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Kasumi Block Cipher Data Encryptors Darshan Gandhi Rushabh Pasad

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Introduction Used in 3GPP Confidentiality and Integrity Algorithms. Technical Specifications: – Key Size: 128 bits – Block Size: 64 bits (64 bit output from a 64 bit input). – Number of Rounds: 8

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Block Diagram

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Statistical Test Suite NIST – Developed to test randomness of binary sequences produced by hardware or software based cryptographic random or pseudorandom number generators. – Focuses on variety of different types of non-randomness that could exist in a sequence. – Consists of 15 sub-tests.

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Random Number Generation Tests 1.Frequency Test 2.Frequency Test within a block 3.Runs Test 4.Longest Run of Ones in a block 5.Binary Matrix Rank Test 6.Discrete Fourier Transform Test 7.Non-overlapping Template Matching Test 8.Overlapping Template Matching Test 9.Universal Statistical Test 10.Linear Complexity Test 11.Serial Test 12.Approximate Entropy Test 13.Cumulative Sums Test 14.Random Excursions Test 15.Random Excursions Variant Test

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Random Input Data Program Generic Program. Can be used with any Block Cipher. Operates in Output Feedback Mode Output is in binary format. Usage: % java GenerateRandomInput – : Name of the implementing Block Cipher Class. – : A Hex String equivalent to block size of cipher. – : Key to be used for Encryption. A Hex string equivalent to key size of cipher. – : Number of Rounds for encryption. – : Generates ( *block size) bits in output.(i.e. Number of iterations to be performed) – : Path to the file in which the output should be saved. Eg. % java GenerateRandomInput Kasumi 62A540981BA6F9B7 8CE33E2CC3C0B5FC1F3DE8A6DC66B1F3 8 1000 output.txt

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Test Suite Results Tests were run on 10 streams of 100,000 bits long data sequences for each reduced rounds. Universal Test requires 1,000 million bits of data for best accuracy. So the test was run only once on the cipher reduced to round 1. The recorded P-Value was: 0.213309

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Test Suite Results

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Literature Search ETSI SAGE 3GPP Standard Algorithms Task Force – Performed 12 statistical tests. – S9 does not show the avalanche effect. – No other statistical weaknesses. Evaluator 1 – Found a key attack when reduced to 5 rounds. – Found a structural attack on the cipher when reduced to 6 rounds.

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Literature Search Evaluator 2 – Performed cryptanalytic attacks. – Could not detect any weaknesses in the cipher. Evaluator 3 – No practical attack possible on the reduced 5 round version. – Theoretically, when reduced to 6 rounds, found a weakness.

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Analysis and Conclusion Analysis On observing the P-Values, we conclude that, If Kasumi Cipher is reduced to Round 1, non-randomness is detected (P-Value is less than 0.01). For further Rounds, non-randomness was detected only in one of the binary rank matrix test (Reduced to 7 Rounds). Conclusion Kasumi Cipher is strong cipher that generates pseudo random data in which non-randomness is not being detected. No practical attacks have been found and the algorithm is well-fitted for the intended use.

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Lessons Learned Principles of Cryptography Implementing Cryptographic Primitives Bit level data manipulation and code optimization Encrypting and Decrypting Data using Cipher Algorithms

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Future Work Testing using other test suites such as – TestU01 – DieHard Perform cryptanalysis to detect any other weaknesses

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