Sami Harari

A new authentication algorithm

In this work we present a new authentication algorithm with modified versions suitable for identification and signature. It uses error correcting codes and binary field arithmetic. It has the property that counterfeiting attacks are equivalent to solving NP complete problems. It is easy to implement and is economical in computing power and memory.

Generalized boolean bent functions

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over

Hidden Field Equations Cryptosystem Performances

\mathbb{F}^{m}_{2}

Non-linear, non-commutative functions for data integrity

. Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of involutions, and to show their equivalence as in the classical case.

FSS2-Id/A Fast Safe Identity-Based Multi Signature Scheme

It is pointed out in (1) that HFE is faster than RSA, but it has larger key storage. In this paper, we will outline some of its advantages and disadvantages. We will also study the fact of the extension field degree and the private key degree on the speed of key generation, encryption and decryption.

HCC: A Hash Function Using Error Correcting Codes

Several authors have recently proposed digital signature schemes [1], [2],... In an environment where identification is not possible, and the transmission safe the use of these schemes certify that the data originated from the legitimate person. However in an environment where identification can be ensured by other means and where transmission is done in an unsafe medium , the use of the same schemes ensure data inteqrity: any modification of the data during transmission shows up when one checks the corresponding signature.

Weakness on Cryptographic Schemes Based on Chained Codes

In this paper, an identity-based multi signature scheme (IBMS) is presented. Many applications require that public keys of the signers to be sent along the signature. Identity strings are likely to be much shorter than randomly generated public keys and are easily verifiable with other applications such as mail or web pages. This property makes the identity based paradigm appealing in such a situation. The new scheme is based on the difficulty of factoring a Rivest Adleman Shamir integer and in particular does not rely on the untested assumptions on bilinear maps. A proof of security for this IBMS is obtained under the assumption of the one wayness of the RSA in the random oracle model. It is analogous but not equivalent to the Bellare scheme. A modified version which uses less network resources and therefore adapted for a large number of signers, is also presented.

A correlation cryptographic scheme

After studying the constraints related to the use of error correcting codes as hash functions, this document introduces a hash function HCC (hash with codes and correlations) having a ’divide and conquer’ approach for calculating the hash, while having an exponential complexity for the search of collisions. Possible generalizations are also sketched.

Secure and Fast Digital Signatures using BCH Codes

We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. This result prohibits the use of chained code on cryptography.

Generalisation of Kipnis and Shamir Cryptanalysis of the HFE public key cryptosystem

In [1] McEliece introduced a public key cryptosystem using error correcting codes. The message is coded into codewords by using a public generator matrix G. The key to the system is an error vector of weight smaller than the error capacity which is added to the coded information vector. Polynomial time attacks have been devised against this scheme.