Barack Obama

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Jul
11
answered Which area of Maths should I pursue?
Jul
11
comment What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
This is not the GLV method - it's just using an efficiently computable endomorphism which is well known. Also, the solution described does not avoid the inversion required to produce an affine point. Finally, I'm not sure what's so "complex" about the multiplication by j!
Jun
2
comment Can i modify data “protected” by a CRC16?
If you post 100 bytes and identify which ones you want changed to what and which ones you don't care about I'll do a demo!
Jun
2
comment Can i modify data “protected” by a CRC16?
If you XOR two 100 byte strings with valid CRCs then the result has a valid CRC (possibly with a tweak if the CRC is inverted). You can calculate the values using Gaussian Elimination mod 2 without having to understand any extra maths. This works because addition mod 2 has essentially the same features as normal addition. But as @CodesInChaos says, you need to be allowed to change at least 16 bits of the rest of the 100 bytes to some arbitrary values to "fix up" the CRC.
May
26
comment What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
Post a comment with some sort of contact details (bitcointalk?) if you want my help.
May
24
comment What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
I have some experience with Bitcoin's curve and I'm very confident that you will be unable to avoid an inversion for your problem as stated. I'm also quite confident that the restrictions you have specified above are more restrictive than are really necessary. Perhaps you can let us know whether you are a) trying to break the curve, b) generate vanity addresses, c) implementing some deterministic wallet scheme or d) implementing transactions which third parties can't link to an address.
May
24
awarded  Commentator
May
24
comment What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
I bet this is a Bitcoin-related question, in which case although people say it uses a Koblitz curve it is in fact not one. I think I have a good candidate solution for your problem but it works for a composite modulus and only if the group order is kept secret. If that's useful then let me know. If you're working in affine coordinates and you want to generate new points without inversions then you're probably limited to the Frobenius endomorphism.
May
9
comment RSA leak bits to factor N
You'd have to look at semismoothness probabilities in the vicinity of p and q to see if you could just search. I believe my idea is likely to win because there's the opportunity to do work on the sending side to encode the information and then more work on the receiving side whereas just leaking bits from $p$ requires the receiver to do all the work. If you could allow the primes to be not chosen uniformly at random but at random from a particular distribution which should have no effect on security then coming up with a suitable curve should be easy using complex multiplication.
May
9
answered How to derive formulas for addition and multiplication in Jacobian coordinates
May
7
comment What does $(\mathbb{Z}_n^*)^2$ mean?
How about a link to the paper? Is it about cryptography?
May
7
answered RSA leak bits to factor N
May
7
answered Solving a discrete logarithm using GDlog
Apr
29
comment Adding and multiplication in jacobian coordinates
This is the relevant page of the Explicit-Formulas Database (thanks @CodesInChaos)
Apr
13
comment ElGamal: Generation of “g” value?
I have experienced people being quite negative about efficiency gains from having $g=2$. I haven't investigated so I have no opinion. Also, I found abc's answer to this post which would lead people (wrongly) to believe that $g=2$ is insecure for signatures in all cases. Perhaps you may care to leave a comment on the linked question to set the record straight for posterity. You have the gravitas I do not.. (yet!)
Apr
13
comment ElGamal: Generation of “g” value?
However, if you look at Appendix A.2 of FIPS 186-3 (the Digital Signature Standard) you will find a more comprehensive treatment of similar issues which boils down to pretty much the same thing.
Apr
12
comment ElGamal: Generation of “g” value?
If your maths knowledge is such that you can't see the truth of this when it's pointed out to you then the best solution is for you to brush up on your maths rather than for me to find someone who agrees with me.
Apr
12
revised ElGamal: Generation of “g” value?
fixed obvious typo and added link
Apr
12
suggested suggested edit on ElGamal: Generation of “g” value?
Apr
12
answered ElGamal: Generation of “g” value?