Lightweight Authenticated Encryption Mode of Operation for - PowerPoint PPT Presentation

Workshop on Cryptographic Hardware and Embedded Systems (CHES 2020) Lightweight Authenticated Encryption Mode of Operation for Tweakable Block Ciphers Yusuke Naito * and Takeshi Sugawara ** * Mitsubishi Electric Corporation ** The University of Electro-Communications

1 Overview Our New Design: PFB (Plaintext Feedback) Mode • Key features • 64-bit security with a 64-bit tweakable block cipher (the beyond-the-birthday-bound security) • Low memory usage with threshold implementation (TI) • By replacing a non-linearly updated 64-bit state into a public tweak Previous work This work Tweak State Key State Key Without TI = 256 = 256 64 128 64 128 128 x1 = 640 = 512 x2 x2 With TI x3 x3

2 Background Lightweight Cryptography • Security for resource-constrained IoT devices • Lightweight block ciphers • Standardization • 64-bit primitives are popular • Memory (register) is a bottleneck in hardware implementation • 4-bit S-box: 20--40 gates • 128-bit register: 600--900 gates

3 Background Lightweight Authenticated Encryption (AE) • NIST is running a competition (LWC) for choosing a lightweight AE • Optimizing the mode of operation for lightweight implementation • Only 32-bit security when combined with a mode of operation with the birthday- bound security, which is subject to a practical attack** Additional states for tag generation State Key *Y. Naito, M. Matsui, T. Sugawara, and D. Suzuki, “SAEB: A Lightweight 128 128 AES GCM 128 128 Blockcipher-Based AEAD Mode of Operation,” CHES 2018. AES SAEB* 128 128 ** K. Bhargavan, G. Leurent "On the Practical (In-)Security of 64-bit Block Ciphers: Collision Attacks on HTTP over We are hitting the limit: TLS and OpenVPN", CCS2016. these 256 bits are necessary for running AES

4 Background Lightweight + SCA Resistance • Resource-constrained devices are used in a hostile environment in which side-channel attack (SCA) is a serious threat • SCA protection in resource-constrained devices is even more challenging • Lightweight cryptography that enable efficient SCA countermeasure is a new frontier of research, e.g., TI-friendly S-box and SCREAM

5 Background (1 st order) Threshold Implementation • Encode a sensitive value as a share, and implement crypto while preserving the shared representation • Efficiency provides security in the presence of glitches • Multiplies the memory cost! x a x b x c x Input share (𝒚 𝒃 , 𝒚 𝒄 , 𝒚 𝒅 ) satisfying 𝒚 𝒃 ⊕ 𝒚 𝒄 ⊕ 𝒚 𝒅 = 𝒚 � � a � b � c 𝜔 𝜔 ! 𝜔 " 𝜔 # Output share (𝒀 𝒃 , 𝒀 𝒄 , 𝒀 𝒅 ) X X a X b X c satisfying 𝒀 𝒃 ⊕ 𝒀 𝒄 ⊕ 𝒀 𝒅 = 𝒀

6 Our approach Reduce the Size of Non-Linearly Updated State • Low memory usage with threshold implementation (TI) • Challenge: birthday-bound security • We use a tweakable block cipher (TBC) to efficiently achieve the beyond-the- birthday-bound security, i.e., 64-bit security with a 64-bit primitive SAEB AES This work Tweak State Key State Key Without TI = 256 = 256 128 64 128 64 128 x1 = 640 = 512 x2 x2 x3 With TI x3

7 Contribution New Mode of Operation PFB (Plaintext Feedback) • A nonce-based authenticated encryption with associated data using TBC • Provides the beyond-the-birthday-bound security: security level = block length • Based on iCOFB (Chakraborti et al. CHES2017) with several improvements: • Adding associate-data processing • Supporting arbitrary-length message • Giving a new proof for a tighter security bound • Hardware performance evaluation with TI X l -1 S H X 2 X l Enc x , N , l -1 ~ x , N ,1 ~ x , N ,2 ~ y , N , l x , N , l ~ ~ E K E K E K E K E K ⊕ Y 2 Y l -1 Y l Y 1 msb t ⊕ ⊕ M 2 ⊕ M l -1 M 1 Plaintext M ozp msb | M * | Tag T ⊕ M l Ciphertext C C l -1 C 1 C 2 C l

8 Preliminary Tweakable block cipher • An extension of a block cipher with the third input called tweak • We get an independent random permutation for each tweak, i.e., efficient rekeying Block cipher Tweakable block cipher Message m Message m ~ E K E K Tweak t Ciphertext c Ciphertext c

9 Preliminary Tweakable block cipher SKINNY • A popular lightweight TBC • Tweakey framework: no discrimination between the key and tweak Tweakey: tweak or key Message m TK 1 TK 2 TK 3 Round 1 f 1 f 2 f 3 Tweakey schedule: Round 2 independent between TKs f 1 f 2 f 3 Beierle et al., “The SKINNY Family of Block Ciphers and Its Low-Latency Variant MANTIS,” In CRYPTO 2016 .

10 Proposed Method V 2 H V 1 V Hash a PFB 1,0 n ,1 1,0 n , a 1,0 n ,2 ~ ~ ~ E K E K E K 0 b ⊕ ⊕ ⊕ ⊕ Associated Data A A 3 A 1 A 2 ozp( A a ) X l -1 S H X 2 X l Enc x , N , l -1 ~ x , N ,1 ~ x , N ,2 ~ y , N , l x , N , l ~ ~ E K E K E K E K E K ⊕ Y 2 Y l Y 1 Y l -1 msb t ⊕ ⊕ M l -1 ⊕ M 2 Plaintext M M 1 ozp msb | M * | Tag T ⊕ M l Ciphertext C C l -1 C 1 C 2 C l X 2 X l H X l -1 S Dec y , N , l x , N ,1 x , N , l x , N , l -1 x , N ,2 ~ ~ ~ ~ ~ E K E K E K E K E K Y 1 Y 2 Y l Y l -1 msb t Plaintext M ⊕ ⊕ ⊕ M 1 M 2 ⊕ M l -1 ? Ciphertext C ^ ozp msb | C l | T = T C 1 C 2 C l -1 M l C l

11 Proposed Method PFB cont. • Memory for running a TDC is sufficient for the entire PFB operation. • Tweak contains public parameters: a constant, nonce, and counter X l -1 Memory size Public tweak Tweak State Key 64 Without TI = 256 64 128 64 ~ x , N , l -1 E K 64 x1 Small constant = 512 x2 M l -1 Nonce With TI x3 Counter C l -1

12 Proposed Method Security of PFB • Target: b-bit security with the b-bit block length • Assumption • TBC as a TRP (Tweakable Random Permutation) • Nonce respect setting (i.e., no nonce misuse) • Privacy • Game: distinguishing a ciphertext from a random sequence • PFB achieves perfect security • Authenticity • Game: forging a valid tag with the query access to the decryption oracle • A successful attack needs 2 b decryption queries, i.e., PFB achieves b-bit security

13 Proposed Method Proof sketch for privacy 1. No repeated tweak in encryption • ∵ the (non-repeated) nonce and a counter 2. TBC’s output Y 1 , Y 2 ,..., T are random and independent by the TRP assumption 3. We cannot distinguish the ciphertexts and tag from a random string, i.e., achieves perfect security X l -1 S H X 2 X l Enc x , N , l -1 ~ x , N ,1 ~ x , N ,2 ~ y , N , l x , N , l ~ ~ E K E K E K E K E K ⊕ Y 2 Y l -1 Y l Y 1 msb t ⊕ ⊕ M 2 ⊕ M l -1 M 1 Plaintext M ozp msb | M * | Tag T ⊕ M l Ciphertext C C l -1 C 1 C 2 C l

14 Proposed Method Proof sketch for authenticity • We consider two attack cases • Attack case #1: guessing the tag in PFB’s decryption • The success probability is roughly 1/2 b for each query because the tag is almost randomly chosen • The probability Pr[#1] ≦ O(q D /2 b ) with q D queries to the Decryption oracle

15 Proposed Method Proof sketch for authenticity cont. • Attack case #2: exploiting the collision in the PFB states • A collision in between the Enc and Dec states with the same nonce results in a collision of the tag, i.e., successful tag forgery • The probability to observe a collision is 1/2 b , so Pr[#2] ≦ O(q D /2 b ) with q D Decryption queries Enc H X 2 X 3 X l S x , N , l y , N , l x , N ,3 x , N ,2 x , N ,1 M 2 M 3 M l M 1 ⊕ ⊕ ⊕ ⊕ C 2 C 3 C l T C 1 Collision Collision Collision Collision Dec X' 2 X 3 X l S H' x , N , l y , N , l x , N ,3 x , N ,2 x , N ,1 M' 2 M 3 M l M' 1 ⊕ ⊕ ⊕ ⊕ C' 2 C 3 C l T C' 1

16 Performance Evaluation Hardware architecture SKINNY • PFB with SKINNY-64-192 (a variant with Tweakey array 64-bit block and 192-bit tweakey) TK1 input TK1 array 4 • A serial SKINNY architecture with 4-bit TK2 input TK2 array 4 datapath Tweak input 4 TK3 array id • The mode of operation is a thin wrapper: 3 with the MUX, XOR, AND gates RC gen. • Heterogeneous number of shares • Green: 1-share (public) g • Red: 2-share (linear secret) State A/M/C C/M/T array 4 4 • Others: 3-share (nonlinear secret) 4

17 Performance Evaluation Comparing memory sizes • We traded a 64-bit non-linear state with a 64-bit public tweak • The proposed method saves 128 bits with TI Previous work: SAEB w/ GIFT-128 This work: PFB w/ Skinny-64-192 Tweak State Key State Key Without TI = 256 = 256 128 128 64 64 128 x1 = 640 = 512 x2 x2 x3 With TI x3

18 Performance Evaluation Hardware performance comparison w/ 3-share TI • Smaller circuit area compared with the state-of-the-art: SAEB with GIFT-128 • Advantage over sponge-based schemes • Key/tweak use the smaller number of shares Ref. Scheme Circuit Area /GE Proposed method This work PFB/Skinny-64 5,858 A 128-bit block cipher-based This work SAEB/GIFT-128 6,229 scheme implemented with the same design policy Groß et al.* Ascon w/o IF 7,970 Groß et al.* Ascon w IF 9,190 Previous AE implementations with TI Arribas et al.** Ketje-JR 18,335 [1] Groß et al., “Suit up! - Made-to-Measure Hardware Implementations of ASCON,” DSD 2015. [2] Arribas et al., “Guards in Action: First- Order SCA Secure Implementations of Ketje Without Additional Randomness,” DSD 2018 .