scholarly journals On the optimality of non-linear computations for symmetric key primitives

2018 ◽  
Vol 12 (4) ◽  
pp. 241-259
Author(s):  
Avik Chakraborti ◽  
Nilanjan Datta ◽  
Mridul Nandi
Keyword(s):  
Block Cipher ◽  
Linear Mapping ◽  
Authenticated Encryption ◽  
Non Linear ◽  
Minimum Number ◽  
Symmetric Key ◽  
Linear Block

Abstract A block is an n-bit string, and a (possibly keyed) block-function is a non-linear mapping that maps one block to another, e.g., a block-cipher. In this paper, we consider various symmetric key primitives with {\ell} block inputs and raise the following question: what is the minimum number of block-function invocations required for a mode to be secure? We begin with encryption modes that generate {\ell^{\prime}} block outputs and show that at least {(\ell+\ell^{\prime}-1)} block-function invocations are necessary to achieve the PRF security. In presence of a nonce, the requirement of block-functions reduces to {\ell^{\prime}} blocks only. If {\ell=\ell^{\prime}} , in order to achieve SPRP security, the mode requires at least {2\ell} many block-function invocations. We next consider length preserving r-block (called chunk) online encryption modes and show that, to achieve online PRP security, each chunk should have at least {2r-1} many and overall at least {2r\ell-1} many block-functions for {\ell} many chunks. Moreover, we show that it can achieve online SPRP security if each chunk contains at least {2r} non-linear block-functions. We next analyze affine MAC modes and show that an integrity-secure affine MAC mode requires at least {\ell} many block-function invocations to process an {\ell} block message. Finally, we consider affine mode authenticated encryption and show that in order to achieve INT-RUP security or integrity security under a nonce-misuse scenario, either (i) the number of non-linear block-functions required to generate the ciphertext is more than {\ell} or (ii) the number of extra non-linear block-functions required to generate the tag depends on {\ell} .

scholarly journals Six shades lighter: a bit-serial implementation of the AES family

2021 ◽  
Author(s):  
Sergio Roldán Lombardía ◽  
Fatih Balli ◽  
Subhadeep Banik
Keyword(s):  
Block Cipher ◽  
Block Ciphers ◽  
Authenticated Encryption ◽  
Current Standard ◽  
Asic Circuit ◽  
The Family ◽  
Encryption And Decryption ◽  
Preliminary Version ◽  
Reduction In Area ◽  
Bit Serial

AbstractRecently, cryptographic literature has seen new block cipher designs such as , or that aim to be more lightweight than the current standard, i.e., . Even though family of block ciphers were designed two decades ago, they still remain as the de facto encryption standard, with being the most widely deployed variant. In this work, we revisit the combined one-in-all implementation of the family, namely both encryption and decryption of each as a single ASIC circuit. A preliminary version appeared in Africacrypt 2019 by Balli and Banik, where the authors design a byte-serial circuit with such functionality. We improve on their work by reducing the size of the compact circuit to 2268 GE through 1-bit-serial implementation, which achieves 38% reduction in area. We also report stand-alone bit-serial versions of the circuit, targeting only a subset of modes and versions, e.g., and . Our results imply that, in terms of area, and can easily compete with the larger members of recently designed family, e.g., , . Thus, our implementations can be used interchangeably inside authenticated encryption candidates such as , or in place of .

scholarly journals Efficient Implementation of PRESENT and GIFT on Quantum Computers

2021 ◽  
Vol 11 (11) ◽  
pp. 4776
Author(s):  
Kyungbae Jang ◽  
Gyeongju Song ◽  
Hyunjun Kim ◽  
Hyeokdong Kwon ◽  
Hyunji Kim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Search Algorithm ◽  
Block Ciphers ◽  
Quantum Circuits ◽  
Security Level ◽  
Symmetric Key ◽  
Grover Search ◽  
Target Block ◽  
Symmetric Key Cryptography ◽  
Grover Search Algorithm

Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.

scholarly journals Provably Quantum-Secure Tweakable Block Ciphers

2021 ◽  
pp. 337-377
Author(s):  
Akinori Hosoyamada ◽  
Tetsu Iwata
Keyword(s):  
Polynomial Time ◽  
Provable Security ◽  
Block Cipher ◽  
Block Ciphers ◽  
Quantum Superposition ◽  
Quantum Cryptanalysis ◽  
Classical Setting ◽  
Time Quantum ◽  
Symmetric Key ◽  
Arbitrary Quantum

Recent results on quantum cryptanalysis show that some symmetric key schemes can be broken in polynomial time even if they are proven to be secure in the classical setting. Liskov, Rivest, and Wagner showed that secure tweakable block ciphers can be constructed from secure block ciphers in the classical setting. However, Kaplan et al. showed that their scheme can be broken by polynomial time quantum superposition attacks, even if underlying block ciphers are quantum-secure. Since then, it remains open if there exists a mode of block ciphers to build quantum-secure tweakable block ciphers. This paper settles the problem in the reduction-based provable security paradigm. We show the first design of quantum-secure tweakable block ciphers based on quantum-secure block ciphers, and present a provable security bound. Our construction is simple, and when instantiated with a quantum-secure n-bit block cipher, it is secure against attacks that query arbitrary quantum superpositions of plaintexts and tweaks up to O(2n/6) quantum queries. Our security proofs use the compressed oracle technique introduced by Zhandry. More precisely, we use an alternative formalization of the technique introduced by Hosoyamada and Iwata.

scholarly journals Cryptanalysis of PMACx, PMAC2x, and SIVx

2017 ◽  
pp. 162-176
Author(s):  
Kazuhiko Minematsu ◽  
Tetsu Iwata
Keyword(s):  
Provable Security ◽  
Block Cipher ◽  
Query Complexity ◽  
Block Length ◽  
Encryption Scheme ◽  
Authenticated Encryption ◽  
Pseudorandom Functions ◽  
Tweakable Block Cipher ◽  
Deterministic Authenticated Encryption ◽  
Provably Secure

At CT-RSA 2017, List and Nandi proposed two variable input length pseudorandom functions (VI-PRFs) called PMACx and PMAC2x, and a deterministic authenticated encryption scheme called SIVx. These schemes use a tweakable block cipher (TBC) as the underlying primitive, and are provably secure up to the query complexity of 2n, where n denotes the block length of the TBC. In this paper, we falsify the provable security claims by presenting concrete attacks. We show that with the query complexity of O(2n/2), i.e., with the birthday complexity, PMACx, PMAC2x, and SIVx are all insecure.

scholarly journals Color Image Encryption using AES and RSA

2020 ◽  
Vol 9 (5) ◽  
pp. 547-550
Keyword(s):  
Data Security ◽  
Block Cipher ◽  
Color Image ◽  
Signal To Noise Ratio ◽  
Security Level ◽  
Change Rate ◽  
The Public ◽  
Key Block ◽  
Symmetric Key ◽  
Encryption Algorithms

Information security is an important task on multimedia and communication world. During storing and sharing maintaining a strategic distance from the outsider access of information is the difficult one. There are many encryption algorithms that can provide data security. In this paper two of the encryption algorithms namely AES and RSA are implemented for color images. AES (Advanced Encryption Standard) is a symmetric key block cipher published in December 2001 by NSIT (National Institute of Standards and Technology). RSA (Rivest-Shamir-Adleman) is an asymmetric key block cipher. It uses two separate keys, one for encryption called the public key and other for decryption called the private key. Both the implementation and analysis are done in Matlab. The quality and security level of both the algorithms is analysed based on various criteria such as Histogram analysis, Correlation analysis, Entropy analysis, NPCR (Number of Pixel Change Rate), UACI (Unified Average Changing Intensity), PSNR (Peak Signal-to-Noise Ratio).

Classification of mineral particles by non-linear mapping of electron microprobe energy dispersive X-ray spectra

The Analyst ◽  
1994 ◽  
Vol 119 (5) ◽  
pp. 971 ◽  
Author(s):  
Boris Treiger ◽  
Igor Bondarenko ◽  
Piet Van Espen ◽  
Ren� Van Grieken ◽  
Fred Adams
Keyword(s):  
Electron Microprobe ◽  
Linear Mapping ◽  
Energy Dispersive ◽  
X Ray ◽  
Mineral Particles ◽  
Non Linear

scholarly journals Simple eigenvalues and bifurcation for a multiparameter problem

1988 ◽  
Vol 31 (1) ◽  
pp. 77-88 ◽  
Author(s):  
D. F. McGhee ◽  
M. H. Sallam
Keyword(s):  
Banach Spaces ◽  
Simple Eigenvalue ◽  
Linear Mapping ◽  
Spectral Parameters ◽  
Non Linear ◽  
Multiparameter Problem ◽  
Image Position ◽  
Bifurcation Of Solutions

We are concerned with the problem of bifurcation of solutions of a non-linear multiparameter problem at a simple eigenvalue of the linearised problem.Let X and Y be real Banach spaces, and let A, Bi, i = 1, …, n∈B(X, Y). Let : Rn × X → Y be a non-linear mapping. We consider the equationwhereand λ=(λ1, λ2,…,λn) ∈ Rn is an n-tuple of spectral parameters.

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