All Questions
8 questions
44
votes
1
answer
17k
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Conjecturally unsafe RSA primes $p=27a^2+27a+7$
We got strong numerical evidence that primes of the form $p=27a^2+27a+7$
are unsafe for cryptographic purposes since they can be found in the factorization.
Consider the following generic factoring ...
- 25.4k
10
votes
3
answers
3k
views
Reduction from factoring to solving Pell equation
The paper Polynomial-Time Quantum Algorithms for Pell's Equation and the Principal Ideal Problem claims
There are reductions from factoring to solving Pell’s equation, and from solving Pell’s
...
- 25.4k
4
votes
1
answer
288
views
Is total degree version and $x,y$ degree version of Coppersmith's theorem correct?
The notes here https://web.eecs.umich.edu/~cpeikert/lic13/lec04.pdf have the note 'Small decryption exponent $d$: so far the best known attack recovers $d$ if it is less than $N^{.292}$. This uses a ...
- 13.9k
3
votes
1
answer
137
views
Subexponential algorithms that apply only one of factoring and discrete logarithm?
Shor (quantum polynomial), Number Field Sieve (subexponential), Pollard rho (square root) all have both factoring and discrete logarithm over $\mathbb F_p^*$ variants.
What are the subexponential ...
- 13.9k
2
votes
1
answer
262
views
Are there any homomorphic analog error correction code?
Are there any analog error correction codes that are additively and multiplicatively homomorphic?
- 41
2
votes
1
answer
258
views
Does this modification of the General Number Field Sieve factor integers?
The General Number Field Sieve
factors composite $n$ basically this way.
Select homogeneous polynomials with integer coefficients $f(x,y),g(x,y)$
s.t. $f(x,1),g(x,1)$ have common root modulo $n$ but ...
- 25.4k
0
votes
1
answer
431
views
Reason Coppersmith fails here?
Take classic problem of finding $P,Q$ in balanced semi-prime $N=PQ$.
$P$ has a binary expansion and so does $Q$. We can set the binary $0/1$ variables to be $x_1$ through $x_{\lceil\log P\rceil}$ and $...
- 13.9k
0
votes
0
answers
135
views
Can factorization of very large numbers be aided by associating them with a series (described below) of quadratic polynomials?
My name is J. Calvin Smith. I graduated in 1979 with a Bachelor of Arts in Mathematics from Georgia College in Milledgeville, Georgia. My Federal career (1979-2012) in the US Department of Defense led ...