Zero-knowledge proofs is a type of non-black box security technique and it is stated by the means of quadratic residuosity problem in this paper. We have used quadratic residuosity problem (QRP) for zero-knowledge proofs security system for the comparative analysis of this technique in comparison with discrete logarithm problem in cryptography. The upper bound of QRP with a prime modulus algorithm for quadratic residuosity problem is growing faster in comparison with discrete logarithm problem used by Henry. After that covariance between two different algorithms for different problems are calculated and obtained result is positive, which means random variables used for both functions are growing in same direction which reflect the fact, they are similar in behavior. Both functions are growing in same direction and our functional valued curve converge with Henry (Discrete Logarithm) functional valued curve at a point.
Xiaoyong Zhang, Ruizhen Wu, Mingming Wang, Lin Wang
The SHA-256 is playing an important role in various applications, such as e-transactions and bitcoins. To achieve more profits, the SHA-256 computation capacity is a main research direction of Hashing Algorithm. In this paper, a high-performance hardware architecture of SHA-256 hash is proposed. The computation of SHA-256 is rescheduled based on hardware characterises. Three pipelines are used to replace the critical path in the round functions which can shorten the long critical path, and divide the computation chain into independent parts. Multi-computation of SHA-256 is working in parallel pipelines, indicating that the computation capacity can be 3 times of standard SHA-256 implementation. The proposed SHA-256 hardware architecture has been implemented and synthesized with Intel 14nm technology. Simulation and synthesis results show the proposed SHA-256 hashing throughput can be improved by 3 times with 50.7% power reduction, at an area cost of 2.9 times compared to the standard implementation.
Since Gentry's breakthrough construction of fully homomorphic encryption from lattice-based assumptions (STOC 2009), homomorphic cryptography has attracted a lot of attention. In short, homomorphic cryptography schemes allow performing computation on encrypted data without knowing anything about the underlying plaintext. This branch of cryptography has become increasingly useful in building new protocols and schemes with intriguing security and functionality features. In this thesis, we continue to study the applications of homomorphic cryptography and the lattice-based techniques underlying them in realizing new and enhanced cryptographic primitives. We obtain the following results: -We construct the first noninteractive zero knowledge argument (and proof) system for all of NP from standard lattice assumptions. Noninteractive zero knowledge argument systems have found many applications in enhancing the functionality as well as the security of cryptographic schemes and protocols. Constructing noninteractive zero knowledge arguments from lattice assumption has been a long standing open question. We finally close this problem. -We consider multi-key fully homomorphic encryption (FHE) schemes. Traditional fully homomorphic encryption schemes allow computation on plaintext encrypted under a single key. The notion of multi-key fully homomorphic encryption allows homomorphic computation on data encrypted under different keys. We construct multi-key FHE schemes which are naturally dynamic: ciphertexts under new keys can join even during the homomorphic computation. -Finally, we focus on constrained pseudorandom functions (C-PRFs), which are pseudorandom functions (PRFs) with additional functional capabilities. We propose a new approach for building C-PRFs from lattices, and also significantly enhance the underlying lattice parameters.
Behzad Abdolmaleki, Hamidreza Khoshakhlagh, Daniel Slamanig
Hash proof systems or smooth projective hash functions (SPHFs) have been proposed by Cramer and Shoup (Eurocrypt’02) and can be seen as special type of zero-knowledge proof system for a language. While initially used to build efficient chosen-ciphertext secure public-key encryption, they found numerous applications in several other contexts. In this paper, we revisit the notion of SPHFs and introduce a new feature (a third mode of hashing) that allows to compute the hash value of an SPHF without having access to neither the witness nor the hashing key, but some additional auxiliary information. We call this new type publicly computable SPHFs (PC-SPHFs) and present a formal framework along with concrete instantiations from a large class of SPHFs.
Over the last few years, there has been a surge of new cryptographic results, including laconic oblivious transfer [13, 16], (anonymous/ hierarchical) identity-based encryption [9], trapdoor functions [19, 20], chosen-ciphertext security transformations [32, 33], designated-verifier zero-knowledge proofs [30, 34, 37], due to a beautiful framework recently introduced in the works of Cho et al. [13], and Dottling and Garg [14]. The primitive of one-way function with encryption (OWFE) [19, 20] and its relatives (chameleon encryption, one-time signatures with encryption, hinting PRGs, trapdoor hash encryption, batch encryption) [9, 14, 16, 17, 33] have been a centerpiece in all these results.
After the work of Impagliazzo and Rudich (STOC, 1989), the black box framework has become one of the main research domain of cryptography. However black box techniques say nothing about non-black box techniques such as making use of zero-knowledge proofs. Brakerski et al. introduced a new black box framework named augmented black box framework, in which they gave a zero-knowledge proof oracle in addition to a base primitive oracle (TCC, 2011). They showed a construction of a non-interactive zero knowledge proof system based on a witness indistinguishable proof system oracle. They presented augmented black box construction of chosen ciphertext secure public key encryption scheme based on chosen plaintext secure public key encryption scheme and augmented black box separation between one-way function and key agreement.
Among the zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARK), the simulation-extractable zk-SNARK (SE-SNARK) introduces a security notion of non-malleability. The existing pairing-based zk-SNARKs designed from linear encoding are known to be vulnerable to algebraic manipulation of the proof. The latest SE-SNARKs check the proof consistency by increasing the proof size and the verification cost. In particular, the number of pairings increases almost doubles due to further verification. In this article, we propose two novel SE-SNARK constructions with a single verification. The consistency check is subsumed in a single verification through employing a hash function. The proof size and verification time of the proposed SE-SNARK schemes are minimal in that it is the same as the state-of-the-art zk-SNARK without non-malleability. The proof in our SE-SNARK constructions comprises only three group elements (type III) in the QAP-based scheme and two group elements (type I) in the SAP-based scheme. The verification time in both requires only 3 pairings. The soundness of the proposed schemes is proven under the hash-algebraic knowledge (HAK) assumption and the (linear) collision-resistant hash assumption.
Daniel Kales, Sebastian Ramacher, Christian Rechberger, Roman Walch · 5 authors
Post-quantum cryptography has received increased attention in recent years, in particular, due to the standardization effort by NIST. One of the second-round candidates in the NIST post-quantum standardization project is Picnic, a post-quantum secure signature scheme based on efficient zero-knowledge proofs of knowledge. In this work, we present the first FPGA implementation of Picnic. We show how to efficiently calculate LowMC, the block cipher used as a one-way function in Picnic, in hardware despite the large number of constants needed during computation. We then combine our LowMC implementation and efficient instantiations of Keccak to build the full Picnic algorithm. Additionally, we conform to recently proposed hardware interfaces for post-quantum schemes to enable easier comparisons with other designs. We provide evaluations of our Picnic implementation for both, the standalone design and a version wrapped with a PCIe interface, and compare them to the state-of-the-art software implementations of Picnic and similar hardware designs. Concretely, signing messages on our FPGA takes 0.25 ms for the L1 security level and 1.24 ms for the L5 security level, beating existing optimized software implementations by a factor of 4.