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Dec
6
comment Why are these techniques not feasible to crack RSA?
It seems I misunderstood what you said earlier. You're correct.
Dec
6
comment Why are these techniques not feasible to crack RSA?
It's actually equivalent to factoring: you can compute $\phi(n)$ quickly from the factors, and you can find the factors quickly from $phi(n)$. No, $d = 1/e \bmod \phi(n)$. This does not result in a fraction, because we are working in modular arithmetic. There are efficient algorithms to do this.
Dec
6
comment Why are these techniques not feasible to crack RSA?
Like factoring, it becomes much harder as $n$ grows. If you try to do it for a $2048$-bit $n$, it will not be so easy.
Dec
6
comment Why are these techniques not feasible to crack RSA?
To solve for $d$, you must find out $\phi(n)$, since $d = e^{-1} \bmod \phi(n)$. That is the hard part.
Dec
6
answered Why are these techniques not feasible to crack RSA?
Dec
5
revised counting points on elliptic curve
added 4 characters in body
Dec
5
revised counting points on elliptic curve
added 3 characters in body
Dec
5
revised counting points on elliptic curve
added 70 characters in body
Dec
5
answered counting points on elliptic curve
Dec
4
comment Keyed digest function with odds of collision below the birthday bound?
Are you aware of any attempt to invert such permutations faster than brute-force? First step would probably be to distinguish the polynomial system from random.
Nov
26
answered Adding and multiplication in jacobian coordinates
Nov
21
comment When using Curve25519, why does the private key always have a fixed bit at 2^254?
It is true that the reference code protects against this by starting with $(P, \infty)$; however, every textbook displays the version I described, so there's a good chance that an independent implementer could make that mistake. Setting that bit to 1 is a preventive measure that costs almost nothing.
Nov
20
answered When using Curve25519, why does the private key always have a fixed bit at 2^254?
Nov
20
answered Why does the crypto_box functionality in NaCl library exposes the nonce to the programmer
Nov
8
comment What is so special about elliptic curves?
A sphere ($x^2 + y^2 + z^2 = 1$) would still not be secure; however, if you intersect two quadric surfaces (i.e. surfaces defined by quadratic polynomials) you actually can get a secure curve, which --- guess what --- is actually an elliptic curve! The Jacobi intersection curves are an example of this.
Nov
5
awarded  Nice Answer
Nov
5
answered What is so special about elliptic curves?
Oct
30
awarded  Civic Duty
Oct
3
revised How should I interpret this note on diffusion of the internal state of a PRNG?
added 68 characters in body
Oct
3
answered How should I interpret this note on diffusion of the internal state of a PRNG?