1,856 research outputs found
Fast and Secure Root Finding for Code-based Cryptosystems
In this work we analyze five previously published respectively trivial
approaches and two new hybrid variants for the task of finding the roots of the error locator polynomial
during the decryption operation of code-based encryption schemes. We compare
the performance of these algorithms and show that optimizations concerning
finite field element representations
play a key role for the speed of software implementations.
Furthermore, we point out a number of timing attack vulnerabilities that
can arise in root-finding algorithms, some aimed at recovering the message,
others at the secret support. We give experimental results of software
implementations showing that
manifestations of these vulnerabilities are present in straightforward
implementations of most of the root-finding variants presented in this
work.
As a result, we find that one of the variants provides security with respect to
all vulnerabilities as well as competitive computation time for code parameters that minimize the public key size
A Non-commutative Cryptosystem Based on Quaternion Algebras
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion
algebras. This cryptosystem uses bivariate polynomials as the underling ring.
The multiplication operation in our cryptosystem can be performed with high
speed using quaternions algebras over finite rings. As a consequence, the key
generation and encryption process of our cryptosystem is faster than NTRU in
comparable parameters. Typically using Strassen's method, the key generation
and encryption process is approximately times faster than NTRU for an
equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure
that makes inefficient standard lattice attacks on the private key. This
entails a higher computational complexity for attackers providing the
opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is
more resistant than NTRU against known attacks at an equivalent parameter set.
Moreover, message protection is feasible through larger polynomials and this
allows us to obtain the same security level as other NTRU-like cryptosystems
but using lower dimensions.Comment: Submitted for possible publicatio
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
Coding Theory-Based Cryptopraphy: McEliece Cryptosystems in Sage
Unlike RSA encryption, McEliece cryptosystems are considered secure in the presence of quantum computers. McEliece cryptosystems leverage error-correcting codes as a mechanism for encryption. The open-source math software Sage provides a suitable environment for implementing and exploring McEliece cryptosystems for undergraduate research. Using our Sage implementation, we explored Goppa codes, McEliece cryptosystems, and Stern’s attack against a McEliece cryptosystem
Post-quantum cryptography
Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.</p
Roadmap on optical security
Postprint (author's final draft
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