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Symmetric Encryption Scheme Based on Quasigroup Using Chained Mode of Operation

Satish Kumar, Harshdeep Singh, Indivar Gupta, Ashok Ji Gupta

TL;DR

This work presents SEBQ, a quasigroup-based symmetric encryption scheme that uses a chaining-like mode of operation with a transformed initial vector to encrypt successive blocks. It provides a formal IND-CPA security proof and, through an unbalanced Feistel transformation, achieves IND-CCA2 security, complemented by randomness assessments via the NIST suite and diffusion analysis through avalanche criteria. The authors benchmark SEBQ against existing quasigroup schemes and AES-128, reporting competitive randomness and favorable efficiency characteristics driven by Latin-square transformations. A key finding is the security-parameter guidance: the Latin square order must exceed 11 for 128-bit security and exceed 13 for 256-bit security against known ciphertext attacks, with a detailed complexity analysis of encryption and decryption operations.

Abstract

In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with in-built properties. We prove that SEBQ shows resistance against chosen plaintext attack (CPA) and by applying unbalanced Feistel transformation [19], it achieves security against chosen ciphertext attacks (CCA). Subsequently, we conduct an assessment of the randomness of the proposed scheme by running the NIST test suite and we analyze the impact of the initial vector, secret key and plaintext on ciphertext through an avalanche effect analysis. We also compare the results with existing schemes based on quasigroups [11,46]. Moreover, we analyze the computational complexity in terms of number of operations needed for encryption and decryption process.

Symmetric Encryption Scheme Based on Quasigroup Using Chained Mode of Operation

TL;DR

This work presents SEBQ, a quasigroup-based symmetric encryption scheme that uses a chaining-like mode of operation with a transformed initial vector to encrypt successive blocks. It provides a formal IND-CPA security proof and, through an unbalanced Feistel transformation, achieves IND-CCA2 security, complemented by randomness assessments via the NIST suite and diffusion analysis through avalanche criteria. The authors benchmark SEBQ against existing quasigroup schemes and AES-128, reporting competitive randomness and favorable efficiency characteristics driven by Latin-square transformations. A key finding is the security-parameter guidance: the Latin square order must exceed 11 for 128-bit security and exceed 13 for 256-bit security against known ciphertext attacks, with a detailed complexity analysis of encryption and decryption operations.

Abstract

In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with in-built properties. We prove that SEBQ shows resistance against chosen plaintext attack (CPA) and by applying unbalanced Feistel transformation [19], it achieves security against chosen ciphertext attacks (CCA). Subsequently, we conduct an assessment of the randomness of the proposed scheme by running the NIST test suite and we analyze the impact of the initial vector, secret key and plaintext on ciphertext through an avalanche effect analysis. We also compare the results with existing schemes based on quasigroups [11,46]. Moreover, we analyze the computational complexity in terms of number of operations needed for encryption and decryption process.
Paper Structure (21 sections, 9 theorems, 12 equations, 3 figures, 9 tables, 7 algorithms)

This paper contains 21 sections, 9 theorems, 12 equations, 3 figures, 9 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Quasigroup based encryption schemes
  3. Security notions for symmetric encryption scheme
  4. Indistinguishability under chosen-plaintext attack (IND-CPA) and chosen-ciphertext attack (IND-CCA) security
  5. Left-or-Right indistinguishability under chosen-plaintext attack (LOR-CPA) and chosen-ciphertext attack (LOR-CCA)
  6. Related works
  7. Main contribution of the paper
  8. Preliminaries
  9. Symmetric encryption scheme based on quasigroup (SEBQ)
  10. Key Generation
  11. Encryption Process
  12. Decryption Process
  13. Security Analysis of the Proposed Cryptosystem SEBQ
  14. Unbalanced Feistel transformation of SEBQ encryption scheme
  15. Randomness testing of SEBQ
  16. ...and 6 more sections

Key Result

Theorem 2.3

Let $B_n=\{(b_{i,j})_{n\times n}\mid b_{i,j}\in\{0,1\}\}$ be the set of all $n\times n$ sized matrices. Then number of Latin squares is:

Figures (3)

  • Figure 1: Transformation of initial vector for encryption function
  • Figure 2: Encryption algorithm
  • Figure 3: Decryption algorithm

Theorems & Definitions (16)

  • Definition 1.1
  • Definition 1.2
  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Remark 1
  • Definition 2.4
  • Definition 2.5
  • Theorem 2.6
  • Theorem 4.1
  • ...and 6 more