Abstract This paper presents a proposal to improve the software implementation of SNOW-V, a candidate for encrypting 5G communications. In particular, we focus on the proposal for 32-bit architectures with limited resources, such as wireless sensor networks. SNOW-V is a pseudorandom number generator, this type of structures are traditionally implemented in hardware. The advent of 5G means that this implementation must be purely software, losing the advantages and speed of a purely hardware or even hybrid implementation. Due to the wide variety of interconnected devices in the IoT, we cannot assume or associate security with a given architecture or unlimited resource devices. For this reason, we have focused our efforts on analyzing and improving the speed of the proposed 5G encryption on lightweight architectures. Specifically, we analyze its software implementation and propose improvements to speed up the encryption process while protecting confidentiality and integrity for 32-bit devices.

In this paper we show how to attain the capacity of discrete symmetric channels with polynomial time decoding complexity by considering iterated (U | U + V) constructions with algebraic geometry (AG) code components. These codes are decoded with a recursive computation of the a posteriori probabilities of the code symbols together with decoding the AG components with the Koetter-Vardy algorithm. We show that, when the number of levels of the iterated (U | U + V) construction tends to infinity, we attain the capacity of any discrete symmetric channel. Moreover the error probability decays quasi-exponentially with the codelength in the case of Reed-Solomon code constituents and exponentially with Tsfasman-Vladuts-Zink code constituents.

We give polynomial time attacks on the McEliece public key cryptosystem-based either on algebraic geometry (AG) codes or on small co-dimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an error correcting pair (ECP), or an error correcting array (ECA) from the single data of an arbitrary generator matrix of a code. An ECP provides a decoding algorithm, that corrects up to ((d* - 1 - g)/2) errors, where d* denotes the designed distance and g denotes the genus of the corresponding curve, while with an ECA the decoding algorithm corrects up to ((d* - 1)/2) errors. Roughly speaking, for a public code of length n over Fq, these attacks run in O(n4log(n)) operations in Fqfor the reconstruction of an ECP and O(n5) operations for the reconstruction of an ECA. A probabilistic shortcut allows to reduce the complexities respectively to O(n3±ε log(n)) and O(n4±ε). Compared with the previous known attack due to Faure and Minder, our attack is efficient on codes from curves of arbitrary genus. Furthermore, we investigate how far these methods apply to subcodes of AG codes.

In this paper we present a modification of Reed-Solomon codes that beats the Guruswami-Sudan 1 − √R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V ) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performance as the (U | U + V )-construction) for being used in code-based cryptography, namely to build a McEliece scheme. The point is here that these codes not only perform nearly as well (or even better in the low rate regime) as Reed-Solomon codes, but also that their structure seems to avoid the Sidelnikov-Shestakov attack which broke a previous McEliece proposal based on generalized Reed-Solomon codes.

We give a polynomial time attack on the McEliece public key cryptosystem based on algebraic geometry codes. Roughly speaking, this attacks runs in O(n4) operations in Fq, where n denotes the code length. Compared to previous attacks, the present one allows to recover a decoding algorithm for the public key even for codes from high genus curves.

There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.

Snow 3G is the backup encryption algorithm used in the mobile phone UMTS technology to ensure data confidentiality. Its design - a combiner with memory - is derived from the stream cipher Snow 2.0, with improvements against algebraic cryptanalysis and distinguishing attacks. No attack is known against Snow 3G today. In this paper, a fault attack against Snow 3G is proposed. Our attack recovers the secret key with only 22 fault injections.