Roots of Unity in Orders
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DOI: 10.1007/s10208-016-9304-1
Abstract: We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete… read more here.
Keywords: unity orders; cryptology; roots unity;
Cybersecurity in India
Sign Up to like & getrecommendations! Published in 2022 at "Communications of the ACM"
DOI: 10.1145/3554910
Abstract: SECURING CYBERSPACE TODAY involves in-depth defense, which in turn requires taking a multilayered view of the systems in play. All layers must be secured, from the hardware processor and platform to the peripherals, firmware, operating… read more here.
Keywords: security iit; cryptology; cybersecurity; security ... See more keywords
Designing Efficient Dyadic Operations for Cryptographic Applications
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Cryptology"
DOI: 10.1515/jmc-2015-0054
Abstract: Abstract Cryptographic primitives from coding theory are some of the most promising candidates for NIST’s Post-Quantum Cryptography Standardization process. In this paper, we introduce a variety of techniques to improve operations on dyadic matrices, a… read more here.
Keywords: dyadic operations; cryptographic applications; operations cryptographic; designing efficient ... See more keywords
Secret sharing and duality
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DOI: 10.1515/jmc-2019-0045
Abstract: Abstract Secret sharing is an important building block in cryptography. All explicit secret sharing schemes which are known to have optimal complexity are multi-linear, thus are closely related to linear codes. The dual of such… read more here.
Keywords: scheme; secret sharing; complexity; cryptology ... See more keywords
Remarks on a Tropical Key Exchange System
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DOI: 10.1515/jmc-2019-0061
Abstract: Abstract We consider a key-exchange protocol based on matrices over a tropical semiring which was recently proposed in [2]. We show that a particular private parameter of that protocol can be recovered with a simple… read more here.
Keywords: tropical key; exchange system; cryptology; key exchange ... See more keywords
The Eleventh Power Residue Symbol
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DOI: 10.1515/jmc-2020-0077
Abstract: Abstract This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11), $ \mathbb{Q}\left( {{\zeta }_{11}} \right), $where 11 is a primitive 11th root of unity. It extends an earlier… read more here.
Keywords: eleventh power; power; cryptology; power residue ... See more keywords
Cryptanalysis of “MAKE”
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Cryptology"
DOI: 10.1515/jmc-2021-0016
Abstract: Abstract Rahman and Shpilrain proposed a Diffie–Hellman style key exchange based on a semidirect product of n × n n\times n -matrices over a finite field. We show that, using public information, an adversary can… read more here.
Keywords: cryptanalysis make; cryptology;
On the supersingular GPST attack
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DOI: 10.1515/jmc-2021-0020
Abstract: Abstract The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this paper, we identify and… read more here.
Keywords: attack; cryptology; supersingular gpst; gpst attack ... See more keywords