Message Expansion Research Articles

Improved homomorphic evaluation for hash function based on TFHE

Homomorphic evaluation of hash functions offers a solution to the challenge of data integrity authentication in the context of homomorphic encryption. The earliest attempt to achieve homomorphic evaluation of SHA-256 hash function was proposed by Mella and Susella (in: Cryptography and coding—14th IMA international conference, IMACC 2013. Lecture notes in computer science, vol 8308. Springer, Heidelberg, pp 28–44, 2013. https://doi.org/10.1007/978-3-642-45239-0_3.) based on the BGV scheme. Unfortunately, their implementation faced significant limitations due to the exceedingly high multiplicative depth, rendering it impractical. Recently, a homomorphic implementation of SHA-256 based on the TFHE scheme (Homomorphic evaluation of SHA-256. https://github.com/zama-ai/tfhe-rs/tree/main/tfhe/examples/sha256_bool) brings it from theory to reality, however, its current efficiency remains insufficient. In this paper, we revisit the homomorphic evaluation of the SHA-256 hash function in the context of TFHE, further reducing the reliance on gate bootstrapping and enhancing evaluation latency. Specifically, we primarily utilize ternary gates to reduce the number of gate bootstrappings required for logic functions in message expansion and addition of modulo 232\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{32}$$\\end{document} in iterative compression. Furthermore, we demonstrate that our optimization techniques are applicable to the Chinese commercial cryptographic hash SM3. Finally, we give specific comparative implementations based on the TFHE-rs library. Experiments demonstrate that our optimization techniques lead to an improvement of approximately 35–50% compared with the state-of-the-art result under different cores.

A Parallel Quantum Circuit Implementations of LSH Hash Function for Use with Grover’s Algorithm

Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To conduct Grover’s search algorithm, the target cipher algorithm should be efficiently implemented in a quantum circuit. Currently, small quantum computers are difficult to operate with large quantum circuits due to limited performance. Therefore, if a large quantum computer that can operate Grover’s algorithm appears, it is expected that a cipher attack will be possible. In this paper, we propose a parallel structure quantum circuit for the Korean hash function standard (i.e., LSH). The proposed quantum circuit designed a parallel operation structure for the message expansion (i.e., MsgExp) function and the mix function, which are the internal structures of the LSH hash function. This approach shows an efficient result for quantum circuit implementation in terms of quantum resources by reducing the depth of the quantum circuit by about 96% through the trade-off of appropriate quantum resources compared to previous work. This result can be a reference for the implementation of a parallel quantum circuit in the future and is expected to advance the attack timing of the search algorithm for Grover’s LSH hash function.

SHA_1 Enhancement Based on Resilent Boolean Function

SHA_1 is a one way hash function which is used in cryptographic systems to provide message authentication and integrity. In recent year this algorithm faced new type of attacks. These attacks make use of the simplicity of message expansion step to leak some information used to build a matching patterns or build differential path according to local collision. In this paper an enhanced version of SHA_1 was proposed depend on using resilent Boolean function which is a Boolean function that offers properties of balancedness, algebraic degree, correlation immunity and nonlinearity. This enhancement tends to countermeasures these attacks. Enhancement was made in two places for the original algorithm, first enhanced message expansion process, second change the value of 32 variable inputs to Boolean function in the algorithm.

A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

Homomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security. We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly. We make an effort to prove the security of the scheme under indistinguishability under chosen-plaintext attack (IND-CPA) through a game-based security proof. The security proof gives a mathematical analysis and its complexity of hardness. Also, it presents security analysis against all the known attacks with respect to the message expansion and homomorphic operations.

A New Message Expansion Structure for Full Pipeline SHA-2

Once there are constant or infrequently changed bits (COIBs) in two adjacent input messages of SHA-2, the switching power of input messages data registers (IMD-REGs) used for COIBs will disappear. Meanwhile, when full pipeline SHA-2 is applied in a certain application scenario where the IMD-REGs used for COIBs can be removed, more area of full pipeline SHA-2 can be saved as the proportion of IMD-REGs in message word registers increases. This paper proposes a new message expansion structure for full pipeline SHA-2 to increase the proportion of IMD-REGs. By inserting two expanders in last part of expansion structure pipeline stages and rescheduling the expander, the consumption rate of input messages will be decreased and the proportion of IMD-REGs will be increased. Compared with normal message expansion structure, the ratio of IMD-REGs to total message word registers in the proposed structure is increased from 15.1% to 41.6% for full pipeline SHA256, and 11.2% to 32.4% for full pipeline SHA512. When COIBs exists in adjacent input messages, the power and area advantages of proposed new message expansion structure have been demonstrated by FPGA and ASIC implementations.

Enhancing the Security in ElGamal Cryptosystem using Paring Functions

The potential disadvantage of ElGamal cryptosystem is the ciphertext produced is always twice as long as the plaintext i.e., the message expansion by a factor of two takes place during encryption. When the message is too long the ciphertext produced by the ElGamal cryptosystem is also too long. i.e., when the ciphertexts are transmitted through the communication channel which lead to provide less security because if anyone of the ciphertext from two ciphertexts for each character of the plaintext is intercepted by the adversary, the other may be retrieved easily because there is a relationship between the two ciphertexts. If two ciphertexts are reduced to one, the adversary may not be able to predict the two ciphertexts from one. To enhance the security of ElGamal cryptosystem, the binary Cantor function , Rosenberg pairing function and Elegant pairing functions are used in this paper. When the said functions are used, the two ciphertexts produced by each plaintext character are reduced to one, so that the adversary cannot easily be recovered the plaintext. Experimental results clearly revealed enhancing the security of ElGamal cryptosystem after incorporating the pairing functions into it.

New Semi-Free-Start Collision Attack Framework for Reduced RIPEMD-160

RIPEMD-160 is a hash function published in 1996, which shares similarities with other hash functions designed in this time-period like MD4, MD5 and SHA-1. However, for RIPEMD-160, no (semi-free-start) collision attacks on the full number of steps are known. Hence, it is still used, e.g., to generate Bitcoin addresses together with SHA-256, and is an ISO/IEC standard. Due to its dual-stream structure, even semifree- start collision attacks starting from the first step only reach 36 steps, which were firstly shown by Mendel et al. at Asiacrypt 2013 and later improved by Liu, Mendel and Wang at Asiacrypt 2017. Both of the attacks are based on a similar freedom degree utilization technique as proposed by Landelle and Peyrin at Eurocrypt 2013. However, the best known semi-free-start collision attack on 36 steps of RIPEMD-160 presented at Asiacrypt 2017 still requires 255.1 time and 232 memory. Consequently, a practical semi-free-start collision attack for the first 36 steps of RIPEMD-160 still requires a significant amount of resources. Considering the structure of these previous semi-free-start collision attacks for 36 steps of RIPEMD-160, it seems hard to extend it to more steps. Thus, we develop a different semi-free-start collision attack framework for reduced RIPEMD-160 by carefully investigating the message expansion of RIPEMD-160. Our new framework has several advantages. First of all, it allows to extend the attacks to more steps. Second, the memory complexity of the attacks is negligible. Hence, we were able to mount semi-free-start collision attacks on 36 and 37 steps of RIPEMD-160 with practical time complexity 241 and 249 respectively. Additionally, we describe semi-free-start collision attacks on 38 and 40 (out of 80) steps of RIPEMD-160 with time complexity 252 and 274.6, respectively. To the best of our knowledge, these are the best semi-free-start collision attacks for RIPEMD-160 starting from the first step with respect to the number of steps, including the first practical colliding message pairs for 36 and 37 steps of RIPEMD-160.

New Semi-Free-Start Collision Attack Framework for Reduced RIPEMD-160

RIPEMD-160 is a hash function published in 1996, which shares similarities with other hash functions designed in this time-period like MD4, MD5 and SHA-1. However, for RIPEMD-160, no (semi-free-start) collision attacks on the full number of steps are known. Hence, it is still used, e.g., to generate Bitcoin addresses together with SHA-256, and is an ISO/IEC standard. Due to its dual-stream structure, even semifree- start collision attacks starting from the first step only reach 36 steps, which were firstly shown by Mendel et al. at Asiacrypt 2013 and later improved by Liu, Mendel and Wang at Asiacrypt 2017. Both of the attacks are based on a similar freedom degree utilization technique as proposed by Landelle and Peyrin at Eurocrypt 2013. However, the best known semi-free-start collision attack on 36 steps of RIPEMD-160 presented at Asiacrypt 2017 still requires 255.1 time and 232 memory. Consequently, a practical semi-free-start collision attack for the first 36 steps of RIPEMD-160 still requires a significant amount of resources. Considering the structure of these previous semi-free-start collision attacks for 36 steps of RIPEMD-160, it seems hard to extend it to more steps. Thus, we develop a different semi-free-start collision attack framework for reduced RIPEMD-160 by carefully investigating the message expansion of RIPEMD-160. Our new framework has several advantages. First of all, it allows to extend the attacks to more steps. Second, the memory complexity of the attacks is negligible. Hence, we were able to mount semi-free-start collision attacks on 36 and 37 steps of RIPEMD-160 with practical time complexity 241 and 249 respectively. Additionally, we describe semi-free-start collision attacks on 38 and 40 (out of 80) steps of RIPEMD-160 with time complexity 252 and 274.6, respectively. To the best of our knowledge, these are the best semi-free-start collision attacks for RIPEMD-160 starting from the first step with respect to the number of steps, including the first practical colliding message pairs for 36 and 37 steps of RIPEMD-160.

Fast Implementation of LSH With SIMD

In this paper, we propose a method of efficient software implementation for the cryptographic hash function LSH with single instruction multiple data (SIMD). The method is based on word-wise permutations of LSH. Using the modified functions Step j ' = P o Step j o P -1 and MsgExp' instead of the original step function Stepj and message expansion function MsgExp, where P is a permutation and P -1 is the inverse permutation of P, we show that the number of the SIMD instructions for implementing LSH is reduced. For efficient implementation of LSH in other environments (e.g., MIMD), various types of word permutations are listed.

Improving Dependability and Precision of Data Encoding in DNA

DNA storage of information is emerging as the next-generation approach to archiving vast amounts of data. Various sophisticated approaches for data storage in DNA have been proposed. Herein we present a multistep algorithm designed to detect and/or correct errors introduced at any stage of the DNA storage process, including those during message DNA generation, and propose refinements designed to ensure authenticity and correctness of each individual encoded DNA block. In addition, the algorithm allows authentic decoding without a reference sequence or message meaning. The algorithm is designed based on principles underlying provably secure cryptographic systems. Importantly, our new algorithm compares favorably with current ones in terms of ease of implementation and message expansion. In cases where reads are error-free, our algorithm should be faster than current alignment techniques. Without knowing the original data, a certificate is generated that confirms that the obtained data are exactly the same as the original. Our algorithm has applications to DNA steganography, sequence alignment, fast identification of correct reads in next generation sequencing and to message security.

Enabling Robust and Privacy-Preserving Resource Allocation in Fog Computing

Fog computing is an extension of cloud computing and enables computing directly at the edge of the network. In fog computing paradigm, the fog nodes reside between smart end devices and the cloud. Benefiting from the structure of fog computing, fog computing can provide services with low latency, location awareness, and mobility. Since the fog nodes are not as powerful as the cloud, resource allocation techniques are usually adapted to optimize the utilization of the resources of fog nodes. However, the current resource allocation techniques are not privacy-preserving, i.e., an attacker can easily find end devices’ sensitive information. In this paper, we propose a privacy-preserving resource allocation scheme for fog computing. The new proposal has constant message expansion, and it is secure against both an eavesdropper and a smart gateway that is employed to perform the resource allocation algorithm. Our scheme is also robust, since it achieves a full key compromise resistance which guarantees that even if the private keys of all the fog nodes in a fog system are corrupted the scheme remains secure.

An Efficient Public Key Encryption Scheme Based on QC-MDPC Lattices

In this paper, we introduce a new family of lattices, namely QC-MDPC lattices, which are a special case of LDPC lattices, and an improved bit flipping algorithm for decoding of these lattices. Encoding and decoding implementations of QC-MDPC lattices are practical in high dimensions. Indeed, to take advantage of practical decoding, we use “Construction-A” lattices which makes a tight connection between the structure of lattices and codes. Using these features, we design a lattice-based public key encryption scheme enjoying linear encryption and decryption complexities. The proposed scheme has a reasonable key size due to the sparseness of the parity-check matrix, and the quasi-cyclic structure of the parity-check and generator matrices. Besides, the message expansion of the proposed scheme is smaller than other lattice-based and code-based cryptosystems with comparative parameters. All these features provide a lattice-based public key encryption scheme with reasonable key size, linear encryption, and decryption algorithms and small message expansion. On the other hand, we show that the cryptosystem is resistant against all known attacks both on lattice-based and code-based cryptosystems for different levels of security.

USE OF NEW EFFICIENT LOSSLESS DATA COMPRESSION METHOD IN TRANSMITTING ENCRYPTED BAPTISTA SYMMETRIC CHAOTIC CRYPTOSYSTEM DATA

A new compression algorithm used to ensure a modified Baptista symmetric cryptosystem which is based on a chaotic dynamical system to be applicable is proposed. The Baptista symmetric cryptosystem able to produce various ciphers responding to the same message input. This modified Baptista type cryptosystem suffers from message expansion that goes against the conventional methodology of a symmetric cryptosystem. A new lossless data compression algorithm based on theideas from the Huffman coding for data transmission is proposed.This new compression mechanism does not face the problem of mapping elements from a domain which is much larger than its range.Our new algorithm circumvent this problem via a pre-defined codeword list. The purposed algorithm has fast encoding and decoding mechanism and proven analytically to be a lossless data compression technique.

Message Expansion of Homomorphic Encryption Using Product Pairing

The Boneh, Goh, and Nissim (BGN) cryptosytem is the first homomorphic encryption scheme that allows additions and multiplications of plaintexts on encrypted data. BGN-type cryptosystems permit very small plaintext sizes. The best-known approach for the expansion of a message size by t times is one that requires t implementations of an initial scheme; however, such an approach becomes impractical when t is large. In this paper, we present a method of message expansion of BGN-type homomorphic encryption using composite product pairing, which is practical for relatively large t. In addition, we prove that the indistinguishability under chosen plaintext attack security of our construction relies on the decisional Diffie–Hellman assumption for all subgroups of prime order of the underlying composite pairing group.

A new fully homomorphic encryption over the integers using smaller public key

Fully homomorphic encryption scheme with practical time complexity is a widely acknowledged research problem in cryptography. In this work, a new somewhat homomorphic encryption with practical time complexities is proposed, from which fully homomorphic encryption is obtained using the optimisations suggested in the contemporary works. The central idea behind the proposition in achieving such reasonable time complexities lies in employing a small public key containing only two big integers with consequent reduction in the message expansion. The scheme may be considered as a variant of the DGHV's integers-based scheme, which was one of the earlier attempts in devising a conceptually simpler fully homomorphic encryption. The semantic security of the proposition is proved in the standard model by reducing the same to the hard problem of solving partial approximate greatest common divisor of two integers.

Second order collision for the 42-step reduced DHA-256 hash function

At the Cryptographic Hash Workshop hosted by NIST in 2005, Lee et al. proposed the DHA-256 (Double Hash Algorithm-256) hash function. The design of DHA-256 builds upon the design of SHA-256, but introduces additional strengthening features such as optimizing the message expansion and step function against local collision attacks. Previously, DHA-256 was analyzed by J. Zhong and X. Lai, who presented a preimage attack on 35 steps of the compression function with complexity 2239.6. In addition, the IAIK Krypto Group provided evidence that there exists a 9-step local collision for the DHA-256 compression function with probability higher than previously predicted. In this paper, we analyze DHA-256 in the context of higher order differential attacks. In particular, we provide a practical distinguisher for 42 out of 64 steps and give an example of a colliding quartet to validate our results.

Preimage and pseudo-collision attacks on step-reduced SM3 hash function

SM3 [12] is the Chinese cryptographic hash standard which was announced in 2010 and designed by Wang et al. It is based on the Merkle–Damgård design and its compression function can be seen as a block cipher used in Davies–Meyer mode. It uses message block of length 512 bits and outputs hash value of length 256 bits.This letter studies the security of SM3 hash function against preimage attack and pseudo-collision attack by using the weakness of diffusion process and linear message expansion. We propose preimage attacks on 29-step and 30-step SM3, and pseudo-preimage attacks on 31-step and 32-step SM3 out of 64 steps. The complexities of these attacks are 2245 29-step operations, 2251.1 30-step operations, 2245 31-step operations and 2251.1 32-step operations, respectively. These (pseudo-)preimage attacks are all from the 1-st step of the reduced SM3. Furthermore, these (pseudo-)preimage attacks can be converted into pseudo-collision attacks on SM3 reduced to 29 steps, 30 steps, 31 steps and 32 steps with complexities of 2122, 2125.1, 2122 and 2125.1 respectively. As far as we know, the previously best known preimage attacks on SM3 cover 28 steps (from the 1-st step) and 30 steps (from the 7-th step).

Diffusion Analysis of Message Expansion in STITCH-256

Cryptographic hash functions are built up from individual components, namely pre-processing, step transformation, and final processing. Some of the hash functions, such as SHA-256 and STITCH-256, employ non-linear message expansion in their pre-processing stage. However, STITCH-256 was claimed to produce high diffusion in its message expansion. In a cryptographic algorithm, high diffusion is desirable as it helps prevent an attacker finding collision-producing differences, which would allow one to find collisions of the whole function without resorting to a brute force search. In this paper, we analyzed the diffusion property of message expansion of STITCH-256 by observing the effect of a single bit difference over the output bits, and compare the result with that of SHA-256. We repeated the same procedure in 3 experiments of different round. The results from the experiments showed that the minimal weight in the message expansion of STITCH-256 is very much lower than that in the message expansion of SHA-256, i.e. message expansion of STITCH-256 produce high diffusion. Significantly, we showed that the probability to construct differential characteristic in the message expansion of STITCH-256 is reduced.

A Fast New Cryptographic Hash Function Based on Integer Tent Mapping System

This paper proposes a novel one-way Hash function which is based on the Coupled Integer Tent Mapping System and termed as THA (THA-160, THA-256). The THA-160 compresses a message of arbitrary length into a fingerprint of 160 bits, well the THA-256 compresses a message of arbitrary length into a fingerprint of 256 bits. The algorithm adopts a piecewise message expansion scheme. Compared with SHA-1 and SHA-256 message expansion, the message expansion scheme has enhanced the degree of nonlinear diffusion of the message expansion, and thus increased the computation efficiency. In addition, as the major nonlinear component of compression function, the traditional logic functions are replaced by the integer tent map, and so the scheme has ideal properties of diffusion and confusion. Furthermore, the parallel iteration structure is adopted in the compression functions, which is advantageous to high speed parallel operation of software and hardware. Preliminary security testing indicates that, this Hash function has a high degree of security, and it can be realized easily with great rapidity. Therefore, it is an ideal substitution for conventional Hash function.

Parallel Hash function construction based on chaotic maps with changeable parameters

A parallel Hash algorithm construction based on chaotic maps with changeable parameters is proposed and analyzed in this paper. The two main characteristics of the proposed algorithm are parallel processing mode and message expansion. The algorithm translates the expanded message blocks into the corresponding ASCII code values as the iteration times, iterates the chaotic asymmetric tent map and then the chaotic piecewise linear map, continuously, with changeable parameters dynamically obtained from the position index of the corresponding message blocks, to generate decimal fractions, then rounds the decimal fractions to integers, and finally cascades these integers to construct intermediate Hash value. Final Hash value with the length of 128-bit is generated by logical XOR operation of intermediate Hash values. Theoretical analysis and computer simulation indicate that the proposed algorithm satisfies the performance requirements of a secure Hash function.