Timeline for Doubt on elliptic curve over a finite field and binary representation
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2021 at 19:15 | comment | added | user1108 | @fgrieu I really thank you. They look great. Those will be my next book :) | |
| Jan 5, 2021 at 12:17 | comment | added | fgrieu♦ | @user1108: For ECC, I often use SECG, esp. SEC 1 and SEC 2. | |
| Jan 5, 2021 at 11:47 | comment | added | fgrieu♦ | @user1108: for a free, online, concise reference on finite fields in a crypto context, I use the Handbook of Applied Cryptography especially section 2.6. The HAC does not cover Elliptic Curves though. With the same authors, but not free, there's Guide to Elliptic Curve Cryptography; it has excellent free pages on finite field arithmetic. | |
| Jan 5, 2021 at 11:00 | comment | added | user1108 | Thanks also to @PaŭloEbermann (apparently I cannot cite more than a user in a comment) | |
| Jan 5, 2021 at 10:58 | comment | added | user1108 | Thanks @fgrieu. Now it's much clearer to me. I still would have a lot of questions about this marvelous branch of mathematics so I ask one more thing: can you suggest me a set (forgive me the joke) of reference (textbook and/or online handouts) that gather elliptic curves theory for cryptographer? I would enjoy them. | |
| Jan 5, 2021 at 7:38 | comment | added | fgrieu♦ | @user1108: I tried to clarify in updated answer (and changed primitive to irreducible as it should be). | |
| Jan 5, 2021 at 7:32 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Primitive->Irreducible
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| Jan 5, 2021 at 7:12 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Expand per comment
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| Jan 5, 2021 at 7:03 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Polish
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| Jan 5, 2021 at 0:58 | comment | added | Paŭlo Ebermann | @user1108 "convenience" is relative. What the author meant here is that the "natural" ($+$ and $·$) operations on the integers modulo $p^m$ are not giving a field (they are a ring, but you have divisors of 0, so division is not unique), but the "normal" operations on polynomials modulo an irreducible polynomial to form a field (and up to isomorphism the only field of order $p^m$), so we don't need to define special operations here. XOR on integers mod $2^m$ is convenient enough, the multiplication is a bit more complicated to implement. | |
| Jan 4, 2021 at 22:42 | comment | added | user1108 | Ok, you've been clear but just to be sure can you confirm the following? If m=1 then coordinates over elliptic curve are just scalars whereas if m>1 then a coordinate is in its turn a "set of coordinate" (in your example belonging to {0,1}^3). And about the integer representation: what are you trying to tell me is that it is not convenient to represent an element of a F when m>1 because in that case I would have, for example, 110 XOR 111 = 101 becoming 6 XOR 7 = 5 that may result meaningless? | |
| Jan 4, 2021 at 20:38 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Typo
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| Jan 4, 2021 at 20:19 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Align
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| Jan 4, 2021 at 18:34 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Polish
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| Jan 4, 2021 at 18:18 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Polish
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| Jan 4, 2021 at 18:13 | history | edited | fgrieu♦ | CC BY-SA 4.0 |
Polish
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| Jan 4, 2021 at 18:01 | history | answered | fgrieu♦ | CC BY-SA 4.0 |