Publication

Cryptanalysis of Enhanced MORE

Serge Vaudenay, Damian Vizár
2018
Conference Papers

Abstract

Fully homomorphic encryption (FHE) has been among the most popular research topics of the last decade. While the bootstrapping-based, public key cryptosystems that follow Gentry's original design are getting more and more efficient, their performance is still far from being practical. This lead to several attempts to construct symmetric FHE schemes that would not be as inefficient as their public key counterparts. Unfortunately, most such schemes were also based on (randomized) linear transformations, and shown completely insecure. One such broken scheme was the Matrix Operation for Randomization and Encryption (MORE). In a recent paper, Hariss, Noura and Samhat propose Enhanced MORE, which is supposed to improve over MORE's weaknesses. We analyze Enhanced MORE, discuss why it does not improve over MORE, and show that it is even less secure by presenting a highly efficient ciphertext-only decryption attack. We implement the attack and confirm its correctness.

Official source

https://infoscience.epfl.ch/entities/publication/3c1e7457-1924-4795-95fc-eba5068a0f43

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Serge Vaudenay, Damian Vizár
2018
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3c1e7457-1924-4795-95fc-eba5068a0f43

About this result

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related concepts (32)

Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.

Matrix multiplication

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .

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