FL Functions Research Articles

Correlation Power Analysis of KASUMI and Power Resilience Analysis of Some Equivalence Classes of KASUMI S-Boxes

The KASUMI block cipher imparts confidentiality and integrity to the 3G mobile communication systems. In this paper, we present power analysis attack on KASUMI as a two-pronged attack: first, the FL function is targeted, and subsequently the recovered output of FL function is used to mount attack on 7 × 7 and 9 × 9 S-boxes embedded in the FO function of the cipher. Our attack recovers all 128 bits of the secret key of KASUMI. Furthermore, we present a countermeasure for this attack which requires lesser resource footprint as compared with existing countermeasures, rendering such implementations practically feasible for resource-constrained applications, such as IoT and RFID devices. In addition, we propose linear equivalent mappings and Permutation-XOR equivalent mappings of 7 × 7 S-boxes which have stronger resilience against power analysis attacks with respect to the improved transparency order and confusion coefficient parameters while restoring the classical cryptographic properties. We point out some properties of linear equivalence (LE) classes of these S-boxes with respect to these metrics as well.

Improved KASUMI block cipher for GSM-based mobile networks

ABSTRACT KASUMI is an eight-round Feistel network that produces 64-bit output from 64-bit input by using 128-bit key. Three functions FL, FO and FI are involved in each round and each function has its respective keys KL, KO and KI . In this work, modifications in the existing KASUMI are proposed to reduce the encryption time. In proposed KASUMI, the single FL function is divided into two functions such as FLleft and FLright. The FLleft function is constructed with two Rijndael’s 32-bit S -boxes. The FLright function is constructed with four stages where third and fourth stages are performing XOR and shift operations before final concatenation of two 16-bit data of FL function. The simulation results are provided in terms of encryption time taken versus number of iteration and encryption speed versus number of iteration to show that the proposed KASUMI block cipher design outperforms the conventional KASUMI block cipher.

Reducing the time required by KASUMI to generate output by modifying the FL and FI functions

KASUMI is an eight-round Fiestel network that produces 64-bit output data from 64-bit input data using a 128-bit key. Three functions, FL, FO, FI , are involved in each round and each function has its respective keys KL, KO, KI. This work proposed the modifications in existing KASUMI block cipher, which can reduce time delay for generating 64-bit encrypted data. Also, we proposed a modification in FL functions: FL(a) and FL(b) of the existing KASUMI block cipher. Rijndael’s 32-bit S-box is introduced in FL (a) function of standard FL function so that it can only work with 16-bit data. The second modification is introduced in the FL(b) function by adding a third stage where XOR and shift operations are involved before the final concatenation of two 16-bit data inside the standard FL function. In addition, the FI function uses S7 and S9 tables only one time instead of two times in the existing KASUMI block cipher, which leads to reduce the overall time delay. The performance improvement of the proposed algorithm over the conventional algorithm is verified by simulation results.

Highly optimised reconfigurable hardware architecture of 64 bit block ciphers MISTY1 and KASUMI

Highly optimised reconfigurable hardware architecture is proposed of 64 bit block ciphers MISTY1 and KASUMI for wide-area cryptographic applications. The reconfigurable hardware architecture is comprised of reconfigurable components consisting of FL function, FO/FI function and XOR function designed to perform MISTY1 and KASUMI algorithms round transformation functions. In addition, reconfigurable FO/FI function is adequate to generate MISTY1 extended keys for onward use in MISTY1 round transformation function. The substitution functions S9 and S7 for MISTY1 and KASUMI algorithms are optimised for area and throughput. Common sub-expression elimination for AND-XOR logic combined with permutation/combination technique for AND gates reduces the area considerably, whereas parallel execution improves the throughput. With this design approach, application specific integrated circuit (ASIC) implementations using Synopsys Design Complier, SMIC 0.18 µm at 1.8 V achieved an area of 3481 NAND gates having throughput of 130.2 and 154.56 Mbits/s for MISTY1 and KASUMI, respectively. Synthesised FPGA implementation using Xilinx Artix 7 FPGA yielded an area of 487 configurable logic block (CLB) Slices having throughput of 209.43 and 248.7 Mbits/s for MISTY1 and KASUMI, respectively. Detailed design and performance analysis of reconfigurable hardware architecture of 64 bit block ciphers MISTY1 and KASUMI for ASIC implementations is described.

Practical-time attacks against reduced variants of MISTY1

MISTY1 is a block cipher designed by Matsui in 1997. It is widely deployed in Japan where it is an e-government candidate recommended cipher, and is recognized internationally as a NESSIE-recommended cipher as well as an ISO/IEC standard and an RFC. Moreover, MISTY1 was selected to be the blueprint on top of which KASUMI, the GSM/3G block cipher, was based. Since its introduction, and especially in recent years, MISTY1 was subjected to extensive cryptanalytic efforts, which resulted in numerous attacks on its reduced variants. Most of these attacks aimed at maximizing the number of attacked rounds, and as a result, their complexities are highly impractical. In this paper we pursue another direction, by focusing on attacks of practical time complexity. We present the first practical-time attack on 5-round MISTY1 which exploits only the linear $$FL$$FL functions, and thus, remains valid even if the non-linear $$FO$$FO functions are replaced. On the other extreme, we show the importance of the $$FL$$FL layers, by presenting a devastating (and experimentally verified) related-key attack that can break MISTY1 with no $$FL$$FL layers, requiring only $$2^{18}$$218 data and time. While our attacks clearly do not compromise the security of the full MISTY1, they expose several weaknesses in the components used in MISTY1, and improve our understanding of its security. These insights are also applicable to future designs which rely on MISTY1 as their base, and should be taken into close consideration by designers.

Finding Higher Order Differentials of MISTY1

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.

Security Analysis of 7-Round MISTY1 against Higher Order Differential Attacks

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper shows that higher order differential attacks can be successful against 7-round versions of MISTY1 with FL functions. The attack on 7-round MISTY1 can recover a partial subkey with a data complexity of 254.1 and a computational complexity of 2120.8, which signifies the first successful attack on 7-round MISTY1 with no limitation such as a weak key. This paper also evaluates the complexity of this higher order differential attack on MISTY1 in which the key schedule is replaced by a pseudorandom function. It is shown that resistance to the higher order differential attack is not substantially improved even in 7-round MISTY1 in which the key schedule is replaced by a pseudorandom function.

Higher Order Differential Attack on 6-Round MISTY1

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.

The New Block Cipher: BC2

In this paper, we propose a new block cipher called BC2 (Block Cipher 2). We make a cipher using components that are believed secure. The structure of BC2 is very simple. We use Feistel network with input-output 128 bits, matrix Maximum Distance Separable (MDS) 8x8 with branch number 9 to give high diffusion, a function affine equivalent to the inverse function in GF(2^8) that we get from Camellia and Hierocrypt S-Box for confusion and we make FN function, based on FL function of Camellia. We use a heuristic method to count the minimum number of active substitution box at Feistel Network. And we also construct a new key schedule that is fast and secure.

Fluffy, the major regulator of conidiation in Neurospora crassa, directly activates a developmentally regulated hydrophobin gene

The fluffy (fl) gene of Neurospora crassa is required for asexual sporulation and encodes an 88 kDa polypeptide containing a typical fungal Zn2Cys6 DNA-binding motif. Identification of genes regulated by fl will provide insight into how fungi regulate growth during morphogenesis. As a step towards identifying the target genes on which FL may act, we sought to define target sequences to which the FL protein binds. The DNA binding domain of FL was expressed in Escherichia coli as a fusion with glutathione S-transferase (GST) and purified using glutathione-sepharose affinity chromatography. The DNA binding sites were selected and amplified by means of a polymerase chain reaction (PCR)-mediated random-site selection method involving affinity bead-binding and gel mobility shift analysis. Sequencing and comparison of the selected clones suggested that FL binds to the motif 5'-CGG(N)9CCG-3'. A potential binding site was found in the promoter region of the eas (ccg-2) gene, which encodes a fungal hydrophobin. In vitro competitive binding assays revealed a preferred binding site for FL in the eas promoter, 5'-CGGAAGTTTC CTCCG-3', which is located 1498 bp upstream of the eas translation initiation codon. In vivo experiments using a foreign DNA sequence tag also confirmed that this sequence resides in a region required for FL regulation. In addition, yeast one hybrid experiments demonstrated that the C-terminal portion of FL functions in transcriptional activation. Transcriptional profiling was used to identify additional potential targets for regulation by fl.

The (Non)Enumerability of the Determinant and the Rank

We investigate the complexity of enumerative approximation of two fundamental problems in linear algebra, computing the rank and the determinant of a matrix. We show that both are as hard to approximate (in the enumerative sense) as to compute exactly. In particular, if there exists an enumerator that, given a matrix over some finite field, outputs a list of constantly many numbers, one of which is guaranteed to be the rank of the matrix, then it can be determined in AC 0 (with oracle access to the enumerator) which of these numbers is the rank. Thus, for example, if the enumerator is an FL function, then the problem of computing the rank is in FL. For the determinant function we establish the following two results: (1) If the determinant is poly-enumerable in logspace, then it can be computed exactly in FL. (2) For any prime p , if computing the determinant modulo p is (p-1) -enumerable in FL (i.e., if one could eliminate a single possible value for the determinant modulo p ), then the determinant modulo p can be computed in FL. Because there is a close connection between these two functions and logspace counting classes, we hope that our results can give a better understanding of the power of counting in logspace, and the relationships among the complexity classes sandwiched between NL and uniform TC 1 .