CipherSaber encryption
Pyth, 100 bytes

$import os$KsM$os.urandom(10)$JuuXN@LN,T=+Z+@NT@+CMzKT)bGQU=b256=Z0sCM+K.exCb@=XJ=N@LJ,hk=+Z@Jhk)sNw


This script uses the $ command, which allows executing Python code. To prevent executing malicious code on the server, the this command is disabled in the online compiler. You have to run it with the off-line compiler which you can find here. 

The input is in the format: 

secret key
5 (number of repeats)
secret message


The program outputs the encrypted string, which might contain unprintable chars. If you want to verify it using the CipherSaber Encryption &amp; Decryption Tool, you can use the following code, which converts the string to a series of hexadecimal digits. 

$import os$KsM$os.urandom(10)$JuuXN@LN,T=+Z+@NT@+CMzKT)bGQU=b256=Z0         
jdm.[2.HCd`0
sCM+K.exCb@=XJ=N@LJ,hk=+Z@Jhk)sNw


Pyth doesn't support cryptographically secure pseudorandom numbers and importing them from Python costs 25 bytes. A shorter code, which uses Pyth's/Python's normar pseudorandom-number generator and also works in the online compiler is: 

KmO=b256TJuuXN@LN,T=+Z+@NT@+CMzKT)bGQUb=Z0sCM+K.exCb@=XJ=N@LJ,hk=+Z@Jhk)sNw


Try it online: returning a string or a series of hexadecimal digits

The code is nothing special. Just a lot of dirty assignments and immediate reuses of computed results and applying twice the list-swap trick. 

Explanation:

                                  implicit: z = 1st input (= key string)
                                  Q = 2nd input (number of repetitions)
$import os$KsM$os.urandom(10)$
$import os$                       import Python's os module
              $os.urandom(10)$    create 10 cryptographically secure 
                                  pseudo-random bytes
            sM                    convert them to ints
           K                      store them in K

JuuXN@LN,T=+Z+@NT@+CMzKT)bGQU=b256
                             =b256assign b with 256
 u                         QUb    start with G = [0, 1, ..., 255], 
                                  evaluate the following expression Q times and
                                  update G with the result each time:
  u                      bG         start with N = G, 
                                    for each T in [0, 1, ..., 255] evaluate the
                                    following expression and update N each time:
                   CMz                convert key to list of ints
                  +   K               extend it with K
                 @     T              take the Tth element (modulo length)
              @NT                     take the Tth element of N
             +                        add these two values
           +Z                         add Z (with is initially 0)
          =                           and update Z with the result
        ,T  Z                         make the pair of indices [T, Z] 
     @LN                              look-up their values in N
   XN                   )             and switch these two values in N
J                                 assign the result (the key setup) to J

=Z0                               set Z to 0

sCM+K.exCb@=XJ=N@LJ,hk=+Z@Jhk)sNw 
                                w read a string from input (message)
     .e                           map each index k, char b in message to:
                         @Jhk       look-up the (k+1)th element in J
                      =+Z           add it to Z and update Z
                   ,hk  Z           make the pair of indices [k+1,Z]
                @LJ                 look-up their values in J
              =N                    assign the result to N
            XJ N             )      swap these values in J
           =                        and update J with the result
          @  J                sN    take the sum(N)th element of J
        Cb                          convert b to int
       x                            bitwise xor of these two elements
   +K                             insert K at the beginning
 CM                               convert each element to char
s                                 sum them (generate a string)
                                  implicitly print