3,298 research outputs found

    Introducing S-index into factoring RSA modulus via Lucas sequences

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    At any instance in the factoring algorithm, the accumulative result stands independently. In effect, there is no clear direction to manoeuvre whether to go left or right. General Lucas sequences are practically useful in cryptography. In the past quarter century, factoring large RSA modulo into its primes is one of the most important and most challenging problems in computational number theory. A factoring technique on RSA modulo is mainly hindered by the strong prime properties. The success of factoring few large RSA modulo within the last few decades has been due to computing prowess overcoming one strong prime of RSA modulo. In this paper, some useful properties of Lucas sequences shall be explored in factoring RSA modulo. This paper will also introduces the S-index formation in solving quadratic equation modulo N. The S-index pattern is very useful in designing an algorithm to factor RSA modulo. The S-index will add another comparative tool to better manoeuvre in a factoring process. On one hand, it shall remain a theoretical challenge to overcome the strong prime properties. On the other hand, it shall remain a computational challenge to achieve a running time within polynomial time to factor RSA modulo. This paper will propose an avenue to do both using general Lucas sequences

    The New South Wales iVote System: Security Failures and Verification Flaws in a Live Online Election

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    In the world's largest-ever deployment of online voting, the iVote Internet voting system was trusted for the return of 280,000 ballots in the 2015 state election in New South Wales, Australia. During the election, we performed an independent security analysis of parts of the live iVote system and uncovered severe vulnerabilities that could be leveraged to manipulate votes, violate ballot privacy, and subvert the verification mechanism. These vulnerabilities do not seem to have been detected by the election authorities before we disclosed them, despite a pre-election security review and despite the system having run in a live state election for five days. One vulnerability, the result of including analytics software from an insecure external server, exposed some votes to complete compromise of privacy and integrity. At least one parliamentary seat was decided by a margin much smaller than the number of votes taken while the system was vulnerable. We also found protocol flaws, including vote verification that was itself susceptible to manipulation. This incident underscores the difficulty of conducting secure elections online and carries lessons for voters, election officials, and the e-voting research community

    Computing square root of a large Positive Integer

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    Dealing in large number is of interest in asymmetric key cryptography using RSA. The security of RSA is solely based on difficulty of factorization of a large number. Factoring a number requires finding all divisible primes less than or equal to the square root of the number. Proposed here is a new algorithm to compute the square root of large positive integer. The algorithm is based on the implementation of long division method also known as manual method we usually use to find the square root of a number. To implement the long division method, the given number is first represented in a radix-10 representa and then Bino’s Model of Multiplication is used to systematically implement the long division method. A representa is a special array to represent a number in the form of an array so as to enable us to treat the representas in the same way as we treat numbers. This simplifies the difficulty of dealing large numbers in a computer. The proposed algorithm is applied to the RSA–challenge numbers for factorization. The square roots of the challenge numbers can be computed easily in less than a second. The square roots of first few challenge number and last few challenge number are also provided, which may be used for factorization of corresponding challenge number.Key words: Asymmetric key cryptogra phy, Bino’s Model of Multiplication, Large number manipulation, Long division method, Prime factorization, RSA challenge numbers, Representa, Square root computatio

    Quantum resource estimates for computing elliptic curve discrete logarithms

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    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 LIQUiUi|\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 nn-bit prime field can be computed on a quantum computer with at most 9n+2log2(n)+109n + 2\lceil\log_2(n)\rceil+10 qubits using a quantum circuit of at most 448n3log2(n)+4090n3448 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
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