A Distinguisher-Based Attack of a Homomorphic Encryption Scheme Relying on Reed-Solomon Codes

Bogdanov and Lee suggested a homomorphic public-key encryption scheme based on error correcting codes. The underlying public code is a modified Reed-Solomon code obtained from inserting a zero submatrix in the Vandermonde generating matrix defining it. The columns that define this submatrix are kept secret and form a set $L$. We give here a distinguisher that detects if one or several columns belong to $L$ or not. This distinguisher is obtained by considering the code generated by component-wise products of codewords of the public code (the so called "square code"). This operation is applied to punctured versions of this square code obtained by picking a subset $I$ of the whole set of columns. It turns out that the dimension of the punctured square code is directly related to the cardinality of the intersection of $I$ with $L$. This allows an attack which recovers the full set $L$ and which can then decrypt any ciphertext.Comment: 11 page

A Distinguisher-Based Attack on a Variant of McEliece's Cryptosystem Based on Reed-Solomon Codes

Baldi et \textit{al.} proposed a variant of McEliece's cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix. The motivation for this change is twofold: it would allow the use of codes that were shown to be insecure in the original McEliece's cryptosystem, and it would reduce the key size while keeping the same security against generic decoding attacks. The authors suggest to use generalized Reed-Solomon codes instead of Goppa codes. The public code built with this method is not anymore a generalized Reed-Solomon code. On the other hand, it contains a very large secret generalized Reed-Solomon code. In this paper we present an attack that is built upon a distinguisher which is able to identify elements of this secret code. The distinguisher is constructed by considering the code generated by component-wise products of codewords of the public code (the so-called "square code"). By using square-code dimension considerations, the initial generalized Reed-Solomon code can be recovered which permits to decode any ciphertext. A similar technique has already been successful for mounting an attack against a homomorphic encryption scheme suggested by Bogdanoc et \textit{al.}. This work can be viewed as another illustration of how a distinguisher of Reed-Solomon codes can be used to devise an attack on cryptosystems based on them.Comment: arXiv admin note: substantial text overlap with arXiv:1203.668

Review of \u3ci\u3eThe Calgary Project: Urban Form/Urban Life. \u3c/i\u3e By Beverly A. Sandalack and Andrei Nicolai.

The Calgary Project is an ambitious narrative. In eight chapters and two appendixes, the authors set about tracing the historical and spatial evolution of Calgary, aiming at drawing conclusions that could inform its planning in the future. The city\u27s development is portrayed through five periods, unfolding from the establishment of a small North West Mounted Police Fort in 1875 to our times. Each period is featured in a chapter that opens with a discussion of the ideas, plans, and planning practices of the time, followed by a discussion of the spatial structure of the urbanized areas, and concludes with an illustrated analysis of characteristic urban and architectural forms. Drawing loosely on Kevin Lynch\u27s cityscape analysis categories and more largely on M. R. G. Conzen\u27s approach to townscape analysis, the authors explore the material manifestations and spatial logics that mark Calgary\u27s different periods of growth. The original and most compelling contribution of the work lies in its systematic documentation and representation in two and three dimensions of the built landscape at different levels of spatial resolution, from the city as a whole, to the evolving settlement configurations of the various suburbs, and down to the platting, architectural vocabulary and syntax, and the resulting streetscapes. Combined with a rich iconography, these representations trace a systematic repertory of Calgary\u27s built landscapes (i.e., the city\u27s morphology). They allow the reader to reflect on how the planning ideas, the purposeful development practices, and the inevitable social and economic forces and contingencies have combined to produce a contrasted cityscape, more complex, considering the city\u27s young age, than the authors initially thought

Developing a Framework to Assess Financial Stability: Conference Highlights and Lessons

Central banks are still defining their approach to financial stability and are at an early stage in the development of useful models. The Bank of Canada's 2007 economic conference was organized to stimulate progress in the development of financial-stability frameworks. Among the highlights reported here are the discussions centred around three proposed frameworks: a contingent-claims-analysis framework, a semi-structural framework, and structural financial-stability models. Participants also reported on their experiences with stress-testing under the International Monetary Fund's Financial Sector Assessment Program and discussed the implications for financial stability of linkages among payment, clearing, and settlement systems.