halacha - What is the origin of Dina DeMalchuta Dina, what is its reason?

As I know, halacha is based on Talmud, and Talmud is based on the Torah. Thus, Dina DeMalchuta Dina should also have the verses in the Torah, on which it is based on.

But as I know the Torah, I can't remember anything on it about the acknowledgement of foreign laws. As I know, Torah is about the Torah Law.

On my knowledge, Dina Demalchuta Dina could serve as an "interface" between the Torah Law and the law of the diaspora. But how is it rooted in the Torah?

Answer

The source for Dina D'malchusa Dina is from several places in the Talmud. One is in Gittin 10b:

אלא מתנה במאי קא קני לאו בהאי שטרא והאי שטרא חספא בעלמא הוא אמר שמואל דינא דמלכותא דינא

[When a transaction is made for a gift using a document processed in secular court], with what is the gift being acquired? Is it not with the document? And the document is worthless! Said Shmuel the law of the the land is the law

The Rishonim give several reasons for Dina D'Malchusa Dina. It is either due to the Torah acknowledging (and even mandating) the court systems of Gentiles (Rashi Gittin 9b):

כשרין - דדינא דמלכותא דינא ואע"פ שהנותן והמקבל ישראלים הם:
חוץ מגיטי נשים - דלאו בני כריתות נינהו הואיל ולא שייכי בתורת גיטין וקידושין אבל על הדינין נצטוו בני נח

(summary translation) documents processed in secular court are valid because of Dina D'Malchusa Dina. Divorce documents are not valid, because [Gentiles] do not have any concept of gittin and kiddushin. But they were commanded to set up courts.

or an implied acceptance of the jurisdiction of the ruler by the residents (Rashbam Bava Basra 54b and Rashba to Yevamos 46a):

כל מסים וארנוניות ומנהגות של משפטי מלכים שרגילים להנהיג במלכותם דינא הוא שכל בני המלכות מקבלים עליהם מרצונם חוקי המלך ומשפטיו

Any taxes and tarrifs and legal customs of the rulers that they apply in their kingdoms are valid, because all the people of the kingdom accept upon themselves willingly the laws and regulations of the king.

or a product of the Kings's ownership of the land (Ran Nedarim 28a):

וכתבו בתוספות דדוקא במלכי עובדי כוכבים אמר דדינא דמלכותא דינא מפני שהארץ שלו ויכול לומר להם אם לא תעשו מצותי אגרש אתכם מן הארץ

In Tosefos it is written that specifically by Gentile kings it is said that the law of the land is the law, because the country is his and he can tell them do what I say or I will exile you from the land

or a form of "hefker beis din hefker (Rabbeinu Yona Bava Basra 54b)