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In this work we present the COLM authenticated encryption (AE) scheme which is the second of the two winners in the defense in depth category of the CAESAR competition. COLM realizes a nonce-based authenticated encryption with associated data and uses the popular AES blockcipher as its underlying primitive. We propose two possible blockcipher instantiations (with key of length 128 or 256 bits). We also define two COLM modes of operation variants: a primary COLM 0 mode for general purpose applications, and a COLM τ variant with intermediate tag generation/verification geared to support low-end devices and applications where frequent verification is required. COLM is designed with security, simplicity, and efficiency in mind. The main design goal of COLM is high security: a primary feature of the defense in depth CAESAR category. COLM provides security beyond the traditional AE security. First, COLM is secure against nonce misuse, namely, it enables security in adversarial settings where the nonce inputs to the AE scheme repeat. In contrast to standardized and popular AE algorithms, such as GCM and OCB1-3 modes, whose AE security trivially breaks down when the nonce is repeated, COLM ensures both confidentiality and authenticity (AE) security with repeated nonces. Second, our COLM τ variant enables increased security levels in situations where release of unverified ciphertext (RUP) occurs due to its ability to limit a potential leakage by frequent verifications. In this work we prove COLM secure with respect to both confidentiality and authenticity (AE) security under nonce misuse in the well-known provable security framework. Our proofs show that COLM maintains n/2-bit security levels for block sizes of n bits. Furthermore, due to the inherent parallelism on both mode and primitive levels, our software performance results show that the price paid for enhanced security does come at the cost of minimal efficiency losses. More concretely, we implement GCM, COLM, and Deoxys-II on the Kaby Lake and Coffee lake Intel platforms. Compared to the other winner in the defense in depth category Deoxys-II, our AE design COLM 0 performs 10–20% faster for the 128-bit key version. Regarding the 256-bit key versions COLM 0 is around 5% faster for short and 2% slower than Deoxys-II for the longer messages. [ABSTRACT FROM AUTHOR]

Linear codes over finite fields are one of the most well-studied areas in coding theory. While codes over finite fields of characteristic two are of particular practical interest due to their good implementation properties, ternary codes have been extensively studied as well. By contrast, there has been essentially no research into ternary cryptographic algorithms. The only exception to date is a cryptocurrency and distributed ledger technology called IOTA which is ternary and has been designed primarily for use in the Internet of Things. Its security depends on using a secure cryptographic hash function over F 3 . With all existing hash designs being binary, a ternary prototype called Curl-P had been developed, however was found to admit practical collision attacks. A ternary adaption of SHA-3 called Kerl is currently used instead, but comparatively inefficient. In this paper, we propose a new ternary hash function called Troika which is tailored for use in IOTA's ternary distributed ledger and can be used as a drop-in replacement for Kerl. The design of Troika leverages elements from the well-established Keccak and Rijndael design philosophies, while being designed for efficiency in terms of basic F 3 operations. In particular, it features a novel 3-trit S-box which is differentially 3-uniform while being implementable in only 7 additions and multiplications over F 3 . Troika is designed to offer a security level comparable to SHA-3. It is expected that Troika, as part of IOTA's distributed ledger, will find widespread commercial real-world use in the near- to mid-term future. We believe that not the least due to its unorthodox ternary design, it will provide both a practically relevant and interesting target for further cryptanalysis. [ABSTRACT FROM AUTHOR]

The implementation of the AES encryption core by Moradi et al. at Eurocrypt 2011 is one of the smallest in terms of gate area. The circuit takes around 2400 gates and operates on an 8-bit datapath. However, this is an encryption-only core and unable to cater to block cipher modes like CBC and ELmD that require access to both the AES encryption and decryption modules. In this paper, we look to investigate whether the basic circuit of Moradi et al. can be tweaked to provide dual functionality of encryption and decryption (ENC/DEC) while keeping the hardware overhead as low as possible. We report two constructions of the AES circuit. The first is an 8-bit serialized implementation that provides the functionality of both encryption and decryption and occupies around 2605 GE with a latency of 226 cycles. This is a substantial improvement over the next smallest AES ENC/DEC circuit (Grain of Sand) by Feldhofer et al. which takes around 3400 gates but has a latency of over 1000 cycles for both the encryption and decryption cycles. In the second part, we optimize the above architecture to provide the dual encryption/decryption functionality in only 2227 GE and latency of 246/326 cycles for the encryption and decryption operations, respectively. We take advantage of clock gating techniques to achieve Shiftrow and Inverse Shiftrow operations in 3 cycles instead of 1. This helps us replace many of the scan flip-flops in the design with ordinary flip-flops. Furthermore, we take advantage of the fact that the Inverse Mixcolumn matrix in AES is the cube of the Forward Mixcolumn matrix. Thus by executing the Forward Mixcolumn operation three times over the state, one can achieve the functionality of Inverse Mixcolumn. This saves some more gate area as one is no longer required to have a combined implementation of the Forward and Inverse Mixcolumn circuit. [ABSTRACT FROM AUTHOR]

We explore the optimality of balanced Feistel ciphers with SP-type F-functions with respect to their resistance against differential and linear cryptanalysis. Instantiations of Feistel ciphers with the wide class of (SP) $$^u$$ and (SP) $$^u$$ S F-functions are considered: one F-function can contain an arbitrary number of S-box layers interleaved with linear diffusion. For the matrices with maximum diffusion, it is proven that SPS and SPSP F-functions are optimal in terms of the proportion of active S-boxes in all S-boxes-a common efficiency metric for substitution-permutation ciphers. Interestingly, one SP-layer in the F-function is not enough to attain optimality whereas taking more than two S-box layers does not increase the efficiency either. [ABSTRACT FROM AUTHOR]

Linear cryptanalysis, along with differential cryptanalysis, is an important tool to evaluate the security of block ciphers. This work introduces a novel extension of linear cryptanalysis: zero-correlation linear cryptanalysis, a technique applicable to many block cipher constructions. It is based on linear approximations with a correlation value of exactly zero. For a permutation on n bits, an algorithm of complexity 2 is proposed for the exact evaluation of correlation. Non-trivial zero-correlation linear approximations are demonstrated for various block cipher structures including AES, balanced Feistel networks, Skipjack, CLEFIA, and CAST256. As an example, using the zero-correlation linear cryptanalysis, a key-recovery attack is shown on 6 rounds of AES-192 and AES-256 as well as 13 rounds of CLEFIA-256. [ABSTRACT FROM AUTHOR]

This work deals with the classification, security and efficiency of generalized Feistel networks (GFNs) with 4 lines. We propose a definition of a GFN, essentially limiting consideration to Feistel-type constructions with domain-preserving F-functions and rotation by one line between rounds. Under this definition, we demonstrate that there are only two non-contracting representatives in the class of 4-line GFNs up to equivalence, namely, the type-I and type-II GFNs that avoid obvious differential effects. We propose to instantiate the GFNs with SPS-functions (two substitution layers separated by a permutation layer) instead of single SP-functions (one substitution-permutation layer only). We prove tight lower bounds on the number of differentially and linearly active functions and S-boxes in such ciphers. We show that the instantiation with SPS-functions using MDS diffusion provides a proportion of differentially and linearly active S-boxes by up to 33 and 50 % higher than that with single SP-functions for type-I and type-II GFNs, respectively, if the same matrix is used in all rounds. Moreover, we present the upper bounds on the differential and the linear hull probability for the type-II GFNs with SPS-functions. This opens up the possibility of designing more efficient block ciphers based on GFN structure. [ABSTRACT FROM AUTHOR]

In 2007, the US National Institute for Standards and Technology (NIST) announced a call for the design of a new cryptographic hash algorithm in response to vulnerabilities like differential attacks identified in existing hash functions, such as MD5 and SHA-1. NIST received many submissions, 51 of which got accepted to the first round. 14 candidates were left in the second round, out of which five candidates have been recently chosen for the final round. An important criterion in the selection process is the SHA-3 hash function security. We identify two important classes of security arguments for the new designs: (1) the possible reductions of the hash function security to the security of its underlying building blocks and (2) arguments against differential attack on building blocks. In this paper, we compare the state of the art provable security reductions for the second round candidates and review arguments and bounds against classes of differential attacks. We discuss all the SHA-3 candidates at a high functional level, analyze, and summarize the security reduction results and bounds against differential attacks. Additionally, we generalize the well-known proof of collision resistance preservation, such that all SHA-3 candidates with a suffix-free padding are covered. [ABSTRACT FROM AUTHOR]

Though unbalanced Feistel networks (UFN) are widely considered as an alternative to balanced Feistel networks (BFN) and substitution-permutation networks (SPN) in symmetric cryptography, little has been known yet about their resistance against differential and linear cryptanalysis. In this work, we tackle the problem at the example of d-branch SP-type UFNs with contracting MDS diffusion ( dCUFN-SP). Under some restrictions on the contracting MDS matrices over multiple rounds, we prove lower bounds on the number of differentially active S-boxes for dCUFN-SP with $${d\in\{3,4\}}$$ and on the number of linearly active S-boxes for dCUFN-SP with d ≥ 3. As opposed to SPNs and BFNs, the number of differentially active S-boxes for such constructions does not directly translate to an upper bound on the probability of differential trails. So we provide a thorough analysis of single-round differentials that yields an upper bound on the probability of a differential trail. It is also shown that the efficiency level of dCUFN-SP is comparable to that of BFNs and SPNs with respect to differential and linear cryptanalysis. [ABSTRACT FROM AUTHOR]