Biblio

We discuss the performance of a new quantumsafe multivariate digital signature scheme proposed recently, called the Multivariate Polynomial Public Key Digital Signature (MPPK DS) scheme. Leveraging MPPK KEM or key exchange mechanism, the MPPK DS scheme is established using modular exponentiation with a randomly chosen secret base from a prime field. The security of the MPPK DS algorithm largely benefits from a generalized safe prime associated with the said field and the Euler totient function. We can achieve NIST security levels I, III, and V over a 64-bit prime field, with relatively small public key sizes of 128 bytes, 192 bytes, and 256 bytes for security levels I, III, and V, respectively. The signature sizes are 80 bytes for level I, 120 bytes for level III, and 160 bytes for level V. The MPPK DS scheme offers probabilistic procedures for signing and verification. That is, for each given signing message, a signer can randomly pick a base integer to be used for modular exponentiation with a private key, and a verifier can verify the signature with the digital message, based on the verification relationship, using any randomly selected noise variables. The verification process can be repeated as many times as the verifier wishes for different noise values, however, for a true honest signature, the verification will always pass. This probabilistic feature largely restricts an adversary to perform spoofing attacks. In this paper, we conduct some performance analyses by implementing MPPK DS in Java. We compare its performance with benchmark performances of NIST PQC Round 3 finalists: Rainbow, Dilithium, and Falcon. Overall, the MPPK DS scheme demonstrates equivalent or better performance, and much smaller public key, as well as signature sizes, compared to the three NIST PQC Round 3 finalists.

In VANET, vehicles periodically transmit beacon messages to the neighboring vehicles and the RSU. To establish the authenticity of these messages, a number of digital signature schemes have been proposed in literature. Many of these schemes enable an RSU to perform aggregate verification of the signatures to deal with high vehicle density scenarios. These schemes are either based on traditional PKC concept involving certificate management overhead or identity based cryptography having key escrow problem. Further, these schemes require the existence of OBU device which is resistant to side channel attacks. In this paper, we propose a hierarchical trusted authority privacy preserving certificateless aggregate signature scheme for VANET. In addition to providing message authentication, integrity and non-repudiation, our scheme is resistant to message forgeability attack. The proposed scheme assumes hierarchical organization of network such that vehicles operate under multiple trusted authorities (TA) which in turn are controlled by single root TA. Using our scheme, the entity could verify messages received from vehicles which operate under multiple TAs. The proposed scheme is free from key escrow problem and resistant to side channel attacks on OBU. It also possesses conditional linkability such that originator of a message could be revealed whenever required. Simulations confirm the efficient nature in terms of verification delay as compared to other well known schemes proposed in literature.

The modular exponentiation is an important operation for cryptographic transformations in public key cryptosystems like the Rivest, Shamir and Adleman, the Difie and Hellman and the ElGamal schemes. computing ax mod n and axby mod n for very large x,y and n are fundamental to the efficiency of almost all pubic key cryptosystems and digital signature schemes. To achieve high level of security, the word length in the modular exponentiations should be significantly large. The performance of public key cryptography is primarily determined by the implementation efficiency of the modular multiplication and exponentiation. As the words are usually large, and in order to optimize the time taken by these operations, it is essential to minimize the number of modular multiplications. In this paper we are presenting efficient algorithms for computing ax mod n and axbymod n. In this work we propose four algorithms to evaluate modular exponentiation. Bit forwarding (BFW) algorithms to compute ax mod n, and to compute axby mod n two algorithms namely Substitute and reward (SRW), Store and forward(SFW) are proposed. All the proposed algorithms are efficient in terms of time and at the same time demands only minimal additional space to store the pre-computed values. These algorithms are suitable for devices with low computational power and limited storage.