I am teaching cryptography this semester for the second time (I taught it in Fall 2019) and will soon tell the students about the paper from 2015:

Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice. There are 14 authors.

The upshot is that as Diffie-Hellman was implemented in 2015, many cases were crackable. In summary (and probably too simple):

DH in a 512-bit group can be cracked by the authors

DH in a 1024-bit group they speculate can be cracked with nation-state resources.

Is this a big deal? If YES then what is being done, and if NOT then why not?

I have come up with some statements that I DO NOT KNOW if they are true, but I am ASKING you, to shed some light on the BIG DEAL or NO BIG DEAL question. (Note- Idea for a game show: BIG DEAL or NO BIG DEAL where contestants are asked if a news story is a BIG DEAL or not.)

So, please comment on the following question:

1) Since 2015 the people who use DH have upped their game and are now using bigger parameters. (I doubt this is true)

2) DH is mostly not used on things that hackers are not interested in, so this is not a big deal.

3) The expertise required to crack DH via this paper is rather difficult, so hackers don't have the skills.

4) This paper is not a problem for a bad reason: Hackers don't need to use the number field sieve DL algorithm when all they need to do is (1) guess that the pin numer is 1234 or the year the user was born (or close to it), (2) put on a uniform from Geek-Squad or some such organization and claim they are here to help, (3) exploit a known security flaw that the company has not bothered fixing.

5) The 14 authors have mysteriously disappeared. (I doubt this is true.)

(Misc: My spell checker thinks that Diffie and crackable are not words, but Hellman is.)

## Monday, September 16, 2019

## Monday, September 09, 2019

### Are there any natural problems complete for NP INTER TALLY? NP INTER SPARSE?

Recall:

A is a

*tally set*if A ⊆ 1

^{*}.

A is a

*sparse set*if there is a polynomial p such that the number of strings of length n is ≤ p(n).

If there exists a sparse set A that is NP-hard under m-reductions (even btt-reductions) then P=NP. (See this post.)

If there exists a sparse set A that is NP-hard under T-reductions then PH collapses. (See this post.)

Okay then!

I have sometimes had a tally set or a sparse set that is in NP and I think that its not in P. I would like to prove, or at least conjecture, that it's NP-complete. But alas, I cannot since then P=NP. (Clarification: If my set is NP-complete then P=NP. I do not mean that the very act of conjecturing it would make P=NP. That would be an awesome superpower.)

So what to do?

A is

*NPSPARSE-complete*if A is in NP, A is sparse, and for all B that are in NP and sparse, B ≤

_{m}A.

Similar for NPTALLY and one can also look at other types of reductions.

So, can I show that my set is NPSPARSE-complete? Are there any NPSPARSE-complete sets? Are there NATURAL ones? (Natural is a slippery notion- see this post by Lance.)

Here is what I was able to find out (if more is known then please leave comments with pointers.)

1) It was observed by Bhurman, Fenner, Fortnow, van Velkebeek that the following set is NPTALLY-complete:

Let M

_{1}, M

_{2}, ... be a standard list of NP-machines. Let

A = { 1

^{(i,n,t)}: M

_{i}(1

^{n}) accepts on some path within t steps }'

The set involves Turing Machines so its not quite what I want.

2) Messner and Toran show that, under an unlikely assumption about proof systems there exists an NPSPARSE-complete set. The set involves Turing Machines. Plus it uses an unlikely assumption. Interesting, but not quite what I want.

3) Buhrman, Fenner, Fortnow, van Melkebeek also showed that there are relativized worlds where there are no NPSPARSE sets (this was their main result). Interesting but not quite what I want.

4) If A is NE-complete then the tally version: { 1

^{x}: x is in A } is likely NPTALLY-complete. This may help me get what I want.

Okay then!

Are there any other sets that are NPTALLY-complete. NPSPARSE-complete? The obnoxious answer is to take finite variants of A. What I really want a set of such problems so that we can proof other problems NPTALLY-complete or NPSPARSE-complete with the ease we now prove problems NP-complete.

## Thursday, September 05, 2019

### Transitioning

You may have noticed, or not, that I haven't posted or tweeted much in the last month. I've had a busy time moving back to Chicago and starting my new position as Dean of the College of Science at Illinois Tech.

Part of that trip involved driving my electric Chevy Bolt from Atlanta to Chicago. You can do it, but it got a bit nerve wracking. There is only one high-speed charging station between Indianapolis and Chicago and you pray the charger outside the Lafayette Walmart actually works (it did). We passed many Tesla charging superstations, I will have to admit they have the better network.

Theoremwise, Ryan Alweiss, Shachar Lovett, Kewen Wu and Jiapeng Zhang had significant improvements on the sunflower conjecture. I posted on the sunflower theorem for Richard Rado's centenary. Nice to see there is still some give in it.

I probably will post less often in this new position. Bill asked me "Why is being a dean (or maybe its just the move) more time then being a chair? Were you this busy when you moved and first became chair?"

When I moved to Atlanta, I moved a year ahead of the rest of the family and rented a condo. We had plenty of time to search for a house in Atlanta and plan the move. Here it all happened in a much more compressed time schedule and, since we've bought a condo, into a much more compressed space.

When I moved to Atlanta, I moved a year ahead of the rest of the family and rented a condo. We had plenty of time to search for a house in Atlanta and plan the move. Here it all happened in a much more compressed time schedule and, since we've bought a condo, into a much more compressed space.

Being a chair certainly ate up plenty of time but it feels different as dean with a more external focus. I won't give up the blog but you'll probably hear a lot more from Bill than from me at least in the near future.

## Tuesday, September 03, 2019

### Can Mathematicians Fix Iphones? Can anyone?

In my last post I noted that if I am asked (since I am a CS prof)

*Can you fix my iphone*

is

*No, I work on the math side of CS*

Some readers emailed me (I told them to comment instead but they were worried that other readers would argue with them) that NO, this is a tired and incorrect stereotype. Here are some samples:

1) People in Mathematics are no better or worse at fixing iphones, fixing cars, programming their VCR's, etc than the public.

2) For that matter, people in academica, even in practical sounding fields like Systems, are no better.

3) Is your nephew Jason who used to fix forklifts for a living better at these things then the general public? I asked him. Answer: No, though he is better at fixing forklifts.

I think something else is going on here. Lets look at fixing your own car. I think this is the sort of thing that some people used to be able to do but now very few can do it. Cars have gotten more complicated.

Iphones are not quite there yet but its getting that way.

Of course somethings have gotten easier--- programming a DVR is much easier than programming a VCR. And people can easily use WORD or write programs without having to know any hardware.

OKAY, after all these random thoughts, here is the question: What do you think?

Are people in CS or Math or CS theory better at X than the general public where X is NOT CS, Math or CS theory, but something like fixing their cars?

And

What has gotten harder? What has gotten easier?

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