New Developments in Quantum Algorithms

In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model. The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in time O(\log^c N). It outputs a quantum state describing the solution of the system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201

Roadmap on optical security

Postprint (author's final draft

A Novel Blind Signature Scheme Based On Discrete Logarithm Problem With Un-traceability

Blind Signatures are a special type of digital signatures which possess two special properties of blindness and untraceability, which are important for today’s real world applications that require authentication , integrity , security , anonymity and privacy. David Chaum[2] was the first to propose the concept of blind signatures. The scheme's security was based on the difficulty of solving the factoring problem [3, 4]. Two properties that are important for a blind signature scheme in order to be used in various modern applications are blindness and untraceability[2, 5, 6] . Blindness means that the signer is not able to know the contents of the message while signing it, which is achieved by disguising (or blinding) the message through various methods. Untraceability refers to preventing the signer from linking the blinded message it signs to a later unblinded version that it may be called upon to verify. Blind signatures based on discrete logarithm problem are still an area with much scope for research. We aim to propose a novel blind signature scheme with untraceability , based on the discrete logarithm problem

A Cipher-Agnostic Neural Training Pipeline with Automated Finding of Good Input Differences

Neural cryptanalysis is the study of cryptographic primitives through machine learning techniques. Following Gohr’s seminal paper at CRYPTO 2019, a focus has been placed on improving the accuracy of such distinguishers against specific primitives, using dedicated training schemes, in order to obtain better key recovery attacks based on machine learning. These distinguishers are highly specialized and not trivially applicable to other primitives. In this paper, we focus on the opposite problem: building a generic pipeline for neural cryptanalysis. Our tool is composed of two parts. The first part is an evolutionary algorithm for the search of good input differences for neural distinguishers. The second part is DBitNet, a neural distinguisher architecture agnostic to the structure of the cipher. We show that this fully automated pipeline is competitive with a highly specialized approach, in particular for SPECK32, and SIMON32. We provide new neural distinguishers for several primitives (XTEA, LEA, HIGHT, SIMON128, SPECK128) and improve over the state-of-the-art for PRESENT, KATAN, TEA and GIMLI

A Bit-Vector Differential Model for the Modular Addition by a Constant

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR, which achieve the best software performances in low-end microcontrollers. To evaluate the resistance of an ARX cipher against differential cryptanalysis and its variants, the recent automated methods employ constraint satisfaction solvers, such as SMT solvers, to search for optimal characteristics. The main difficulty to formulate this search as a constraint satisfaction problem is obtaining the differential models of the non-linear operations, that is, the constraints describing the differential probability of each non-linear operation of the cipher. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this operation from being evaluated with automated methods. In this paper, we present the first bit-vector differential model for the n-bit modular addition by a constant input. Our model contains O(log2(n)) basic bit-vector constraints and describes the binary logarithm of the differential probability. We also represent an SMT-based automated method to look for differential characteristics of ARX, including constant additions, and we provide an open-source tool ArxPy to find ARX differential characteristics in a fully automated way. To provide some examples, we have searched for related-key differential characteristics of TEA, XTEA, HIGHT, and LEA, obtaining better results than previous works. Our differential model and our automated tool allow cipher designers to select the best constant inputs for modular additions and cryptanalysts to evaluate the resistance of ARX ciphers against differential attacks.acceptedVersio