Multiple Keys for 1 File

中文

Multiple keys for multiple files packed into one large file.

Given a key, you can extract the corresponding file.

At the same time, you can generate multiple partly true and partly false key sequences. In this way, you can safely hide the files you want to hide under duress.

Algorithm

Function

$$ \rm Encrypt(key_1,\cdots,key_n,file_1,\cdots,file_n)=bigfile, $$

$$ \rm Decrypt(key_x,bigfile)=file_x. $$

Even if know one $\rm key$, the rest still needs to be brute-force attacked.

Sequence

In the encoding process, each $\rm key_x$ is used to generate the sequence $\rm l_x.$ It becomes an infinite sequence through the ring structure, and satisfies

$$ \rm l_i[k]\neq l_j[k],l_i[k]\in\N\cap[0,n),\forall i\neq j,\forall k. $$

As you can see, these requirements are very demanding. So it is recommended to use the program to generate key sequences.

$\rm key\to int(base\ n)\to l_x.$

File Structure

The $\rm l_x$-th bit of the $\rm k$-th consecutive $\rm n$ bits of the large file, is exactly the $\rm k$-th bit of the small file $\rm file_x,$ i.e.

$$ \rm bigfile[(k-1)*n+l_x[k]]=file_x[k]. $$

When $\rm file_x[k]$ is not available, randomly generate it.

Brute-force Attack Time Complexity

$k$ keys, key length $l$ and number of files $n$ are known.

The maximum minimum cycle length of the subscript sequence is $m=\lceil\log_n256^l\rceil=\lceil8l\frac{\ln2}{\ln n}\rceil,$ and the time complexity of traversing all possible passwords is $O((n-k)^m)\simeq O(256^l).$

Other Possible Ways to Crack

One of the files is known, but the number of files, any keys or its length are not known. In this case, the time complexity required to crack the key corresponding to this file by means of brute-force attacking is $O(m^2n\log n).$

Interface

encrypt

Declaration

int encrypt(int n, int kn, char **ks, char **fs, const char *big = "big.bin");

Variables

Name	Type	Explain
n	int	the number of files (and keys) $n$
ks	int	key length $l$
fs	char **	small file path
big	const char *	large file (generation) path
return	int	0 is the normal return

Function

Save the keys and generate the large file.

decrypt

Declaration

int decrypt(const char *fk, const char *big, const char *fx);

Variables

Name	Type	Explain
fk	const char *	key file path
big	const char *	large file path
fx	const char *	corresponding small file (generation) path
return	int	0 is the normal return

Function

Decrypt the corresponding small file.