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I'm an engineer with experience in applied cryptography, in particular in Smart Card systems.


Dec
10
revised Statistical properties of hash functions when calculating modulo
Improve the TeX content
Dec
10
answered Statistical properties of hash functions when calculating modulo
Dec
10
comment How Brittle Are LCG-Cracking Techniques?
If with enough output your method (or that of Stern improved by Contini & Shparlinski) could solve Case 2 with only say the 4 top bits of the output, then we could enumerate the $2^4$ possible values of the XOR mask, and solve Case 3 by solving Case 2 at most 16 times.
Dec
10
revised How Brittle Are LCG-Cracking Techniques?
Simplify the formula; some duplicate SAT variables can be eliminated
Dec
10
revised Streaming API to authenticated encryption
Improve understandability of the last example
Dec
9
comment Polynomial Modulus
Hint: for a.) the first steps are: $x^{16}=x^{12}(x^4+x^3+1)+x^{15}+x^{12}$, therefore $x^{16}\equiv x^{15}+x^{12}\pmod{f(x)}$; $\;$ $x^{15}+x^{12}=x^{11}(x^4+x^3+1)+x^{14}+x^{12}+x^{11}$, therefore $x^{16}\equiv x^{14}+x^{12}+x^{11}\pmod{f(x)}$.
Dec
9
revised Polynomial Modulus
Texify
Dec
9
comment How Brittle Are LCG-Cracking Techniques?
@Charphacy: I have adapted my answer per your last comment.
Dec
9
revised How Brittle Are LCG-Cracking Techniques?
Further align notation; take comment into account
Dec
9
comment Cocks IBE Scheme: why is -a a quadratic residue mod n?
Quoting Wikipedia: modulus some composite not a prime power, the product of two nonresidues may be either a residue, a nonresidue, or zero
Dec
9
revised How Brittle Are LCG-Cracking Techniques?
Align to other answer's notation for the multiplier
Dec
9
revised How Brittle Are LCG-Cracking Techniques?
Repair adder formula, link for that
Dec
9
revised How Brittle Are LCG-Cracking Techniques?
Leave Case 2 to others; slight simplification by searchign for i' rather than i; use M rather than n; polish.
Dec
9
comment Fermats Little Theorem, primitive root
Hint: assume $x$ is such that $2^x\equiv3\pmod p$ with $p=3\cdot2^k−1$. $\;$ What's the smallest $y$ such that $2^{x+y}\equiv1\pmod p$? $\;$ Now, assume $p$ is prime, what would be a value of $x+y$ such that $2^{x+y}\equiv1\pmod p$? That should be enough to find a value of $x$ that could do the job. Now, prove that it does.
Dec
8
comment How Brittle Are LCG-Cracking Techniques?
@Charphacy: I have an itch to try the SAT approach (no insurance). I think that I can't use the LLL, because there is too little output to carry it, at least the way that I have sketched it (did not check the references in detail).
Dec
8
revised How Brittle Are LCG-Cracking Techniques?
Link to SAT solvers
Dec
8
revised How Brittle Are LCG-Cracking Techniques?
Give references
Dec
8
revised How Brittle Are LCG-Cracking Techniques?
Some polish
Dec
8
answered How Brittle Are LCG-Cracking Techniques?
Dec
7
comment How Brittle Are LCG-Cracking Techniques?
@Thomas M. DuBuisson: interesting; if time allows I'll try translation to SAT by more primitive means, and state-of-the-art solvers. $\;$ Side note: the @ sign before a name in a comment creates a notification; the name itself does not.