STRIBOB : Authenticated Encryption from GOST R 34.11-2012 LPS or Whirlpool Markku-Juhani O. Saarinen mjos@item.ntnu.no Norwegian University of Science and Technology Directions in Authentication Ciphers '14 24 August 2014, Santa Barbara USA 1 / 19 STRIBOB Ideas ▶ Security bounds derived from Sponge Theory. ▶ Well-understood fundamental permutation: Security reduction to Streebog or Whirlpool, with rounds increased 10 → 12. Recyclable hardware components. ▶ ▶ ▶ ▶ ▶ STRIBOBr1: Streebog LPS. STRIBOBr2d1: Streebog LPS. STRIBOBr2d2: Whirlpool LPS - "WhirlBob". Flexible, extensible domain separation with the BLNK Mode ["Beyond Modes: Building a Secure Record Protocol from a Cryptographic Sponge Permutation", CT-RSA 2014.] ▶ ▶ ▶ "Explicit Domain Separation". Fully adjustable security parameters. MAC-then-continue / sessions, Half-duplex protocols.. Fairly conservative design.. 2 / 19 History & Real World Crypto Stewed beef, GOST 5284-84 GOST Spam a.k.a. Tushonka ▶ 28149-89 Block Cipher (KGB, 1970s) ▶ R 34.11-94 was a hash (based on 28149-89) for R 34.10-94 signatures. ▶ Cryptanalysis by F. Mendel et al (2008): 2105 collision, 2192 preimage. ▶ R 34.11-2012 "Streebog" hash algorithm proposed in 2009. ▶ Since January 1, 2013, the Russian Federation has mandated the use of R 34.11-2012 (with R 34.10-2012). ▶ AES "monoculture" is not universally trusted in some parts of the world. ▶ STRIBOB builds a sponge AEAD algorithm from Streebog, perhaps acceptable in those markets. 3 / 19 GOST R 34.11-2012 "Streebog" Streebog is a (non-keyed) hash function that produces a 256-bit or 512-bit message digest for a bit string of arbitrary length. Streebog is Clearly AES & Whirlpool-inspired. Intended for Digital Signatures (R 34.10-2012). Also used in HMAC mode. Standard security claims: ▶ Collision resistance: n m1 and m2 , h(m1 ) = h(m2 ) requires 2 2 effort. ▶ Pre-image resistance: m for given h in h = H(m) requires 2n effort. ▶ Second pre-image resistance: 2n m2 for given m1 with h(m1 ) = h(m2 ) requires |m effort. 2| Not a Sponge, but a Miyaguchi–Preneel - inspired construction: hi = Eg(Hi−1 ) (mi ) ⊕ hi−1 ⊕ mi . 4 / 19 GOST Streebog: Computing h(M ) Pn i=0 =0 g0 h=0 g512 g1024 mi (mod 2512 ) g512n g0 g0 total length “checksum” h(M ) |M | M= m0 m1 m2 ··· mn pad Padded message M is processed in 512-bit blocks M = m0 | m1 | · · · | mn by a compression function h′ = gN (h, mi ). Chaining variable h has 512 bits. N is the bit offset of the block. There are finalization steps involving two invocations of g, first on the total bit length of M , and then on checksum ϵ, which is computed over all input blocks mod 2512 . 5 / 19 Streebog: The Compression Function gN (h, m) N h0 = gN (h, m) C1 h LPS C2 LPS K1 m C3 LPS K2 LPS K3 LPS C12 LPS 4, 5, · · · , 11 K12 LPS LPS h0 LPS N : bit offset h: chaining value m: 512-bit message block The compression function is built form a 512 × 512 - bit keyless permutation LPS and XOR operations. All data paths are 512 bits. The 12 random round constants Ci are given in the standard spec. One can see the upper "line" (kinda) keying the lower line via Ki . 6 / 19 Streebog: LPS = L ◦ P ◦ S = L(P (S(x))) S P L S S S S S S S S 0 S S S S S S S S 1 S S S S S S S S 2 10 18 26 34 42 50 58 S 3 S ( 8 × 8-bit S-Box ) 8 16 24 32 40 48 56 L 9 17 25 33 41 49 57 L ( byte transpose ) 59 S 4 S S S S S S S S 5 13 21 29 37 45 53 61 L S S S S S S S S 6 14 22 30 38 46 54 62 L S S S S S S S S 7 15 23 31 39 47 55 63 L S 60 L ( 64 × 64-bit matrix ) L◦P◦S S : ("Substitution") An 8 × 8 - bit S-Box applied to each one of 64 bytes (8 × 64 = 512 bits). P : ("Permutation") Transpose of 8 × 8 - byte matrix. L : ("Linear") Mixing of rows with a 64 × 64 binary matrix. [KaKa13] L is actually an 8 × 8 MDS Matrix in GF(28 ) 7 / 19 vs.. Sponge Construction for Hashing (SHA3) ▶ Built from a b-bit permutation f (π) with b = r + c ▶ ▶ ▶ r bits of rate, related to hashing speed c bits of capacity, related to security More general than traditional hash: arbitrary-length output 8 / 19 vs.. Sponge-based Authenticated Encryption Æ d0 p0 c0 d··· p1 c1 p··· c··· h0 h··· r π IV π π π π π π c absorbtion phase 1. 2. 3. 4. encryption phase squeezing phase Absorption. Key, nonce, and associated data (di ) are mixed. Encryption. Plaintext pi is used to produce ciphertext ci . Squeezing. Authentication Tag hi is squeezed from the state. Why not use that final state as IV for reply and go straight to Step 2 ? (feature called "sessions" in Ketje and Keyak) [Sa14a] BLNK mode defines "explicit domain separation" and applies that to build ultra-light weight half-duplex protocols. 9 / 19 DuplexWrap (basic Sponge Æ Scheme) Bounds Theorem The DuplexWrap and BLNK authenticated encryption modes satisfy the following privacy and authentication security bounds: M 2 + 4M N 2c+1 2 M + 4M N −k Advauth + sbob (A) < (M + N )2 2c+1 −k Advpriv + sbob (A) < (M + N )2 $ against any single adversary A if K ← {0, 1}k , tags of l ≥ t bits are used, and π is a randomly chosen permutation. M is the data complexity (total number of blocks queried) and N is the time complexity (in equivalents of π). Proof. Theorem 4 of [KeyakV1]. See also [AnMePr10,BeDaPeAs11]. 10 / 19 STRIBOB: Sponge Permutation π For some vector of twelve 512-bit subkeys Ci we define a 512-bit permutation πC (X1 ) = X13 with iteration xi+1 = LPS(Xi ⊕ Ci ) for 1 ≤ i ≤ 12. We adopt 12 rounds of LPS as the Sponge permutation with: b Permutation size b = r + c = 512, the LPS permutation size. r Rate r = 256 bits. c Capacity c = 256 bits. As π satisfies the indistinguishability criteria, we may choose: k Key size k = 192 bits. t Authentication tag (MAC) size t = 128 bits. k Nonce (IV) size t = 128 bits. 11 / 19 Easy Security Reduction Theorem If πC (x) can be effectively distinguished from a random permutation for some Ci , so can gN (h, x) for any h and N . Proof. If h is known, so are all of the subkeys Ki as those are a function of h alone. We have the equivalence gN (h, x) ⊕ x ⊕ h = πK (x ⊕ N ). Assuming that the round constants Ci offer no advantage over known round keys Ki , πC is as secure as πK and any distinguisher should have the same complexity. We see that a generic powerful attack against π is also an attack on g. A distinguishing attack against g does not imply a collision attack against Streebog as a whole. 12 / 19 Security Reduction Explained STRIBOB: Just replace C with K in π: x0 = πK (x) K1 x K2 LPS K3 K12 LPS LPS LPS x0 Streebog: We have gN (h, x) ⊕ x ⊕ h = πK (x ⊕ N ): N h0 = gN (h, m) C1 h LPS C2 LPS K1 m C3 LPS K2 LPS K3 LPS C12 LPS 4, 5, · · · , 11 K12 LPS LPS h0 LPS 13 / 19 WHIRLBOB Variant (STRIBOBr2d2) Whirlpool is a NESSIE final portfolio algorithm and an ISO standard. If STRIBOB is accepted to R2, we will add a variant which is more directly based on Whirlpool [RiBa00] v3.0 [RiBa03]. ▶ ▶ ▶ STRIBOBr1 STRIBOBr2d1 = STRIBOBr1 STRIBOBr2d2 a.k.a. WHIRLBOB S E −1 E R E E −1 S-Box structure saves hardware gates & makes bitslicing faster. Current constant-time (timing attack resistant) bitsliced version runs at about 35 % of table lookup -based implementation. 14 / 19 STRIBOB Software Performance STRIBOB requires 12 LPS invocations per 256 bits processed whereas Streebog requires 25 LPS invocations per 512 bits: STRIBOB is faster. Also the runtime memory requirement is cut down to 25 %. WHIRLBOB performance is equal to STRIBOB. Implementation techniques are similar to AES. 64-bit "rows" are better suited for 64-bit architectures (AES is from 90s, 32-bit era). Algorithm AES - 128 / 192 / 256 SHA - 256 / 512 GOST 28147-89 GOST R 34.11-1994 GOST R 34.11-2012 STRIBOB ( bitsliced WHIRLBOB ) Throughput 109.2 / 90.9 / 77.9 MB/s 212.7 / 328.3 MB/s 53.3 MB/s 20.8 MB/s 109.4 MB/s 115.7 MB/s > 40 MB/s -- w. current S-Boxes ..as measured on my few years old Core i7 @ 2.80. 15 / 19 Briefly about FPGA Implementations Total logic on Xilinx Artix-7: WHIRLBOB: 4,946, Keyak 7,972 Report on these & a Proposal for CAESAR HW/SW API: "Simple AEAD Hardware Interface (SÆHI) in a SoC: Implementing an On-Chip Keyak/WhirlBob Coprocessor", ePrint 2014/575. 16 / 19 Mikko Hypponen, CRO of F-Secure, 29 Apr 2014. ▶ ▶ ▶ ▶ Implementation of secure links over TCP using the BLNK protocol. Can be used as a secure replacement for netcat. File encryption and decryption using an authenticated chunked file format; you can efficiently encrypt a backup stream up to terabytes in size. Hashing of files and streams. StriCat can also do 256- and 512-bit standard-compliant GOST Streebog hashes. Portable, self-contained, open source, POSIX compliant, relatively small (couple of thousand lines). 17 / 19 Originally written to debug real-world BLNK.. $ ./stricat -h stricat: STRIBOB / Streebog Cryptographic Tool. (c) 2013-4 Markku-Juhani O. Saarinen <mjos@iki.fi>. See LICENSE. stricat [OPTION].. [FILE].. -h This help text -t Quick self-test and version information Shared secret key (use twice to verify): -q Prompt for key -f <file> Use file as a key -k <key> Specify key on command line Files: -e -d -s -g -G Encrypt stdin or files (add .sb1 suffix) Decrypt stdin or files (must have .sb1 suffix) Hash stdin or files in STRIBOB BNLK mode (optionally keyed) GOST R 34.11-2012 unkeyed Streebog hash with 256-bit output GOST R 34.11-2012 unkeyed Streebog hash with 512-bit output Communication via BLNK protocol: -p <port> Specify TCP port (default 48879) -c <host> Connect to a specific host (client) -l Listen to incoming connection (server) http://www.stribob.com/stricat 18 / 19 References.. Sa14a "Beyond Modes: Building a Secure Record Protocol from a Cryptographic Sponge Permutation" CT-RSA 2014, IACR ePrint 2013/772. Sa14b "STRIBOB: Authenticated Encryption from GOST R 34.11-2012 LPS Permutation (Extended Abstract)" CTCrypt '14, IACR ePrint 2014/271. Sa14c "Lighter, Faster, and Constant-Time: WHIRLBOB, the Whirlpool variant of STRIBOB", Submitted for publication, ePrint 2014/501. Sa14d "Simple AEAD Hardware Interface (SÆHI) in a SoC: Implementing an On-Chip Keyak/WhirlBob Coprocessor", Submitted for publication, IACR ePrint 2014/575. http://www.stribob.com http://www.mjos.fi 19 / 19

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