KASUMI is a block cipher used in UMTS, GSM, and GPRS mobile communications systems.
In UMTS, KASUMI is used in the confidentiality (f8) and integrity algorithms (f9) with names UEA1 and UIA1, respectively.
In GSM, KASUMI is used in the A5/3 and A5/4 key stream generator and in GPRS in the GEA3 and GEA4 key stream generator.
KASUMI was designed for 3GPP to be used in UMTS security system by the Security Algorithms Group of Experts
(SAGE), a part of the European standards body ETSI.
Because of schedule pressures in 3GPP standardization, instead of developing a new cipher, SAGE agreed with
3GPP technical specification group (TSG) for system aspects of 3G security (SA3) to base the development
on an existing algorithm that had already undergone some evaluation.
They chose the cipher algorithm MISTY1 developed
and patented
by Mitsubishi Electric Corporation.
The original algorithm was slightly modified for easier hardware implementation and to
meet other requirements set for 3G mobile communications security.
KASUMI is named after the original algorithm MISTY1 — 霞み (hiragana かすみ, romaji kasumi) is the Japanese word for "mist".
In January 2010, Orr Dunkelman, Nathan Keller and Adi Shamir released a paper showing that they could break Kasumi with a related-key attack and very modest computational resources; this attack is ineffective against MISTY1.
Contents
Description
KASUMI algorithm is specified in a 3GPP technical specification.
KASUMI is a block cipher with 128-bit key and 64-bit input and output.
The core of KASUMI is an eight-round Feistel network. The round functions
in the main Feistel network are irreversible Feistel-like network
transformations. In each round the round function uses a round key
which consists of eight 16-bit sub keys
derived from the original 128-bit key using a fixed key schedule.
Key schedule
The 128-bit key K is divided into eight 16-bit sub keys Ki:
K
=
K
1
‖
K
2
‖
K
3
‖
K
4
‖
K
5
‖
K
6
‖
K
7
‖
K
8
{\displaystyle K=K_{1}\|K_{2}\|K_{3}\|K_{4}\|K_{5}\|K_{6}\|K_{7}\|K_{8}\,}
Additionally a modified key K', similarly divided into 16-bit
sub keys K'i, is used. The modified key is derived from
the original key by XORing with 0x123456789ABCDEFFEDCBA9876543210 (chosen as a "nothing up my sleeve" number).
Round keys are either derived from the sub keys by bitwise rotation to left
The algorithm
KASUMI algorithm processes the 64-bit word in two 32-bit halves, left (
L
i
{\displaystyle L_{i}}
)
and right (
R
i
{\displaystyle R_{i}}
).
The input word is concatenation of the left and right halves of the first round:
i
n
p
u
t
=
R
0
‖
L
0
{\displaystyle {\rm {input}}=R_{0}\|L_{0}\,}
.
In each round the right half is XOR'ed with the output of the round function
after which the halves are swapped:
L
i
=
F
Cryptanalysis
In 2001, an impossible differential attack on six rounds of KASUMI was presented by Kühn (2001).
In 2003 Elad Barkan, Eli Biham and Nathan Keller demonstrated man-in-the-middle attacks against the GSM protocol which avoided the A5/3 cipher and thus breaking the protocol. This approach does not attack the A5/3 cipher, however. The full version of their paper was published later in 2006.
In 2005, Israeli researchers Eli Biham, Orr Dunkelman and Nathan Keller published a related-key rectangle (boomerang) attack on KASUMI that can break all 8 rounds faster than exhaustive search.
The attack requires 254.6 chosen plaintexts, each of which has been encrypted under one of four related keys, and has a time complexity equivalent to 276.1 KASUMI encryptions. While this is obviously not a practical attack, it invalidates some proofs about the security of the 3GPP protocols that had relied on the presumed strength of KASUMI.
In 2010, Dunkelman, Keller and Shamir published a new attack that allows an adversary to recover a full A5/3 key by related-key attack. The time and space complexities of the attack are low enough that the authors carried out the attack in two hours on an Intel Core 2 Duo desktop computer even using the unoptimized reference KASUMI implementation. The authors note that this attack may not be applicable to the way A5/3 is used in 3G systems; their main purpose was to discredit 3GPP's assurances that their changes to MISTY wouldn't significantly impact the security of the algorithm.