Matricial Public Key Cryptosystem with Digital Signature

We describe a new public key cryptosystem using block upper triangular matrices with elements in Zp , based on a generalization of the discrete logarithm problem over a finite group. The proposed cryptosystem is very efficient, requiring very few operations and also allows an ElGamal based digital signature scheme. The main benefit is that the security level is higher than other algorithms for the same key size.

Information is recognized by many organizations as an important asset. Few businesses could function effectively without the ability to rely, to some extent, on information as a resource: banks need to know the details of each account, and hospitals need to access patient medical records. Information security is concerned with providing assurances about data. Broadly speaking, information security is frequently classified as the provision of the following services: confidentiality (the assurance that data is not disclosed to unauthorized parties), integrity (the assurance that data is genuine) and availability (the assurance that data is readily accessible). Communication over open networks is very cheap, but represents easy pickings for an adversary who wants to intercept, modify, or inject data; data stored on networked computers faces similar threats. If society is to benefit from the advantages offered by electronic data storage and open networks, information security must therefore provide techniques capable of supplying confidentiality, integrity, and availability in this new environment. In order to establish a confidential channel between two users of such a network, classical singlekey cryptography requires them to exchange a common secret key over a secure channel. This may work if the network is small and local, but it is infeasible in non-local or large networks. To simplify the key exchange problem, modern public-key cryptography provides a mechanism in which the keys to be exchanged do not need to be secret. In such a framework, every user possesses a key pair consisting of a (non-secret) public key and a (secret) private key; only public keys are published. They are used to encrypt the messages to be sent to the owner of the key or to verify digital signatures issued by the owner of the key. Before using someone else’s public key to encrypt a message or verify a signature, one should make sure that the key really belongs to the intended recipient or the indicated issuer of the signature. Achieving authenticity of public keys can be done in several ways. Public key cryptosystems are essential for electronic commerce or electronic banking transactions; they assure privacy as well as integrity of the transactions between two parties. Digital signatures are used to sign electronic documents and they are also mostly based on publickey techniques.

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