Discrete Logarithm and Integer Factorization Using ID-based Encryption

Shamir proposed the concept of the ID-based Encryption (IBE) in [1]. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design a transformation process that can transfer the entire discrete logarithm and integer factorization based cryptosystems into the ID-based systems rather than re-invent a new system. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system

Practical IBC Using Hybrid-Mode Problems: Factoring and Discrete Logarithm

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system

Practical IBC using Hybrid-Mode Problems: Factoring and Discrete Logarithm

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system

Cryptographic scheme for group passwords distribution in steganographic systems

This paper proposes a new scheme of passwords distribution for user groups via a hidden communication channel. The previously known models explicitly demonstrated the presence of passwords and cannot be used in any hidden communication channel. The considered model assumes the presence of a coordinator who regulates the composition of the groups and is the source of the overwhelming proportion of messages. The composition of the groups is not known in advance and may change during transmission messages. It is assumed that the data transmitted in a container will consist of two parts: a service part, which contains information about groups and passwords, and a useful part, which contains the target message that encrypted with a group-password. The scheme is based on the Kronecker-Capelli theorem. To find a group password the subscriber-receiver, is included in the group, calculates the product of the roots of a joint system of linear algebraic equations. This system consists of n equations and contains n+1variables. For an outside subscriber, who is not included in the group, the system of equations has not a single solution. A subscriber in the group is able to calculate one variable by a predefined formula. Consequently, the system of equations for such subscriber has the unique solution. The paper describes the processes of changing a composition of groups: creating, adding a participant, removing. The removing users from a group is realized by reuniting members of the old group. The scheme provides the possibility of combining previously created subgroups into large group without significant overhead costs. The proposed scheme can be used in practice by some organization to manage its branches when communicating via hidden data transmission channels

Constructing Identity-Based Cryptosystems for Discrete Logarithm Based Cryptosystems

[[abstract]]In 1984, Shamir proposed the concept of the Identity-Based (ID-Based) cryptosystem. Instead of generating and publishing a public key for each user, the ID-Based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public-key file is not required. Since new cryptographic schemes always face security challenges and many discrete logarithm-based cryptographic systems have been deployed, therefore, the purpose of this paper is to design a transformation process that can transfer all of the discrete logarithm based cryptosystems into the ID-based systems rather than re-invent a new system. In addition, no modification of the original discrete logarithm based cryptosystems is necessary

Accelerating ID-based Encryption based on Trapdoor DL using Pre-computation

The existing identity-based encryption (IBE) schemes based on pairings require pairing computations in encryption or decryption algorithm and it is a burden to each entity which has restricted computing resources in mobile computing environments. An IBE scheme (MY-IBE) based on a trapdoor DL group for RSA setting is one of good alternatives for applying to mobile computing environments. However, it has a drawback for practical use, that the key generation algorithm spends a long time for generating a user\u27s private key since the key generation center has to solve a discrete logarithm problem. In this paper, we suggest a method to reduce the key generation time of the MY-IBE scheme, applying modified Pollard rho algorithm using significant pre-computation (mPAP). We also provide a rigorous analysis of the mPAP for more precise estimation of the key generation time and consider the parallelization and applying the tag tracing technique to reduce the wall-clock running time of the key generation algorithm. Finally, we give a parameter setup method for an efficient key generation algorithm and estimate key generation time for practical parameters from our theoretical analysis and experimental results on small parameters. Our estimation shows that it takes about two minutes using pre-computation for about 50 days with 27 GB storage to generate one user\u27s private key using the parallelized mPAP enhanced by the tag tracing technique with 100 processors

On the Relations Between Non-Interactive Key Distribution, Identity-Based Encryption and Trapdoor Discrete Log Groups

We investigate the relationships between identity-based non-interactive key distribution and identity-based encryption. We provide constructions for these schemes that make use of general trapdoor discrete log groups. We then investigate the schemes that result in two concrete settings, obtaining new, provably secure, near-practical identity-based encryption schemes

Compact Identity Based Encryption Based on n^{th} - Residuosity Assumption

Practical Identity Based Encryption (IBE) schemes use the costly bilinear pairing computation. Clifford Cock proposed an IBE based on quadratic residuosity in 2001 which does not use bilinear pairing but was not efficient in practice, due to the large ciphertext size. In 2007, Boneh et al. proposed the first space efficient IBE that was also based on quadratic residuosity problem. It was an improvement over Cock\u27s scheme but still the time required for encryption was quartic in the security parameter. In this paper, we propose a compact, space and time efficient identity based encryption scheme without pairing, based on a variant of Paillier Cryptosystem and prove it to be CPA secure. We have also proposed a CCA secure scheme based on the basic IBE scheme using the Fujisaki-Okamoto transformation. We have proved both the schemes in the random oracle model

On Cryptographic Building Blocks and Transformations

Cryptographic building blocks play a central role in cryptography, e.g., encryption or digital signatures with their security notions. Further, cryptographic building blocks might be constructed modularly, i.e., emerge out of other cryptographic building blocks. Essentially, one cryptographically transforms the underlying block(s) and their (security) properties into the emerged block and its properties. This thesis considers cryptographic building blocks and new cryptographic transformations