Quantum resource estimates for computing elliptic curve discrete logarithms

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve defined over an $n$-bit prime field can be computed on a quantum computer with at most $9n + 2\lceil\log_2(n)\rceil+10$ qubits using a quantum circuit of at most $448 n^3 \log_2(n) + 4090 n^3$ Toffoli gates. We are able to classically simulate the Toffoli networks corresponding to the controlled elliptic curve point addition as the core piece of Shor's algorithm for the NIST standard curves P-192, P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to recent resource estimates for Shor's factoring algorithm. The results also support estimates given earlier by Proos and Zalka and indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added. ASIACRYPT 201

Can NSEC5 be practical for DNSSEC deployments?

NSEC5 is proposed modification to DNSSEC that simultaneously guarantees two security properties: (1) privacy against offline zone enumeration, and (2) integrity of zone contents, even if an adversary compromises the authoritative nameserver responsible for responding to DNS queries for the zone. This paper redesigns NSEC5 to make it both practical and performant. Our NSEC5 redesign features a new fast verifiable random function (VRF) based on elliptic curve cryptography (ECC), along with a cryptographic proof of its security. This VRF is also of independent interest, as it is being standardized by the IETF and being used by several other projects. We show how to integrate NSEC5 using our ECC-based VRF into the DNSSEC protocol, leveraging precomputation to improve performance and DNS protocol-level optimizations to shorten responses. Next, we present the first full-fledged implementation of NSEC5—extending widely-used DNS software to present a nameserver and recursive resolver that support NSEC5—and evaluate their performance under aggressive DNS query loads. Our performance results indicate that our redesigned NSEC5 can be viable even for high-throughput scenarioshttps://eprint.iacr.org/2017/099.pdfFirst author draf

Enhancing an Embedded Processor Core with a Cryptographic Unit for Performance and Security

We present a set of low-cost architectural enhancements to accelerate the execution of certain arithmetic operations common in cryptographic applications on an extensible embedded processor core. The proposed enhancements are generic in the sense that they can be beneficially applied in almost any RISC processor. We implemented the enhancements in form of a cryptographic unit (CU) that offers the programmer an extended instruction set. The CU features a 128-bit wide register file and datapath, which enables it to process 128-bit words and perform 128-bit loads/stores. We analyze the speed-up factors for some arithmetic operations and public-key cryptographic algorithms obtained through these enhancements. In addition, we evaluate the hardware overhead (i.e. silicon area) of integrating the CU into an embedded RISC processor. Our experimental results show that the proposed architectural enhancements allow for a significant performance gain for both RSA and ECC at the expense of an acceptable increase in silicon area. We also demonstrate that the proposed enhancements facilitate the protection of cryptographic algorithms against certain types of side-channel attacks and present an AES implementation hardened against cache-based attacks as a case study

Computational and Energy Costs of Cryptographic Algorithms on Handheld Devices

Networks are evolving toward a ubiquitous model in which heterogeneous devices are interconnected. Cryptographic algorithms are required for developing security solutions that protect network activity. However, the computational and energy limitations of network devices jeopardize the actual implementation of such mechanisms. In this paper, we perform a wide analysis on the expenses of launching symmetric and asymmetric cryptographic algorithms, hash chain functions, elliptic curves cryptography and pairing based cryptography on personal agendas, and compare them with the costs of basic operating system functions. Results show that although cryptographic power costs are high and such operations shall be restricted in time, they are not the main limiting factor of the autonomy of a device

Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any finite abelian group. Their algorithm stimulated a lot of interest in the cryptography community, especially in the context of `bit security'. This manuscript attempts to be a friendly and comprehensive guide to the tools and results in this field. The intended readership is cryptographers who have heard about these tools and seek an understanding of their mechanics and their usefulness and limitations. A compact overview of the algorithm is presented with emphasis on the ideas behind it. We show how these ideas can be extended to a `modulus-switching' variant of the algorithm. We survey some applications of this algorithm, and explain that several results should be taken in the right context. In particular, we point out that some of the most important bit security problems are still open. Our original contributions include: a discussion of the limitations on the usefulness of these tools; an answer to an open question about the modular inversion hidden number problem

Year 2010 Issues on Cryptographic Algorithms

In the financial sector, cryptographic algorithms are used as fundamental techniques for assuring confidentiality and integrity of data used in financial transactions and for authenticating entities involved in the transactions. Currently, the most widely used algorithms appear to be two-key triple DES and RC4 for symmetric ciphers, RSA with a 1024-bit key for an asymmetric cipher and a digital signature, and SHA-1 for a hash function according to international standards and guidelines related to the financial transactions. However, according to academic papers and reports regarding the security evaluation for such algorithms, it is difficult to ensure enough security by using the algorithms for a long time period, such as 10 or 15 years, due to advances in cryptanalysis techniques, improvement of computing power, and so on. To enhance the transition to more secure ones, National Institute of Standards and Technology (NIST) of the United States describes in various guidelines that NIST will no longer approve two-key triple DES, RSA with a 1024-bit key, and SHA-1 as the algorithms suitable for IT systems of the U.S. Federal Government after 2010. It is an important issue how to advance the transition of the algorithms in the financial sector. This paper refers to issues regarding the transition as Year 2010 issues in cryptographic algorithms. To successfully complete the transition by 2010, the deadline set by NIST, it is necessary for financial institutions to begin discussing the issues at the earliest possible date. This paper summarizes security evaluation results of the current algorithms, and describes Year 2010 issues, their impact on the financial industry, and the transition plan announced by NIST. This paper also shows several points to be discussed when dealing with Year 2010 issues.Cryptographic algorithm; Symmetric cipher; Asymmetric cipher; Security; Year 2010 issues; Hash function

Review on DNA Cryptography

Cryptography is the science that secures data and communication over the network by applying mathematics and logic to design strong encryption methods. In the modern era of e-business and e-commerce the protection of confidentiality, integrity and availability (CIA triad) of stored information as well as of transmitted data is very crucial. DNA molecules, having the capacity to store, process and transmit information, inspires the idea of DNA cryptography. This combination of the chemical characteristics of biological DNA sequences and classical cryptography ensures the non-vulnerable transmission of data. In this paper we have reviewed the present state of art of DNA cryptography.Comment: 31 pages, 12 figures, 6 table

Internet security for mobile computing

Mobile devices are now the most dominant computer platform. Every time a mobile web application accesses the internet, the end user’s data is susceptible to malicious attacks. For instance, when paying a bill at a store with NFC mobile payment, navigating through a city operating GPS on a smartphone, or dictating the temperature at a household with a home automation device. These activities seem routine, yet, when vulnerabilities are present they can leave holes for hackers to access bank accounts, pinpoint a user’s recent location, or tell when someone is not at home. The awareness of the end user cannot be trusted. Device vendors and developers must provide safeguards. An ongoing issue is that the present security standards are outdated and were never envisioned with mobile devices in mind. It can be suggested that security is only idling the progress of mobile computing. Still, many application developers and IT professionals do not adopt security standards fast enough to keep up-to-date with known vulnerabilities. The main goals of the next generation of security standards, TLS, will provide developers with greater security efficiency and improved mobile throughput. These proposed capabilities of the TLS protocol will streamline mobile computing into the forefront of security practices. The analysis of this report demonstrates concepts on the direction mobile security, usability, and performance from a development standpoint.Electrical and Computer Engineerin