Quantum security of subset cover problems

In post-quantum cryptography, hash-based signature schemes are attractive choices because of the weak assumptions. Most existing hash-based signature schemes are proven secure against post-quantum chosen message attacks (CMAs), where the adversaries are able to execute quantum computations and classically query to the signing oracle. In some cases, the signing oracle is also considered quantum-accessible, meaning that the adversaries are able to send queries with superpositions to the signing oracle. Considering this, Boneh and Zhandry propose a stronger security notion called existential unforgeability under quantum chosen message attacks (EUF-qCMA). We call it quantum-access security (or Q2 security in some literature). The quantum-access security of practical signature schemes is lacking in research, especially of the hash-based ones. In this paper, we analyze the quantum-access security of hash-based signature schemes in two directions. First, we show concrete quantum chosen message attacks (or superposition attacks) on existing hash-based signature schemes, such as SPHINCS and SPHINCS+. The complexity of the attacks is obviously lower than that of optimal classical chosen message attacks, implying that quantum chosen message attacks are more threatening than classical ones to these schemes. Second, we propose a simple variant of SPHINCS+ and give security proof against quantum chosen message attacks. As far as we know, it is the first practical hash-based stateless signature scheme against quantum chosen message attacks with concrete provable security.

Recently, a fast and secure hash function SFHA - 256 has been proposed and claimed as more secure and as having a better performance than the SHA - 256. In this paper an improved version of SFHA - 256 is proposed and analyzed using two parameters, namely the avalanche effect and uniform deviation. The experimental results and further analysis ensures the performance of the newly proposed and improved SFHA-256. From the analysis it can be concluded that the newly proposed algorithm is more secure, efficient, and practical.

Currently, significant efforts at the international and national levels are focused on the creation of practical quantum-resistant digital signature (DS) mechanisms. The first round of the international PQC competition has been conducted [1], which resulted in the creation and standardization of the finalists of the 3rd round of the competition, recommended as international standards, as US federal standards, in particular FIPS 205, a stateless digital signature standard based on a hash function (SPHINCS+ algorithm). A hash-based signature is one of the most promising candidates (and perhaps the most conservative approach) for a post-quantum digital signature. The advantage of hash-based signatures is that their (classical and quantum) security strength is better understood (and easier to evaluate) than other candidates relying solely on the idealized strength of cryptographic hash functions. The signature scheme standardized in FIPS 205 is constructed using other hash-based signature schemes as components: a few-time signature scheme, forest of random subsets (FORS), and a multi-time signature scheme, the eXtended Merkle Signature Scheme (XMSS). The standard defines a DS scheme designed to withstand future quantum and classical quantum computer attacks that threaten the security of existing standards. Since the algorithm has already been standardized, an important task is to study its structure and practical implementation of the requirements for its components: parameter construction, key pair generation, DS production and verification, etc. Its solution depends to a large extent on improving the algorithm in terms of execution complexity (speed), which can be reduced to optimizing basic operations. In this article, we consider and propose practical improvements to optimize the DS for the FIPS 205 algorithm based on the use of parallel computing. This is achieved mainly by optimizing the SHAKE256, SHA256, and SHA512 algorithms. The importance of optimizing the calculation of hash values is related to the fact that hashing is the main operation in FIPS 205. The results obtained indicate the feasibility and relevance of the improvements made. Optimization provides a minimum speedup of 10% for all operations and all parameters.

Hash functions, which can extract message digest from input messages as output, play an important role in digital signature and authentication. Meanwhile, Hash functions are essential in many cryptographic protocols and regimes. With the research becoming more and more in depth, a series of Hash functions is proposed, such as MD series and SHA series. At the same time, the security analysis and attacks against Hash functions are carried out. The security of Hash functions is threatened. In this case, how to improve the security of the Hash functions becomes the primary concern. In this paper, an optical Hash function based on the interaction between light and multiple scattering media is proposed. Unlike most of the traditional Hash functions which are based on mathematical transformations or complex logic operations, this method innovatively takes advantage of the natural random scattering effect of multiple scattering media on coherently modulated light, and realizes the “confusion” and “diffusion” of modulated light, which satisfies the core functional requirement of the Hash function: one-way encoding/encryption with strong security. The photoelectric hybrid system designed by this method can effectively simulate the "compression function" in the Hash function. Combined with the Sobel filter with feature extraction function, the input data of arbitrary length can be compressed and encrypted into the output with a fixed length of 256-bit (Hash value). The principle of the proposed optical Hash function can be described as follows. 1) Two 8-bit images with a size of 16×16 pixels are loaded in SLM<sub>1</sub> (amplitude-only spatial modulator) and SLM<sub>2</sub> (phase-only spatial modulator) respectively. 2) The coherent wavefront is modulated by SLM<sub>1</sub> and SLM<sub>2</sub>, and then propagates on multiple scattering media. 3) A speckle pattern is recorded by CCD because of the confusion of multiple scattering media. 4) The features of the speckle pattern, which is extracted by Sobel filter, serve as the input of the next compression function. For the unpredicted and non-duplicated disorder multiple scattering media, it is tremendously difficult to determine the internal state of the multiple scattering media. Therefore, the proposed optical Hash function is considered to have a high security. A series of simulation results shows that the proposed optical Hash function has a good “avalanche effect” and “collision resistance”, and its security performance is comparable to that of the most widely used traditional Hash functions (MD5 and SHA-1).

This paper analyzes the computer security of systems and importance of the digital signature and hashing message algorithm. The proposed digital signature algorithm gives a new technology for producing effective output of digital signature as a result the signing 1 and verifying of signatures are very fast compared to earlier ones. To improve the security and authentication of sending data, this method uses "Message Digest", "IDEA" and "GOST" 2 algorithms. The new message digest algorithm is to provide high security, to transfer data by combination of digital signature algorithm and symmetric key cryptography algorithm. The new hashing algorithm proposed creates a unique digital fingerprint along with symmetric key encryption generated IDEA and GOST algorithms 3,4 . The receiver used the symmetric key and hashing algorithm to form a signature. If this message digest match with the sender digests the message the content will be decrypted and read by sender.

In this paper, we clarify the security of practical cryptosystems with hash functions based on key derivation functions (KDFs). We use the indifferentiability framework in order to discuss the security because the indifferentiability from Random Oracle (and its variants) guarantees that cryptosystems remain secure even if Random Oracles (ROs) are instantiated with hash functions. Though previous works on the indifferentiability of Merkle-Damgård (MD) hash functions focus on stand-alone hash functions, there is no work which focuses on MD hash functions with KDFs. Many cryptosystems need longer output lengths of hash functions than stand-alone hash functions and KDFs are used to generate longer digests as specified in PKCS #1 v2.1 and IEEE P1363. Specifically, we obtain the following results. We denote the MD hash function using Stam’s type-II compression function by MD-SCFII and MD-SCFII with KDFs by KDF-MD-SCFII. Cryptosystems secure in the pub-RO model (FDH, PSS, Fiat-Shamir, and so on): Dodis et al. proposed the indifferentiability from pub-RO to prove the security of these cryptosystems using MD-SCFII while did not consider the KDF structures. So we propose a different framework, indifferentiability from privleak-RO. Using this framework and their result, we show that these cryptosystems using KDF-MD-SCFIIs are secure. Encryption schemes secure in the RO model (OAEP, RSA-KEM, PSEC-KEM, ECIES-KEM and so on): The encryption schemes are secure in the “fixed inputl length” RO model because the input lengths of ROs from the encryption schemes are fixed. We show that this fact guarantees the security of the encryption schemes using KDF-MD-SCFII. KeywordsHash FunctionEncryption SchemeRandom OracleCompression FunctionRandom Oracle ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Recently, formal complexity-theoretic treatment of cryptographic hash functions was suggested. Two primitives of Collision-free hash functions and Universal one-way hash function families have been defined. The primitives have numerous applications in secure information compression, since their security implies that finding collisions is computationally hard. Most notably, Naor and Yung have shown that the most secure signature scheme can be reduced to the existence of universal one-way hash (this, in turn, gives the first trapdoor-less provably secure signature scheme).In this work, we first present reductions from various one-way function families to universal one-way hash functions. Our reductions are general and quite efficient and show how to base universal one-way hash functions on any of the known concrete candidates for one-way functions. We then show equivalences among various definitions of hardness for collision-free hash functions.

We present a new tighter security proof for unbounded hash tree keyless signature (time-stamping) schemes that use Merkle-Damgård (MD) hash functions with Preimage Aware (PrA) compression functions. It is known that the PrA assumption alone is insufficient for proving the security of unbounded hash tree schemes against back-dating attacks. We show that many known PrA constructions satisfy a stronger Bounded Pre-Image Awareness (BPrA) condition that assumes the existence of an extractor \(\mathcal{E}\) that is bounded in the sense that for any efficiently computable query string α, the number of outputs y for which \(\mathcal{E}(y,\alpha)\) succeeds does not exceed the number of queries in α. We show that blockcipher based MD-hash functions with rate-1 compression functions (such as Davies-Meyer and Miyaguchi-Preneel) of both type I and type II are BPrA. We also show that the compression function of Shrimpton-Stam that uses non-compressing components is BPrA. The security proof for unbounded hash-tree schemes is very tight under the BPrA assumption. In order to have 2s-security against back-dating, the hash function must have n = 2s + 4 output bits, assuming that the security of the hash function is close to the birthday barrier, i.e. that there are no structural weaknesses in the hash function itself. Note that the previous proofs that assume PrA gave the estimation n = 2s + 2 log2 C + 2, where C is the maximum allowed size of the hash tree. For example, if s = 100 (2100-security) and C = 260, the previous proofs require n = 322 output bits, while the new proof requires n = 204 output bits.KeywordsHash FunctionSuccess ProbabilityBlock CipherRandom OracleCompression FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

While numerous digital signature schemes exist in the literature, most real-world system rely on RSA-based signature schemes or on the digital signature algorithm (DSA), including its elliptic curve cryptography variant ECDSA. In this position paper we review a family of alternative signature schemes, based on hash functions, and we make the case for their application in Internet of Things (IoT) settings. Hash-based signatures provide postquantum security, and only make minimal security assumptions, in general requiring only a secure cryptographic hash function. This makes them extremely flexible, as they can be implemented on top of any hash function that satisfies basic security properties. Hash-based signatures also feature numerous parameters defining aspects such as signing speed and key size, that enable trade-offs in constrained environments. Simplicity of implementation and customization make hash based signatures an attractive candidate for the IoT ecosystem, which is composed of a number of diverse, constrained devices.

Hash functions are important security primitives used for authentication and data integrity. Among the most popular hash functions are MD5, SHA-1, and RIPEMD-160, which are all based on the function MD4. This similarity can be exploited for designing a unified engine to perform all three hash functions. Hash message authentication code (HMAC) is a shared-key security algorithm that uses these hash functions alternatively for IPSec authentication. Since some other security applications, such as digital signature, also use these three hash functions, it is prudent to design a unified, reconfigurable engine that can perform any one of them alone or with HMAC. In this work, we design an HMAC-hash unit that can be reconfigured to perform one of six standard security algorithms; namely, MD5, SHA-1, RIPEMD-160, HMAC-MD5, HMAC-SHA-1, and HMAC-RIPEMD-160. This paper applied pipelining and parallelism to the design of the HMAC-hash unit to improve throughput, especially for large message sizes. We achieved higher throughput than engines that integrated three hash functions or more and comparable throughput to those integrated only two hash functions.

This paper reports a thorough standard-model investigation on how attacks on hash functions impact the security of hash-and-sign signature schemes. We identify two important properties that appear to be crucial in analyzing the nature of security relations between signature schemes and their inner hash functions: primitiveness and injectivity. We then investigate the security relations in the general case of hash-and-sign signatures and in the particular case of first-hash-then-sign signatures, showing a gap of security guarantees between the two paradigms. We subsequently apply our results on two operating modes to construct a hash function family from a hash function based on the well-known Merkle-Damgård construction (such as MD5 and SHA-1). For completeness, we give concrete attack workloads for attacking operating modes used in practical implementations of signature schemes.KeywordsHash FunctionSignature SchemeRandom OracleCompression FunctionSecurity ProofThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The hash function used is known for implementing algorithmic solutions in programming. Hash functions encrypt and optimize work with processed and stored data, as well as in various operating systems, ranking data to ensure their integrity. The application of the hash function is quite extensive. The usage of the hash function allows the possibility to solve almost all problems of protecting electronic information, from ensuring the authenticity of subjects and objects of information interaction to introducing uncertainty into the operation of means and objects of protection. The article deals with hash functions used in electronic digital signature (EDS) algorithms. Modern hashing methods and the areas in which they are applicable are described. The hash function is used to secure data. These functions can vary in bit depth, complexity, and cryptographic strength. Cryptographic hashing algorithms are given parameters, structures, and methods, as well as their scope. The work is devoted to analyzing hash functions and their application in the electronic digital signature. The article presents the results of calculating collisions of hashing algorithms, allowing you to choose the most optimal option for its application in the algorithm under consideration. The practical application of the hashing algorithm for the digital signature system, which can be used in systems and networks to transmit and store information, is considered

With the drastic growth in the addition of smart objects into the Internet, it has led to many challenges like standardizing the infrastructure, ensuring communication security and keeping user credential private. As these devices are having less resources it is necessity to have a lighter encryption and authentication schemes to ensure data integrity and user privacy. This work concentrates on evaluating the faster hashing function used for elliptic curve digital signature algorithm (ECDSA) that enables user authentication. Traditionally, SHA hash functions are used in various public key cryptography and applications. But SHA has 80 different iterations that consumes smart device's energy. Thus a lighter hash function called BLAKE2 based hashing is used to compare the time efficiency of ECDSA. BLAKE2 uses 8 rounds of permutations and combinations to produce the message digest of 256/512bits. This reduction in computation has attracted researchers to use BLAKE2 hashing functions for various applications. Thence this study concentrates on comparison of the time efficiency under ECDSA based digital signature for different message sizes and hashing functions. Through various experiments conducted on different operating systems, BLAKE2 has shown better computational efficiency than SHA family of hashing functions for ECDSA based scheme on different operating system.

Efficient generic on-line/off-line (threshold) signatures without key exposure

In this paper we consider the problem of securely instantiating Probabilistic Signature Scheme (PSS) in the standard model. PSS, proposed by Bellare and Rogaway [3] is a widely deployed randomized signature scheme, provably secure (unforgeable under adaptively chosen message attacks) in Random Oracle Model.Our main result is a black-box impossibility result showing that one can not prove unforgeability of PSS against chosen message attacks using blackbox techniques even assuming existence of ideal trapdoor permutations (a strong abstraction of trapdoor permutations which inherits all security properties of a random permutation, introduced by Kiltz and Pietrzak in Eurocrypt 2009) or the recently proposed lossy trapdoor permutations [20]. Moreover, we show onewayness, the most common security property of a trapdoor permutation does not suffice to prove even the weakest security criteria, namely unforgeability under zero message attack. Our negative results can easily be extended to any randomized signature scheme where one can recover the random string from a valid signature.KeywordsPSSBlackbox ReductionsRandomized SignatureStandard Model