8,003 research outputs found
Introduction to Quantum Error Correction
In this introduction we motivate and explain the ``decoding'' and
``subsystems'' view of quantum error correction. We explain how quantum noise
in QIP can be described and classified, and summarize the requirements that
need to be satisfied for fault tolerance. Considering the capabilities of
currently available quantum technology, the requirements appear daunting. But
the idea of ``subsystems'' shows that these requirements can be met in many
different, and often unexpected ways.Comment: 44 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/ecprhtm
On the security of digital signature schemes based on error-correcting codes
We discuss the security of digital signature schemes based on error-correcting codes. Several attacks to the Xinmei scheme are surveyed, and some reasons given to explain why the Xinmei scheme failed, such as the linearity of the signature and the redundancy of public keys. Another weakness is found in the Alabbadi-Wicker scheme, which results in a universal forgery attack against it. This attack shows that the Alabbadi-Wicker scheme fails to implement the necessary property of a digital signature scheme: it is infeasible to find a false signature algorithm D from the public verification algorithm E such that E(D*(m)) = m for all messages m. Further analysis shows that this new weakness also applies to the Xinmei scheme
Ternary Syndrome Decoding with Large Weight
The Syndrome Decoding problem is at the core of many code-based
cryptosystems. In this paper, we study ternary Syndrome Decoding in large
weight. This problem has been introduced in the Wave signature scheme but has
never been thoroughly studied. We perform an algorithmic study of this problem
which results in an update of the Wave parameters. On a more fundamental level,
we show that ternary Syndrome Decoding with large weight is a really harder
problem than the binary Syndrome Decoding problem, which could have several
applications for the design of code-based cryptosystems
Cryptanalysis of a One-Time Code-Based Digital Signature Scheme
We consider a one-time digital signature scheme recently proposed by
Persichetti and show that a successful key recovery attack can be mounted with
limited complexity. The attack we propose exploits a single signature
intercepted by the attacker, and relies on a statistical analysis performed
over such a signature, followed by information set decoding. We assess the
attack complexity and show that a full recovery of the secret key can be
performed with a work factor that is far below the claimed security level. The
efficiency of the attack is motivated by the sparsity of the signature, which
leads to a significant information leakage about the secret key.Comment: 5 pages, 1 figur
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