doi: 10.3934/amc.2021021

Designing tweakable enciphering schemes using public permutations

1. 

Indian Statistical Institute, 203, B.T. Road, Kolkata, India 700108

2. 

Institute for Advancing Intelligence, TCG-CREST, Sector V, Salt Lake, Kolkata, India 700091

* Corresponding author: Debrup Chakraborty

Received  February 2021 Revised  April 2021 Published  June 2021

A tweakable enciphering scheme (TES) is a length preserving (tweakable) encryption scheme that provides (tweakable) strong pseudorandom permutation security on arbitrarily long messages. TES is traditionally built using block ciphers and the security of the mode depends on the strong pseudorandom permutation security of the underlying block cipher. In this paper, we construct TESs using public random permutations. Public random permutations are being considered as a replacement of block cipher in several cryptographic schemes including AEs, MACs, etc. However, to our knowledge, a systematic study of constructing TES using public random permutations is missing. In this paper, we give a generic construction of a TES which uses a public random permutation, a length expanding public permutation based PRF and a hash function which is both almost xor universal and almost regular. Further, we propose a concrete length expanding public permutation based PRF construction. We also propose a single keyed TES using a public random permutation and an AXU and almost regular hash function.

Citation: Debrup Chakraborty, Avijit Dutta, Samir Kundu. Designing tweakable enciphering schemes using public permutations. Advances in Mathematics of Communications, doi: 10.3934/amc.2021021
References:
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https://csrc.nist.gov/projects/hash-functions/sha-3-project. Google Scholar

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M. Abbadi, et al., Deterministic authenticated-encryption: A provable-security treatment of the keywrap problem, Journal of Applied Sciences, 8 (1996), 1. Google Scholar

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Z. Bao, A. Chakraborti, N. Datta, J. Guo, M. Nandi, T. Peyrin and K. Yasuda, Photon-beetle authenticated encryption and hash family, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/PHOTON-Beetle-spec.pdf. Google Scholar

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A. Bogdanov, M. Knezevic, G. Leander, D. Toz, K. Varici and I. Verbauwhede, Spongent: A lightweight hash function, in Cryptographic Hardware and Embedded Systems - CHES 2011 - 13th International Workshop, Nara, Japan, September 28 - October 1, 2011. Proceedings (eds. B. Preneel and T. Takagi), Lecture Notes in Computer Science, 6917, Springer, 2011,312–325. doi: 10.1007/978-3-642-23951-9_21.  Google Scholar

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D. Chakraborty, C. Mancillas-López and P. Sarkar, STES: A stream cipher based low cost scheme for securing stored data, IACR Cryptology ePrint Archive, 2013 (2013), 347. doi: 10.1109/TC.2014.2366739.  Google Scholar

[19]

D. Chakraborty and M. Nandi, An improved security bound for HCTR, in Fast Software Encryption, 15th International Workshop, FSE 2008, Lausanne, Switzerland, February 10-13, 2008, Revised Selected Papers, 2008,289–302. Google Scholar

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D. Chakraborty and P. Sarkar, HCH: A new tweakable enciphering scheme using the hash-counter-hash approach, IEEE Transactions on Information Theory, 54 (2008), 1683-1699.  doi: 10.1109/TIT.2008.917623.  Google Scholar

[21]

D. Chang, N. Datta, A. Dutta, B. Mennink, M. Nandi, S. Sanadhya and F. Sibleyras, Release of unverified plaintext: Tight unified model and application to ANYDAE, IACR Trans. Symmetric Cryptol., 2019 (2019), 119–146. Google Scholar

[22]

D. Chang and M. Nandi, A short proof of the PRP/PRF switching lemma, IACR Cryptol. ePrint Arch., 2008 (2008), 78. Google Scholar

[23]

S. Chen and J. P. Steinberger, Tight security bounds for key-alternating ciphers, in EUROCRYPT 2014. Proceedings, 2014,327–350. doi: 10.1007/978-3-642-55220-5_19.  Google Scholar

[24]

Y. L. Chen, E. Lambooij and B. Mennink, How to build pseudorandom functions from public random permutations, in Advances in Cryptology - CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part I, 2019,266–293. doi: 10.1007/978-3-030-26948-7_10.  Google Scholar

[25]

B. Cogliati and Y. Seurin, On the provable security of the iterated even-mansour cipher against related-key and chosen-key attacks, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 2015,584–613. doi: 10.1007/978-3-662-46800-5_23.  Google Scholar

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J. Daemen, S. Hoffert, M. Peeters, G. V. Assche and R. V. Keer, Xoodyak, a lightweight cryptographic scheme, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/Xoodyak-spec.pdf. Google Scholar

[27]

Y. Dai, Y. Seurin, J. Steinberger and A. Thiruvengadam, Indifferentiability of iterated even-mansour ciphers with non-idealized key-schedules: Five rounds are necessary and sufficient, in Annual International Cryptology Conference, Springer, 2017,524–555. doi: 10.1007/978-3-319-63697-9_18.  Google Scholar

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N. Datta, A. Dutta, M. Nandi and G. Paul, Double-block hash-then-sum: A paradigm for constructing bbb secure prf, IACR Transactions on Symmetric Cryptology, 36–92. Google Scholar

[29]

N. Datta, A. Dutta, M. Nandi, G. Paul and L. Zhang, Single key variant of pmac_plus, IACR Transactions on Symmetric Cryptology, 268–305. Google Scholar

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A. Dutta and M. Nandi, Tweakable HCTR: A BBB secure tweakable enciphering scheme, in Progress in Cryptology - INDOCRYPT 2018 - 19th International Conference on Cryptology in India, New Delhi, India, December 9-12, 2018, Proceedings, 2018, 47–69. doi: 10.1007/978-3-030-05378-9_3.  Google Scholar

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A. Dutta, M. Nandi and S. Talnikar, Beyond birthday bound secure mac in faulty nonce model, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 2019,437–466. doi: 10.1007/978-3-030-17653-2_15.  Google Scholar

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S. Halevi, EME*: Extending EME to handle arbitrary-length messages with associated data. Google Scholar

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S. Halevi and P. Rogaway, A tweakable enciphering mode, in CRYPTO (ed. D. Boneh), Lecture Notes in Computer Science, 2729, Springer, 2003,482–499. doi: 10.1007/978-3-540-45146-4_28.  Google Scholar

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show all references

References:
[1]

https://csrc.nist.gov/projects/hash-functions/sha-3-project. Google Scholar

[2]

M. Abbadi, et al., Deterministic authenticated-encryption: A provable-security treatment of the keywrap problem, Journal of Applied Sciences, 8 (1996), 1. Google Scholar

[3]

Z. Bao, A. Chakraborti, N. Datta, J. Guo, M. Nandi, T. Peyrin and K. Yasuda, Photon-beetle authenticated encryption and hash family, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/PHOTON-Beetle-spec.pdf. Google Scholar

[4]

D. J. Bernstein, et al., Gimli : A cross-platform permutation, in Cryptographic Hardware and Embedded Systems - CHES 2017 - 19th International Conference, Taipei, Taiwan, September 25-28, 2017, Proceedings (eds. W. Fischer and N. Homma), Lecture Notes in Computer Science, 10529, Springer, 2017,299–320. doi: 10.1007/978-3-319-66787-4_15.  Google Scholar

[5]

G. Bertoni, J. Daemen, S. Hoffert, M. Peeters, G. V. Assche and R. V. Keer, Farfalle: Parallel permutation-based cryptography, IACR Trans. Symmetric Cryptol., 2017 (2017), 1–38. Google Scholar

[6]

G. Bertoni, J. Daemen, M. Peeters and G. V. Assche, Sponge-based pseudo-random number generators, in Cryptographic Hardware and Embedded Systems, CHES 2010, 12th International Workshop, Santa Barbara, CA, USA, August 17-20, 2010. Proceedings (eds. S. Mangard and F. Standaert), Lecture Notes in Computer Science, 6225, Springer, 2010, 33–47. doi: 10.1007/978-3-642-15031-9_3.  Google Scholar

[7]

G. Bertoni, J. Daemen, M. Peeters and G. Van Assche, Sponge functions, in ECRYPT Hash Workshop, 2007, Citeseer, 2007. Google Scholar

[8]

G. Bertoni, J. Daemen, M. Peeters and G. Van Assche, Keccak, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 2013,313–314. Google Scholar

[9]

T. Beyne, Y. L. Chen, C. Dobraunig and B. Mennink, Elephant, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/elephant-spec.pdf. Google Scholar

[10]

S. Bhattacharya and M. Nandi, Revisiting variable output length XOR pseudorandom function, IACR Cryptol. ePrint Arch., 2019 (2019), 249. Available from: URL https://eprint.iacr.org/2019/249. Google Scholar

[11]

R. Bhaumik and M. Nandi, An inverse-free single-keyed tweakable enciphering scheme, in Advances in Cryptology - ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Auckland, New Zealand, November 29 - December 3, 2015, Proceedings, Part II (eds. T. Iwata and J. H. Cheon), Lecture Notes in Computer Science, 9453, Springer, 2015,159–180. doi: 10.1007/978-3-662-48800-3_7.  Google Scholar

[12]

R. Bhaumik and M. Nandi, An inverse-free single-keyed tweakable enciphering scheme, in International Conference on the Theory and Application of Cryptology and Information Security, Springer, 2015,159–180. doi: 10.1007/978-3-662-48800-3_7.  Google Scholar

[13]

A. Bogdanov, M. Knezevic, G. Leander, D. Toz, K. Varici and I. Verbauwhede, Spongent: A lightweight hash function, in Cryptographic Hardware and Embedded Systems - CHES 2011 - 13th International Workshop, Nara, Japan, September 28 - October 1, 2011. Proceedings (eds. B. Preneel and T. Takagi), Lecture Notes in Computer Science, 6917, Springer, 2011,312–325. doi: 10.1007/978-3-642-23951-9_21.  Google Scholar

[14]

A. Bogdanov, L. R. Knudsen, G. Leander, F.-X. Standaert, J. Steinberger and E. Tischhauser, Key-alternating ciphers in a provable setting: Encryption using a small number of public permutations, in Advances in Cryptology – EUROCRYPT 2012, Springer, 2012, 45–62. doi: 10.1007/978-3-642-29011-4_5.  Google Scholar

[15]

B. Chakraborty and M. Nandi, Orange, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/orange-spec.pdf. Google Scholar

[16]

D. Chakraborty, S. Ghosh, C. Mancillas-López and P. Sarkar, FAST: Disk encryption and beyond, IACR Cryptology ePrint Archive, 2017 (2017), 849. Available from: URL http://eprint.iacr.org/2017/849. Google Scholar

[17]

D. ChakrabortyV. Hernandez-Jimenez and P. Sarkar, Another look at XCB, Cryptography and Communications, 7 (2015), 439-468.  doi: 10.1007/s12095-015-0127-8.  Google Scholar

[18]

D. Chakraborty, C. Mancillas-López and P. Sarkar, STES: A stream cipher based low cost scheme for securing stored data, IACR Cryptology ePrint Archive, 2013 (2013), 347. doi: 10.1109/TC.2014.2366739.  Google Scholar

[19]

D. Chakraborty and M. Nandi, An improved security bound for HCTR, in Fast Software Encryption, 15th International Workshop, FSE 2008, Lausanne, Switzerland, February 10-13, 2008, Revised Selected Papers, 2008,289–302. Google Scholar

[20]

D. Chakraborty and P. Sarkar, HCH: A new tweakable enciphering scheme using the hash-counter-hash approach, IEEE Transactions on Information Theory, 54 (2008), 1683-1699.  doi: 10.1109/TIT.2008.917623.  Google Scholar

[21]

D. Chang, N. Datta, A. Dutta, B. Mennink, M. Nandi, S. Sanadhya and F. Sibleyras, Release of unverified plaintext: Tight unified model and application to ANYDAE, IACR Trans. Symmetric Cryptol., 2019 (2019), 119–146. Google Scholar

[22]

D. Chang and M. Nandi, A short proof of the PRP/PRF switching lemma, IACR Cryptol. ePrint Arch., 2008 (2008), 78. Google Scholar

[23]

S. Chen and J. P. Steinberger, Tight security bounds for key-alternating ciphers, in EUROCRYPT 2014. Proceedings, 2014,327–350. doi: 10.1007/978-3-642-55220-5_19.  Google Scholar

[24]

Y. L. Chen, E. Lambooij and B. Mennink, How to build pseudorandom functions from public random permutations, in Advances in Cryptology - CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part I, 2019,266–293. doi: 10.1007/978-3-030-26948-7_10.  Google Scholar

[25]

B. Cogliati and Y. Seurin, On the provable security of the iterated even-mansour cipher against related-key and chosen-key attacks, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 2015,584–613. doi: 10.1007/978-3-662-46800-5_23.  Google Scholar

[26]

J. Daemen, S. Hoffert, M. Peeters, G. V. Assche and R. V. Keer, Xoodyak, a lightweight cryptographic scheme, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/Xoodyak-spec.pdf. Google Scholar

[27]

Y. Dai, Y. Seurin, J. Steinberger and A. Thiruvengadam, Indifferentiability of iterated even-mansour ciphers with non-idealized key-schedules: Five rounds are necessary and sufficient, in Annual International Cryptology Conference, Springer, 2017,524–555. doi: 10.1007/978-3-319-63697-9_18.  Google Scholar

[28]

N. Datta, A. Dutta, M. Nandi and G. Paul, Double-block hash-then-sum: A paradigm for constructing bbb secure prf, IACR Transactions on Symmetric Cryptology, 36–92. Google Scholar

[29]

N. Datta, A. Dutta, M. Nandi, G. Paul and L. Zhang, Single key variant of pmac_plus, IACR Transactions on Symmetric Cryptology, 268–305. Google Scholar

[30]

N. Datta, A. Dutta, M. Nandi and K. Yasuda, Encrypt or decrypt? To make a single-key beyond birthday secure nonce-based mac, in Annual International Cryptology Conference, Springer, 2018,631–661. doi: 10.1007/978-3-319-96884-1_2.  Google Scholar

[31]

I. DinurO. DunkelmanN. Keller and A. Shamir, Key recovery attacks on iterated even–mansour encryption schemes, Journal of Cryptology, 29 (2016), 697-728.  doi: 10.1007/s00145-015-9207-3.  Google Scholar

[32]

C. Dobraunig, M. Eichlseder, F. Mendel and M. Schläffer, Ascon v1.2, NIST LWC. Available from: URL https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/ascon-spec.pdf. Google Scholar

[33]

A. Dutta, Minimizing the two-round tweakable even-mansour cipher, in Advances in Cryptology - ASIACRYPT 2020 - 26th International Conference on the Theory and Application of Cryptology and Information Security, Daejeon, South Korea, December 7-11, 2020, Proceedings, Part I (eds. S. Moriai and H. Wang), Lecture Notes in Computer Science, 12491, Springer, 2020,601–629. doi: 10.1007/978-3-030-05378-9_3.  Google Scholar

[34]

A. Dutta and M. Nandi, Tweakable HCTR: A BBB secure tweakable enciphering scheme, in Progress in Cryptology - INDOCRYPT 2018 - 19th International Conference on Cryptology in India, New Delhi, India, December 9-12, 2018, Proceedings, 2018, 47–69. doi: 10.1007/978-3-030-05378-9_3.  Google Scholar

[35]

A. Dutta, M. Nandi and S. Talnikar, Beyond birthday bound secure mac in faulty nonce model, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 2019,437–466. doi: 10.1007/978-3-030-17653-2_15.  Google Scholar

[36]

S. Even and Y. Mansour, A construction of a cipher from a single pseudorandom permutation, J. Cryptology, 10 (1997), 151-162.  doi: 10.1007/s001459900025.  Google Scholar

[37]

S. Halevi, EME*: Extending EME to handle arbitrary-length messages with associated data. Google Scholar

[38]

S. Halevi and P. Rogaway, A tweakable enciphering mode, in CRYPTO (ed. D. Boneh), Lecture Notes in Computer Science, 2729, Springer, 2003,482–499. doi: 10.1007/978-3-540-45146-4_28.  Google Scholar

[39]

S. Halevi and P. Rogaway, A parallelizable enciphering mode, in CT-RSA (ed. T. Okamoto), Lecture Notes in Computer Science, 2964, Springer, 2004,292–304. doi: 10.1007/978-3-540-24660-2_23.  Google Scholar

[40]

V. T. Hoang, T. Krovetz and P. Rogaway, Robust authenticated-encryption AEZ and the problem that it solves, in Advances in Cryptology - EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30, 2015, Proceedings, Part I (eds. E. Oswald and M. Fischlin), Lecture Notes in Computer Science, 9056, Springer, 2015, 15–44. doi: 10.1007/978-3-662-46800-5_2.  Google Scholar

[41]

M. Kumar, Security of XCB and HCTR, in M. Tech. (Computer Science) Thesis Google Scholar

[42]

M. Liskov, R. L. Rivest and D. Wagner, Tweakable block ciphers, in Annual International Cryptology Conference, Springer, 2002, 31–46. doi: 10.1007/3-540-45708-9_3.  Google Scholar

[43]

M. LiskovR. L. Rivest and D. A. Wagner, Tweakable block ciphers, J. Cryptology, 24 (2011), 588-613.  doi: 10.1007/s00145-010-9073-y.  Google Scholar

[44]

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Figure 3.1.  $ \textsf{HCTR} $ construction based on an $ n $-bit block cipher $ \textsf{E}_k $ and an $ n $-bit Polyhash function. Left part of the algorithm is the encryption function and right part is the decryption function
Figure 3.2.  $ \textsf{HCTR} $ construction with tweak $ T $ and message $ M_1 \| M_2 \| \ldots \| M_{l} $ and the corresponding ciphertext $ C_1 \| C_2 \| \ldots \| C_{l} $. $ \textsf{Poly}_{K_h} $ is the polynomial hash function with hash key $ K_h $. $ \textsf{Ctr}_{ \textsf{E}_K} $ is the block cipher based counter mode of encryption
Figure 4.1.  $ \textsf{ppTES} $ based on an $ n $-bit public random permutations $ \pi_1 $, an AXUAR hash function $ \textsf{H}_{k_h} $ and a public permutation based length expanding PRF $ \textsf{F}^{\pi_2}_k $. $ M \in \{0,1\}^{\geq n} $ is the input message and $ T \in \{0,1\}^{\tt tw} $ is the tweak. Left part of the algorithm is the encryption function and right part is the decryption function
Figure 4.2.  Algorithm corresponding to a length expanding random function. $ \mathbb{T}[x]_{1, \ldots, b} $ denotes the first $ b $ many blocks stored at the $ x $-th entry of table $ \mathbb{T} $
Figure 6.1.  $ \textsf{ppCTR} $ construction with an $ n $-bit input $ z $ and an integer $ b = 3 $ and corresponding output $ S_1\|S_2\|S_3 $. $ \pi $ is the public random permutation, $ k $ is the key and $ \gamma $ is the root of a primitive polynomial of $ \mathrm{GF}(2^n) $
Figure 7.1.  $ \textsf{ppHCTR+} $ based on an $ n $-bit public random permutation $ \pi $ and an $ n $-bit random hash key $ k_h $. Left part is the encryption algorithm and right part is its decryption algorithm
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