32바이트) |
| 키 합의 | ECDH P-256 (TLS secp256r1) | X25519 |
| 서명 | ECDSA P-256 | Ed25519 (같은 곡선의 다른 형태) |
상수 · 표준이 정해 두어 누구나 같은 값
P-256 (secp256r1)FIPS 186-5 · SEC 2
| 기호 | 이름 | 정의 · 출처 | 값 |
|---|---|---|---|
| p | 소수 p (체의 크기) | 2²⁵⁶ − 2²²⁴ + 2¹⁹² + 2⁹⁶ − 1 | ffffffff00000001000000000000000000000000ffffffffffffffffffffffff |
| a | 곡선 계수 a | −3 ≡ p − 3 | ffffffff00000001000000000000000000000000fffffffffffffffffffffffc |
| b | 곡선 계수 b | 시드의 SHA-1에서 생성 | 5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b |
| G | 기준점 G (생성원) | (Gx, Gy) | 6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 |
| n | 위수 n | [n]G = O인 가장 작은 n (소수) | ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 |
| h | 보조인자 h (cofactor) | 곡선 위 점의 개수 / n | 1 |