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Experiment 2 Problem 1 Grain-128 stream cipher

Experiment 2 Problem 1 Grain-128 stream cipher. Cipher. Message / Ciphertext. m bits. Cryptographic Key. Encrypt/Decrypt. k bits. 1 bit. m bits. Ciphertext / Message. Secret-Key Ciphers. key of Alice and Bob - K AB. key of Alice and Bob - K AB. Network. Decryption.

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Experiment 2 Problem 1 Grain-128 stream cipher

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  1. Experiment 2 Problem 1 Grain-128 stream cipher

  2. Cipher Message / Ciphertext m bits Cryptographic Key Encrypt/Decrypt k bits 1 bit m bits Ciphertext / Message

  3. Secret-Key Ciphers key of Alice and Bob - KAB key of Alice and Bob - KAB Network Decryption Encryption Bob Alice

  4. Block vs. stream ciphers M1, M2, …, Mn m1, m2, …, mn memory Block cipher K K Stream cipher C1, C2, …, Cn c1, c2, …, cn Ci=fK(Mi) ci = fK(mi, mi-1, …, m2, m1) Every block of ciphertext is a function of only one corresponding blockof plaintext Every block of ciphertext is a function of the current and all proceeding blocks of plaintext

  5. Typical stream cipher Sender Receiver Initialization Vector - IV Initialization Vector - IV Key - K Key - K Pseudorandom Key Generator Pseudorandom Key Generator keystream ki keystream ki mi ci ci mi plaintext ciphertext ciphertext plaintext

  6. Example ci = mi ki message mi ki ci 01110110101001010110101 11011101110110101110110 10101011011111111000011 keystream ciphertext mi = ci ki ci ki mi ciphertext 10101011011111111000011 11011101110110101110110 01110110101001010110101 keystream message

  7. Grain-128: Keystream Generator zi keystream

  8. Example of a simpler 5-stage LFSR LFSR = Linear Feedback Shift Register si si+1 si+2 si+3 si+4 si+5 si+5 = si + si+1 + si+3 + is used to denote XOR

  9. LFSR in Grain-128 si+7 si+96 si+38 si+70 si+81 . . . . si si+1 si+2 si+126 si+127 si+128 + is used to denote XOR

  10. Example of a simpler 5-stage NFSR NFSR = Non-Linear Feedback Shift Register bi bi+1 bi+2 bi+3 bi+4 bi+5 bi+5 = bibi+1 + bi+3 + is used to denote XOR bmbn is used to denote bm AND bn

  11. NFSR in Grain-128 bi+26 bi+68 bi+84 . . . . bi+56 bi+91 si . . . . bi bi+1 bi+2 bi+126 bi+127 bi+128 + is used to denote XOR bmbn is used to denote bm AND bn

  12. Output function in Grain-128

  13. Grain-128: Keystream Generator zi keystream

  14. Key and IV Initialization Phase 1 Initial state of NFSR: bi = ki for i=0..127, where ki are bits of the key, k Initial state of LFSR: si = IVi for i=0..95, where IVi are bits of the si = ‘1’ for i=96..127 initialization vector, IV Phase 2 256 clock cycles of key mixing using connections shown in the next slide (output fed back and xor’ed with inputs to LFSR and NFSR)

  15. Grain-128: Connections in the circuit during Key & IV Initialization, Phase 2

  16. Grain-128: Keystream Generation Optimization for 2 bits per clock cycle

  17. Example Programmable LFSR-based Pseudorandom Number Generator

  18. cL-1 cL-2 c1 c0 sin Current_state

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