A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance

Non-Malleable Secret Sharing for General Access Structures

Goyal and Kumar (STOC\u2718) recently introduced the notion of non-malleable secret sharing. Very roughly, the guarantee they seek is the following: the adversary may potentially tamper with all of the shares, and still, either the reconstruction procedure outputs the original secret, or, the original secret is ``destroyed and the reconstruction outputs a string which is completely ``unrelated to the original secret. Prior works on non-malleable codes in the 2 split-state model imply constructions which can be seen as 2-out-of-2 non-malleable secret sharing (NMSS) schemes. Goyal and Kumar proposed constructions of t-out-of-n NMSS schemes. These constructions have already been shown to have a number of applications in cryptography. We continue this line of research and construct NMSS for more general access structures. We give a generic compiler that converts any statistical (resp. computational) secret sharing scheme realizing any access structure into another statistical (resp. computational) secret sharing scheme that not only realizes the same access structure but also ensures statistical non-malleability against a computationally unbounded adversary who tampers each of the shares arbitrarily and independently. Instantiating with known schemes we get unconditional NMMS schemes that realize any access structures generated by polynomial size monotone span programs. Similarly, we also obtain conditional NMMS schemes realizing access structure in monotoneP (resp. monotoneNP) assuming one-way functions (resp. witness encryption). Towards considering more general tampering models, we also propose a construction of n-out-of-n NMSS. Our construction is secure even if the adversary could divide the shares into any two (possibly overlapping) subsets and then arbitrarily tamper the shares in each subset. Our construction is based on a property of inner product and an observation that the inner-product based construction of Aggarwal, Dodis and Lovett (STOC\u2714) is in fact secure against a tampering class that is stronger than 2 split-states. We also show applications of our construction to the problem of non-malleable message transmission

Secure Key Encapsulation Mechanism with Compact Ciphertext and Public Key from Generalized Srivastava code

Code-based public key cryptosystems have been found to be an interesting option in the area of Post-Quantum Cryptography. In this work, we present a key encapsulation mechanism (KEM) using a parity check matrix of the Generalized Srivastava code as the public key matrix. Generalized Srivastava codes are privileged with the decoding technique of Alternant codes as they belong to the family of Alternant codes. We exploit the dyadic structure of the parity check matrix to reduce the storage of the public key. Our encapsulation leads to a shorter ciphertext as compared to DAGS proposed by Banegas et al. in Journal of Mathematical Cryptology which also uses Generalized Srivastava code. Our KEM provides IND-CCA security in the random oracle model. Also, our scheme can be shown to achieve post-quantum security in the quantum random oracle model

Classic McEliece Implementation with Low Memory Footprint

The Classic McEliece cryptosystem is one of the most trusted quantum-resistant cryptographic schemes. Deploying it in practical applications, however, is challenging due to the size of its public key. In this work, we bridge this gap. We present an implementation of Classic McEliece on an ARM Cortex-M4 processor, optimized to overcome memory constraints. To this end, we present an algorithm to retrieve the public key ad-hoc. This reduces memory and storage requirements and enables the generation of larger key pairs on the device. To further improve the implementation, we perform the public key operation by streaming the key to avoid storing it as a whole. This additionally reduces the risk of denial of service attacks. Finally, we use these results to implement and run TLS on the embedded device

Localised multisecret sharing

localised multisecret sharing scheme is a multisecret sharing scheme for an ordered set of players in which players in the smallest sets who are authorised to access secrets are close together in the underlying ordering. We define threshold versions of localised multisecret sharing schemes, we provide lower bounds on the share size of perfect localised multisecret sharing schemes in an information theoretic setting, and we give explicit constructions of schemes to show that these bounds are tight. We then analyse a range of approaches to relaxing the model that provide trade-offs between the share size and the level of security guarantees provided by the scheme, in order to permit the construction of schemes with smaller shares. We show how these techniques can be used in the context of an application to key distribution for RFID-based supply-chain management motivated by the proposal of Juels, Pappu and Parno from USENIX 2008

On the CCA2 Security of McEliece in the Standard Model

In this paper we study public-key encryption schemes based on error-correcting codes that are IND-CCA2 secure in the standard model. In particular, we analyze a protocol due to Dowsley, Muller-Quade and Nascimento, based on a work of Rosen and Segev. The original formulation of the protocol contained some ambiguities and incongruences, which we point out and correct; moreover, the protocol deviates substantially from the work it is based on. We then present a construction which resembles more closely the original Rosen-Segev framework, and show how this can be instantiated with the McEliece scheme