## encryption – Group Instant Messaging: How to securely store messages on the backend while supporting cross-device message history in a group chat?

I want to build a group chat app where messages are transmitted and stored as securely as they can be, but where the message history is still visible after you or others in the group have changed devices. From my understanding, PFS isn’t possible here.

It seems that WhatsApp has implemented PFS, which makes sense because its experience is such that, if you change devices, the previous history is gone/not decryptable. But, after researching Messenger and Discord, seems that they store everything in cleartext? Messenger has a “secret messages” mode, which appears to use PFS, however.

Anyway, my first thought here is to have two public/private key pairs for the user (account, and device), and one symmetric key for the group to decrypt messages. For the sake of simplicity, this example assumes that a user can only be in one group chat. My thought is that it would work this way:

1. A user has a public/private key pair generated when they sign up (we will refer to this as the account encryption key pair). This will be used for direct user-to-user messaging where history needs to be kept.
2. When a user logs into a device, they generate a public/private key pair for the device. The public key from this pair is sent to the server. The server then sends the user the account key pair and the group chat’s symmetric key, and both are encrypted with the device’s public key.
3. If the user changes devices, a new device key pair is generated.

This obviously adds a level of safety, but I’m still uncomfortable with this approach, because nothing prevents someone from getting around the server permissions (though there will be IAM) and grabbing all these keys. I also am not sure the best way to store the group chats’ symmetric keys.

Another constraint is that I may not be able to store duplicate messages that are encrypted with everyone’s public keys because of storage costs. Please also assume that a key management service like Keysafe or KMS is available, though they obviously come with limits.

What do you guys think? Am I being stupid? I looked at some other similar posts, but saw answers that didn’t include tangible solutions.

I manage a Facebook page on which we use Messenger quite a lot to interact with our audience. For other tools I’d like to download transcripts of all conversations over time but I cannot find how.

## visas – Accidentally entered wrong dates in my travel history

I submitted am application for Tier 4 Student Visa UK. I’ve submitted the online application. I just realized i entered wrong dates in my travel history. I traveled to Russia and Egypt in summer 2018, I accidentally entered Egypt’s entry and exit dates for Russia and vice versa. How big of an issue will it be?

## history – Satoshi introduced the 1MB block size limit in a commit. Why did Andresen make an identical commit some days later?

Satoshi added the 1MB block size limit in this commit on 15 July 2010

Why did Andresen make an identical commit on 19 Jul 2010?

I realise it was enforced in a later commit via UASF, but the question remains, why are there two identical commits? Have I misunderstood the workflow? Did Andresen make changes when transitioning from SourceForge to GitHub in 2011?

TLDR: What is the purpose of two identical commits with different dates in the GitHub history?

## windows – Is it legal for schools to view your internet history?

Basically, my school “upgraded” their internet so we can only connect to it if we link our computers to Education Queensland microsoft accounts (we need to use our own laptops for school). This means they can ‘manage’ security and wifi, and basically they can view our full internet history at any time, including incognito (as shown on the Chrome incognito New Tab page). We’re children – is this even legal?

## darktable – How to go back to a snapshot after moving elsewhere in history?

I was editing my photo in DarkTable.

I took a snapshot and then went back in the history and tried to use a different approach to editing my photo.

My new approach looked worse than the snapshot of my previous edits.

How can I now go back to the snapshot that I took and keep editing from there?

Kinda weird the manual doesn’t even mention it.

## fa.functional analysis – History of the Lewis-Stegall theorem on factorization of representable operators

The following questions are about the history of a particular result in functional analysis, hence not “mathematical questions” per se; but I think they are relevant to the business of writing research papers in mathematics and to curating the research literature, and I think that they concern something sufficiently specialized and “recent” that MO is a more suitable place for the question than HSM.SE.

A bounded operator $$T$$ from $$L_1(0,1)$$ to a Banach space $$X$$ is said to be representable if it can be written as
$$T(f) = int_0^1 f(t) {bf h}(t),dt quadquadhbox(fin L_1)$$
for some bounded and strongly measurable function $${bf h}: (0,1)to X$$. The following result is known as the Lewis—Stegall theorem:

Theorem. $$T:L_1(0,1)to X$$ is representable if and only if there exist bounded operators $$S:L_1(0,1)toell_1$$ and $$R:ell_1to X$$ such that $$T=RS$$.

The proof can be found in various books, with varying degrees of self-contained-ness. (Three such sources known to me are the Diestel–Uhl book on Vector Measures, the appendices of the Defant–Floret book on Tensor Norms and Operator Ideals, and Ryan’s Introduction to Tensor Products of Operator Spaces) However, I am having difficulty tracking down the first place in the literature where this result was explicitly stated and attributed to Lewis and Stegall.

Diestel and Uhl give as a reference the 1973 paper of Lewis and Stegall (J. Functional Analysis) on Banach spaces whose duals are isomorphic to $$l_1(Gamma)$$ but the paper itself never actually mentions representable operators. It does seem that one can extract a proof of this factorization result from results in their paper, provided one knows an alternative characterization of representable operators as those whose composition with the canonical map $$L_infty(0,1)to L_1(0,1)$$ is nuclear, but the earliest explicit reference I have found for that fact is a 1976 paper of Linde (Math. Nachricten).

The best I have managed so far is the appendix of Rosenthal’s 1975 Bull. AMS article on The Banach spaces $$C(K)$$ and $$L^p(mu)$$ where the theorem stated above occurs, albeit with slightly different terminology, as Theorem A3. In the proof Rosenthal does not explicitly credit the result to Lewis and Stegall, but he mentions that for a representable $$T$$

We are indebted to D. Lewis for the observation that $$T$$ may be realized as an “$$l^1$$-sum” of compact operators, each of which may be factored through $$l^1$$ by the “lifting property”
of $$L^1(lambda)$$-spaces.

Indeed this decomposition as a block-diagonal “sum” of compact operators does occur in the original paper of Lewis and Stegall, but as mentioned above they were working with the “$$L_infty(0,1)to L_1(0,1)to X$$ is nuclear” formulation rather than representability by an element of $$L_infty((0,1);X)$$.

Question 1. What is the earliest record in the literature of the Lewis–Stegall theorem, in the form stated at the start of my post, being attributed to Lewis and Stegall?

(I am not trying to deny them credit since there seems to be consensus that they were fully aware that methods from their paper yielded this result, but I am a little frustrated when I have to hunt down papers in the literature only to find that they do not say what the secondary literature claims they say.)

Question 2. Given that the MO readership includes some long-standing members of the community of Banach space theory, does anyone have anecdotal/verbal information of how this particular result — rather than the headline result of the JFA 1973 paper — came to be known as the Lewis–Stegall theorem?

## What is the abbreviation standard that the U.S. Customs and Border Protection’s travel history is following for the locations?

What is the abbreviation standard that the U.S. Customs and Border Protection’s travel history is following for the locations?

E.g. I see BOS = Boston; HOU = Houston; LOS = Los Angeles; SEA = Seattle; SFR = San Francisco.

## exchanges – Bittrex API market history — interpreting OrderType

The Bittrex API has a request to get the market history:

``` https://bittrex.com/api/v1.1/public/getmarkethistory?market=BTC-DOGE ```

which gives a response containing the following fields:

• “Id”
• “TimeStamp”
• “Quantity”
• “Price”
• “Total”
• “FillType”
• “OrderType”

`"OrderType"` can be one of `"BUY"` or `"SELL"`. What does this refer to?

Let’s assume it has a value of “SELL”. Does this mean:

1. The person who initially placed the order was selling (Seller is Maker).
2. The person who closed the order was selling (Seller is Taker)