Parallelized Side-Channel Attack Resisted Scalar Multiplication Using q-Based Addition-Subtraction k-chains

This paper presents parallel scalar multiplication techniques for elliptic curve cryptography using q-based addition-subtraction k-chain which can also effectively resist side-channel attack. Many techniques have been discussed to improve scalar multiplication, for example, double-and-add, NAF, w-NAF, addition chain and addition-subtraction chain. However, these techniques cannot resist side-channel attack. Montgomery ladder, random w-NAF and uniform operation techniques are also widely used to prevent side-channel attack, but their operations are not efficient enough comparing to those with no side-channel attack prevention. We have found a new way to use k-chain for this purpose. In this paper, we extend the definition of k-chain to q-based addition-subtraction k-chain and modify an algorithm proposed by Jarvinen et al. to generate the q-based addition-subtraction k-chain. We show the upper and lower bounds of its length which lead to the computation time using the new chain techniques. The chain techniques are used to reduce the cost of scalar multiplication in parallel ways. Comparing to w-NAF, which is faster than double-and-add and Montgomery ladder technique, the maximum computation time of our q-based addition-subtraction k-chain techniques can have up to 25.92% less addition costs using only 3 parallel computing cores. We also discuss on the optimization for multiple operand point addition using hybrid-double multiplier which is proposed by Azarderakhsh and Reyhani-Masoleh. The proposed parallel chain techniques can also tolerate side-channel attack efficiently

Faster cellular automata cryptosystems with neighbor sequences

The encryption processes and cryptosystems are very important. We use them to protect our private information over the Internet. Cellular automata are ones of the computational models that can also be used in cryptosystems. The advantage of the cellular automata is their abilities to work in parallel, and thus can reduce the encryption time. Some applications require the encryption time to be small, so this paper aims to reduce the encryption time of the cellular automata cryptosystems. We propose a new technique to permit the cryptosystems to get the avalanche effect faster. This avalanche effect is one of the desired properties for cryptosystems. In the proposed technique, the new type of neighbor is defined, a sequence of neighbor tuples. We apply our technique to Seredynski and Bouvry’s work, and the results show that the number of iterations can be reduced up to three times. This makes our cellular automata cryptosystems run faster. The relationship between the size of the neighbor and the size of the cellular automata, and the effect of neighbor sequences to the hardware implementations are left for further studies

Efficient Oblivious Evaluation Protocol and Conditional Disclosure of Secrets for DFA

In oblivious finite automata evaluation, one party holds a private automaton, and the other party holds a private string of characters. The objective is to let the parties know whether the string is accepted by the automaton or not, while keeping their inputs secret. The applications include DNA searching, pattern matching, and more. Most of the previous works are based on asymmetric cryptographic primitives, such as homomorphic encryption and oblivious transfer. These primitives are significantly slower than symmetric ones. Moreover, some protocols also require several rounds of interaction. As our main contribution, we propose an oblivious finite automata evaluation protocol via conditional disclosure of secrets (CDS), using one (potentially malicious) outsourcing server. This results in a constant-round protocol, and no heavy asymmetric-key primitives are needed. Our protocol is based on a building block called an oblivious CDS scheme for deterministic finite automata\u27\u27 which we also propose in this paper. In addition, we propose a standard CDS scheme for deterministic finite automata as an independent interest

Evolving Homomorphic Secret Sharing for Hierarchical Access Structures

Secret sharing is a cryptographic primitive that divides a secret into several shares, and allows only some combinations of shares to recover the secret. As it can also be used in secure multi-party computation protocol with outsourcing servers, several variations of secret sharing are devised for this purpose. Most of the existing protocols require the number of computing servers to be determined in advance. However, in some situations we may want the system to be evolving . We may want to increase the number of servers and strengthen the security guarantee later in order to improve availability and security of the system. Although evolving secret sharing schemes are available, they do not support computing on shares. On the other hand, homomorphic secret sharing allows computing on shares with small communication, but they are not evolving. As the contribution of our work, we give the definition of evolving homomorphic secret sharing supporting both properties. We propose two schemes, one with hierarchical access structure supporting multiplication, and the other with partially hierarchical access structure supporting computation of low degree polynomials. Comparing to the work with similar functionality of Choudhuri et al. (IACR ePrint 2020), our schemes have smaller communication costs

Constructive tt-secure Homomorphic Secret Sharing for Low Degree Polynomials

This paper proposes $t$-secure homomorphic secret sharing schemes for low degree polynomials. Homomorphic secret sharing is a cryptographic technique to outsource the computation to a set of servers while restricting some subsets of servers from learning the secret inputs. Prior to our work, at Asiacrypt 2018, Lai, Malavolta, and Schröder proposed a $1$-secure scheme for computing polynomial functions. They also alluded to $t$-secure schemes without giving explicit constructions; constructing such schemes would require solving set cover problems, which are generally NP-hard. Moreover, the resulting implicit schemes would require a large number of servers. In this paper, we provide a constructive solution for threshold-$t$ structures by combining homomorphic encryption with the classic secret sharing scheme for general access structure by Ito, Saito, and Nishizeki. Our scheme also quantitatively improves the number of required servers from $O(t^2)$ to $O(t)$, compared to the implicit scheme of Lai et al. We also suggest several ideas for future research directions