On the Statistical Analysis of ZUC, Espresso and Grain v1

Saurabh Shrivastava,K V Lakshmy,Chungath Srinivasan

doi:10.47839/ijc.20.3.2284

Abstract

A stream cipher generates long keystream to be XORed with plaintext to produce ciphertext. A stream cipher is said to be secure if the keystream that it produces is consistently random. One of the ways by which we can analyze stream ciphers is by testing randomness of the keystream. The statistical tests mainly try to find if any output keystream leaks any information about the secret key or the cipher’s internal state and also check the randomness of the keystream. We have applied these tests to different keystreams generated by ZUC, Espresso and Grain v1 stream ciphers to check for any weaknesses. We have also proposed four new statistical tests to analyze the internal state when the hamming weight of key and IV used is very high or low. Out of these four tests, Grain v1 fails the last test i.e. internal state correlation using high hamming weight IV.

Highlights

ONE Time Pad (OTP) is the perfectly secure cipher which generates truly random keystream
The security requirement of these stream ciphers are: (a) The pseudorandom keystream should be indistinguishable from truly random sequences (b) the keystream should not reveal any information about key or cipher’s initial state [11]
After obtaining results from these tests, we have proposed four new tests to analyze the correlation of internal states when the hamming weight of key or IV is very low or very high

Summary

INTRODUCTION

ONE Time Pad (OTP) is the perfectly secure cipher which generates truly random keystream. Today’s stream ciphers generate a long keystream using a small fixed length key. These keystreams are pseudo-random and are not theoretically as secure as OTP but practically both are secure. The security requirement of these stream ciphers are: (a) The pseudorandom keystream should be indistinguishable from truly random sequences (b) the keystream should not reveal any information about key or cipher’s initial state [11]. After obtaining results from these tests, we have proposed four new tests to analyze the correlation of internal states when the hamming weight of key or IV is very low or very high.

STREAM CIPHERS

PROPOSED TESTS AND RESULTS

CONCLUSION