{"action":"created","comment":{"url":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/pulls/comments/227166112","pull_request_review_id":167143278,"id":227166112,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDIyNzE2NjExMg==","diff_hunk":"@@ -722,6 +839,68 @@ Elligator2 can be simplified with projective coordinates.\n \n ((TODO: write this variant))\n \n+## FT-hash {#fthash}\n+\n+{{FT12}} outline a method for hashing onto a set of curves which includes BN curves, which are suitable\n+for bilinear pairings. A number of cryptographic schemes rely on pairings, including some identity-based\n+encryption (IBE) and attribute-based encryption (ABE) schemes.  BN curves are not one specific curve but a\n+class of curves which can be constructed using Barreto and Naehrig's algorithm {{BN05}}. BN curves are a\n+preferred option for asymmetric pairings as they provide relatively efficient computation for pairings, which are\n+usually the slowest computation in any cryptosystem using them. There is also work giving parameter selection\n+for 256-bit BN-curves, resulting in 128 bits of security for hashing onto BN curves. Suggestions for suitable 224,\n+256, 384, and 512-bit curves which are compliant with the ISO document and are based on M-type twisted curve can\n+be found in {{ISO09EC}}. Other work on parameter selection for suitable curves can be found in {{BGMO+10}}\n+{{AKLG+11}} {{Scott13}} {{BCMN+16}}.\n+\n+This method is suitable for BN-curves, which have the form E: f(x) = y^2 = x^3 + b, where operations\n+are over a field Fp,  where p = 7 (mod 12) and 1 + b is a nonzero square in Fp. Fouque and Tibouchi give an \n+encoding F which makes the hash function Hash(m) = F(H1(m)) + F(H2(m)) indifferentiable from a random oracle,\n+where H1 and H2 are independent hash functions into Fp. We give this encoding and hash function construction\n+in the steps below.\n+\n+~~~\n+map2curve_BN(t)\n+\n+Input:\n+\n+  t - the input, an element in Fp\n+\n+  f() - Curve function\n+\n+Output:\n+\n+  (x, y) - a point in E\n+\n+Steps:\n+\n+1.   s = (-3)^(1/2) (mod p)","path":"draft-irtf-cfrg-hash-to-curve.md","position":195,"original_position":195,"commit_id":"43143b4c4b99889bad485ddd21de88435236d247","original_commit_id":"43143b4c4b99889bad485ddd21de88435236d247","user":{"login":"chris-wood","id":2172048,"node_id":"MDQ6VXNlcjIxNzIwNDg=","avatar_url":"https://avatars3.githubusercontent.com/u/2172048?v=4","gravatar_id":"","url":"https://api.github.com/users/chris-wood","html_url":"https://github.com/chris-wood","followers_url":"https://api.github.com/users/chris-wood/followers","following_url":"https://api.github.com/users/chris-wood/following{/other_user}","gists_url":"https://api.github.com/users/chris-wood/gists{/gist_id}","starred_url":"https://api.github.com/users/chris-wood/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chris-wood/subscriptions","organizations_url":"https://api.github.com/users/chris-wood/orgs","repos_url":"https://api.github.com/users/chris-wood/repos","events_url":"https://api.github.com/users/chris-wood/events{/privacy}","received_events_url":"https://api.github.com/users/chris-wood/received_events","type":"User","site_admin":false},"body":"In #68, we removed (mod p) from each step. Should we do the same here?","created_at":"2018-10-22T22:55:37Z","updated_at":"2018-10-22T22:58:40Z","html_url":"https://github.com/chris-wood/draft-sullivan-cfrg-hash-to-curve/pull/20#discussion_r227166112","pull_request_url":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/pulls/20","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/pulls/comments/227166112"},"html":{"href":"https://github.com/chris-wood/draft-sullivan-cfrg-hash-to-curve/pull/20#discussion_r227166112"},"pull_request":{"href":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/pulls/20"}}},"pull_request":{"url":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/pulls/20","id":187449512,"node_id":"MDExOlB1bGxSZXF1ZXN0MTg3NDQ5NTEy","html_url":"https://github.com/chris-wood/draft-sullivan-cfrg-hash-to-curve/pull/20","diff_url":"https://github.com/chris-wood/draft-sullivan-cfrg-hash-to-curve/pull/20.diff","patch_url":"https://github.com/chris-wood/draft-sullivan-cfrg-hash-to-curve/pull/20.patch","issue_url":"https://api.github.com/repos/chris-wood/draft-sullivan-cfrg-hash-to-curve/issues/20","number":20,"state":"open","locked":false,"title":"Hashing to pairing-friendly curves","user":{"login":"Ela-BLee","id":26417656,"node_id":"MDQ6VXNlcjI2NDE3NjU2","avatar_url":"https://avatars1.githubusercontent.com/u/26417656?v=4","gravatar_id":"","url":"https://api.github.com/users/Ela-BLee","html_url":"https://github.com/Ela-BLee","followers_url":"https://api.github.com/users/Ela-BLee/followers","following_url":"https://api.github.com/users/Ela-BLee/following{/other_user}","gists_url":"https://api.github.com/users/Ela-BLee/gists{/gist_id}","starred_url":"https://api.github.com/users/Ela-BLee/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Ela-BLee/subscriptions","organizations_url":"https://api.github.com/users/Ela-BLee/orgs","repos_url":"https://api.github.com/users/Ela-BLee/repos","events_url":"https://api.github.com/users/Ela-BLee/events{/privacy}","received_events_url":"https://api.github.com/users/Ela-BLee/received_events","type":"User","site_admin":false},"body":"Added a section on hashing onto BN curves, which are pairing-friendly.\r\nIncludes a brief introduction to BN curves, the FT-encoding function, and steps for the overall hash 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