A Review of Existing 4-bit Crypto S-box cryptanalysis Techniques and Two New Techniques with 4-bit Boolean Functions for Cryptanalysis of 4-bit Crypto S-boxes.

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective Crypto S-boxes. 4-bit finite differences also a major part of cryptanalysis of 4-bit substitution boxes. Count of existence of all 4-bit linear relations, for all of 16 input and 16 output 4-bit bit patterns of 4-bit bijective crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new Analysis Techniques, one to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number existent linear relations among all 16 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced 4-bit BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security

Bent Boolean functions A better procedure to generate non-crypto 4-bit S-boxes

crypto 4-bit substitution boxes or crypto 4-bit S-boxes are used in block ciphers for nonlinear substitution very frequently. If the 16 elements of a 4-bit S-box are unique, distinct and vary between 0 and f in hex then the said 4-bit S-box is called as a crypto 4-bit S-box. There are 16! crypto 4-bit S-boxes available in crypto literature. Other than crypto 4-bit S-boxes there are another type of 4-bit S-boxes exist. In such 4-bit S-boxes 16 elements of the 4-bit S-box are not unique and distinct i.e. at least one element must repeat more than one time. They are called as non-crypto 4-bit S-boxes. There are 16^16-factorial 16 Numbers of non-crypto 4-bit S-boxes can be found in crypto-literature. The non-crypto 4-bit S-boxes can be generated from 4-bit Boolean Functions (BFs) in the same manner as crypto 4-bit S-boxes are generated in [1]. But to generate crypto 4-bit S-boxes the security of the generated 4-bit S-boxes is sacrificed into some extend. Since 12870 4-bit balanced BFs are responsible for factorial 16 crypto 4-bit S-boxes and the nonlinearity of the balanced 4-bit BFs are at most 4. So the 4-bit BFs with highest nonlinearity 6 are left abandoned. These 4-bit BFs are called as 4-bit Bent BFs. Here in this paper we generate non-crypto 4-bit S-boxes from 4-bit Bent BFs. The generated non-crypto 4-bit S-boxes are analyzed with the existing cryptanalysis techniques to prove them much secure 4-bit S-boxes from crypto angle

4-bit Boolean functions in generation and cryptanalysis of secure 4-bit crypto S-boxes.

In modern ciphers of commercial computer cryptography 4-bit crypto substitution boxes or 4-bit crypto S-boxes are of utmost importance since the late sixties. Since then the 4 bit Boolean functions (BFs) are proved to be the best tool to generate the said 4-bit crypto S-boxes. In this paper the crypto related properties of the 4-bit BFs such as the algebraic normal form (ANF) of the 4-bit BFs, the balancedness, the linearity, the nonlinearity, the affinity and the non-affinity of the 4-bit BFs and the strict avalanche criterion (SAC) of 4-bit BFs are studied in detail. An exhaustive study of 4-bit BFs with some new observations and algorithms on SAC of 4-bit BFs is also reported in this paper. A bit later in the end of nineties the Galois field polynomials over Galois field GF(28) are in use to generate the 8-bit crypto S-box of the Advance Encryption Standard (AES). A detailed study on generation of the 4-bit crypto S-boxes with such Galois field polynomials over the binary as well as non-binary extended Galois fields is also given in this paper. The generated 4-bit crypto S-boxes are analyzed with four cryptanalysis techniques and the well-defined SAC algorithms of 4-bit crypto S-boxes to search for the best possible 4-bit crypto S-boxes. Some existing 4-bit crypto S-boxes like the 32 4-bit crypto S-boxes of the Data Encryption Standard (DES) and the four 4-bit crypto S-boxes of the two variants of the Lucifer are analyzed to report the weakness of such S-boxes. A comparative study of the ancient as well as the modern 4-bit crypto S-boxes with the generated 4-bit crypto S-boxes proves the said generated 4-bit crypto S-boxes to be the best possible one

A review of cryptographic properties of S-boxes with Generation and Analysis of crypto secure S-boxes.

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of utmost importance in modern cryptography. In this paper, a detailed review of cryptographic properties of S-boxes has been illustrated. The generation of crypto S-boxes with 4-bit as well as 8-bit Boolean functions (BFs) and Polynomials over Galois field GF(p^q) has also been of keen interest of this paper. The detailed analysis and comparison of generated 4-bit and 8-bit S-boxes with 4-bit as well as 8-bit S-boxes of Data Encryption Standard (DES) and Advance Encryption Standard (AES) respectively, has incorporated with example. Detailed analysis of generated S-boxes claims a better result than DES and AES in view of security of crypto S-boxes

Ongoing Research Areas in Symmetric Cryptography

This report is a deliverable for the ECRYPT European network of excellence in cryptology. It gives a brief summary of some of the research trends in symmetric cryptography at the time of writing. The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the recently proposed algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

D.STVL.9 - Ongoing Research Areas in Symmetric Cryptography

This report gives a brief summary of some of the research trends in symmetric cryptography at the time of writing (2008). The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

Applications of Neural Network-Based AI in Cryptography

Artificial intelligence (AI) is a modern technology that allows plenty of advantages in daily life, such as predicting weather, finding directions, classifying images and videos, even automatically generating code, text, and videos. Other essential technologies such as blockchain and cybersecurity also benefit from AI. As a core component used in blockchain and cybersecurity, cryptography can benefit from AI in order to enhance the confidentiality and integrity of cyberspace. In this paper, we review the algorithms underlying four prominent cryptographic cryptosystems, namely the Advanced Encryption Standard, the Rivest--Shamir--Adleman, Learning With Errors, and the Ascon family of cryptographic algorithms for authenticated encryption. Where possible, we pinpoint areas where AI can be used to help improve their security

Survey and Benchmark of Block Ciphers for Wireless Sensor Networks

Cryptographic algorithms play an important role in the security architecture of wireless sensor networks (WSNs). Choosing the most storage- and energy-efficient block cipher is essential, due to the facts that these networks are meant to operate without human intervention for a long period of time with little energy supply, and that available storage is scarce on these sensor nodes. However, to our knowledge, no systematic work has been done in this area so far.We construct an evaluation framework in which we first identify the candidates of block ciphers suitable for WSNs, based on existing literature and authoritative recommendations. For evaluating and assessing these candidates, we not only consider the security properties but also the storage- and energy-efficiency of the candidates. Finally, based on the evaluation results, we select the most suitable ciphers for WSNs, namely Skipjack, MISTY1, and Rijndael, depending on the combination of available memory and required security (energy efficiency being implicit). In terms of operation mode, we recommend Output Feedback Mode for pairwise links but Cipher Block Chaining for group communications

Algebraic Attacks on RAIN and AIM Using Equivalent Representations

Designing novel symmetric-key primitives for advanced protocols like secure multiparty computation (MPC), fully homomorphic encryption (FHE) and zero-knowledge proof systems (ZK), has been an important research topic in recent years. Many such existing primitives adopt quite different design strategies from conventional block ciphers. Notable features include that many of these ciphers are defined over a large finite field, and that a power map is commonly used to construct the nonlinear component due to its efficiency in these applications as well as its strong resistance against the differential and linear cryptanalysis. In this paper, we target the MPC-friendly ciphers AIM and RAIN used for the post-quantum signature schemes AIMer (CCS 2023 and NIST PQC Round 1 Additional Signatures) and Rainier (CCS 2022), respectively. Specifically, we can find equivalent representations of 2-round RAIN and full-round AIM, respectively, which make them vulnerable to either the polynomial method, or the crossbred algorithm, or the fast exhaustive search attack. Consequently, we can break 2-round RAIN with the 128/192/256-bit key in only 2111/2170/2225 bit operations. For full-round AIM with the 128/192/256-bit key, we could break them in 2136.2/2200.7/2265 bit operations, which are equivalent to about 2115/2178/2241 calls of the underlying primitives. In particular, our analysis indicates that AIM does not reach the required security levels by the NIST competition.</p

4-bit crypto S-boxes: Generation with irreducible polynomials over Galois field GF(24) and cryptanalysis.

4-bit crypto S-boxes play a significant role in encryption and decryption of many cipher algorithms from last 4 decades. Generation and cryptanalysis of generated 4-bit crypto S-boxes is one of the major concerns of modern cryptography till now. In this paper 48, 4-bit crypto S-boxes are generated with addition of all possible additive constants to the each element of crypto S-box of corresponding multiplicative inverses of all elemental polynomials (EPs) under the concerned irreducible polynomials (IPs) over Galois field GF(2^4). Cryptanalysis of 48 generated 4-bit crypto S-boxes is done with all relevant cryptanalysis algorithms of 4-bit crypto S-boxes. The result shows the better security of generated 4-bit crypto S-boxes