I read this question in my book (that doesn't have a response).
2DES is doubly more secure than DES?
I know that 2DES can be attacked from meet in the middle attack.
In fact, from Wikipedia Meet in the middle say :
The MITM attack is one of the reasons why Data Encryption Standard (DES) was replaced with Triple DES and not Double DES. An attacker can use a MITM attack to bruteforce Double DES with 2^57 operations and 2^56 space, making it only a small improvement over DES. Triple DES uses a "triple length" (168-bit) key and is also vulnerable to a meet-in-the-middle attack in 2^56 space and 2^112 operations, but is considered secure due to the size of its keyspace.
But DES use key from 2^56. 2DES with meet in the middle have 2^57 operation (that is exactly a double of 2^56) I'm not sure if the question ask a "doubly secure " in order to key space , so want a key big as 2^112 (that is double of 56 in previous DES).
I think that DES is double secure from this other phrase on Wikipedia that says:
Diffie and Hellman first proposed the meet-in-the-middle attack on a hypothetical expansion of a block cipher in 1977. Their attack used a space-time tradeoff to break the double-encryption scheme in only twice the time needed to break the single-encryption scheme.
So if 2 times Diffie/Hellman uses twice time to break the algorithm, also for 2DES we can use a double time of DES to break this algorithm.
Anyone can confirm my hypothesis?