Cryptography Reference
In-Depth Information
1. Let's assume that one core iteration can be performed in one clock cycle. De-
velop an expression for the required clock frequency for encrypting a stream of
data with a data rate
r
[bit/sec]. Ignore the time needed for the initial and final
permutation.
2. What clock frequency is required for encrypting a fast network link running at a
speed of 1 Gb/sec? What is the clock frequency if we want to support a speed of
8 Gb/sec?
3.11.
As the example of COPACOBANA [105] shows, key-search machines need
not be prohibitive from a monetary point of view. We now consider a simple brute-
force attack on DES which runs on COPACOBANA.
1. Compute the runtime of an average exhaustive key-search on DES assuming the
following implementational details:
COPACOBANA platform with 20 FPGA modules
6 FPGAs per FPGA module
4 DES engines per FPGA
Each DES engine is fully pipelined and is capable of performing one encryp-
tion per clock cycle
100 MHz clock frequency
2. How many COPACOBANA machines do we need in the case of an average
search time of one hour?
3. Why does any design of a key-search machine constitute only an upper security
threshold? By
upper security threshold
we mean a (complexity) measure which
describes the maximum security that is provided by a given cryptographic algo-
rithm.
3.12.
We study a real-world case in this problem. A commercial file encryption
program from the early 1990s used standard DES with 56 key bits. In those days,
performing an exhaustive key search was considerably harder than nowadays, and
thus the key length was sufficient for some applications. Unfortunately, the imple-
mentation of the key generation was flawed, which we are going to analyze. Assume
that we can test 10
6
keys per second on a conventional PC.
The key is generated from a password consisting of 8 characters. The key is a
simple concatenation of the 8 ASCII characters, yielding 64 = 8
·
8 key bits. With
the permutation
PC
1 in the key schedule, the least significant bit (LSB) of each
8-bit character is ignored, yielding 56 key bits.
−
1. What is the size of the key space if all 8 characters are randomly chosen 8-bit
ASCII characters? How long does an average key search take with a single PC?
2. How many key bits are used, if the 8 characters are randomly chosen 7-bit ASCII
characters (i.e., the most significant bit is always zero)? How long does an aver-
age key search take with a single PC?
3. How large is the key space if, in addition to the restriction in Part 2, only let-
ters are used as characters. Furthermore, unfortunately, all letters are converted
