EVHEN. Asymmetric SPN-cipher (RusCrypto-2017)
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The document describes a proposed chaotic asymmetric white-box cipher called EVHEN. It uses randomly generated S-boxes and MDS matrices for each round to conceal the linear relationships between elements. The cipher transforms a symmetric block cipher into an asymmetric one by hiding the symmetric key in an obfuscated implementation of the encryption algorithm, allowing both encryption and signing. The goal is to create a fast asymmetric cipher that reduces communication overhead compared to traditional public key cryptography.
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EVHEN. Asymmetric SPN-cipher (RusCrypto-2017)
- 1. CREATING ASYMMETRIC SPN-CIPHER WITH WHITE-BOX CRYPTOGRAPHY AND CHAOTIC MAPS PhD, Dmitry Schelkunov Bauman Moscow State Technical University, Kaluga branch RusCrypto-2017
- 2. White-box cryptography Allows to transform a symmetric block cipher to the asymmetric one by hiding a symmetric key in the obfuscated implementation (white-box implementation) of the encryption algorithm Aims to create fast asymmetric ciphers that allow both encryption and signing Would make a communication much lighter, faster and secure (there would be no need for Diffie-Hellman key exchange algorithm) One would communicate simultaneously with 2 and more others encryptingdecrypting a content "on-the-fly" without fear of the sender spoofing
- 3. Related work Chow S., Eisen P., Johnson H., Van Oorschot P.C. (2003), White-Box Cryptography and an AES Implementation. In: Nyberg K., Heys H. (eds) Selected Areas in Cryptography. SAC 2002. Lecture Notes in Computer Science, vol 2595. Springer, Berlin, Heidelberg Olivier Billet and Henri Gilbert. A Traceable Block Cipher. In Advances in Cryptology - ASIACRYPT 2003, volume 2894 of Lecture Notes in Computer Science, pages 331-346. Springer-Verlag, 2003 Olivier Billet, Henri Gilbert, and Charaf Ech-Chatbi. Cryptanalysis of a White-Box AES Implementation. In Proceedings of the 11th International Workshop on Selected Areas in Cryptography (SAC 2004), volume 3357 of Lecture Notes in Computer Science, pages 227240. Springer-Verlag, 2004. Brecht Wyseur, White-box cryptography, PhD thesis, March 2009 Dmitry Schelkunov, White-Box Cryptography and SPN ciphers. LRC method, Cryptology ePrint Archive: Report 2010/419 Brecht Wyseur, White-box cryptography: hiding keys in software, MISC magazine, April 2012 Joppe W. Bos and Charles Hubain and Wil Michiels and Philippe Teuwen, Differential Computation Analysis: Hiding your White-Box Designs is Not Enough, Cryptology ePrint Archive: Report 2015/753
- 4. Attacks on white-box implementations Almost all attacks are based on separation of known linear and non- linear parts of the source symmetric cipher and added white-box transformations Differential cryptanalysis (including fault injection) Algebraic cryptanalysis Extraction of the non-linear part (Olivier Billet, Henri Gilbert, and Charaf Ech-Chatbi. Cryptanalysis of a White-Box AES Implementation)
- 5. Method of concealing of a linear relationship n,xa,b,c,d,x npp ppcbax pcpbax thanlessdegreeswithspolinomial degreewithspolynomialeirreducibl, (1) )))(mod)(mod(( ))(mod))(mod(( 21 21 122 211 21 xx
- 6. Method of concealing of a linear relationship tableslookupassetare)(),( unknownare,,,,,,, thanlessdegreeswith)(overspolynomialarbitrary,,,, degreewith)( overspolynomialeirreduciblunequalpairwice,, )2( )(mod))(mod)(()( )(mod))(mod)(()( 21 321 321 312 211 xyxy dcbaxppp nGFdcbax nGF ppp pdpcxsxy pbpaxsxy
- 7. Method of concealing of a linear relationship )(mod)(and)(mod)( betweeniprelationshlinearafind:PROBLEM )2( )(mod))(mod)(()( )(mod))(mod)(()( 11 312 211 pcxspaxs pdpcxsxy pbpaxsxy
- 8. Method of concealing of a linear relationship caxyxy p dqpdcxs q p bqpbaxs q p cxs q p axs q qpdqpdcxsxy qpbqpbaxsxy pdqpcxsxy pbqpaxsxy andFindtables).(lookupknownare)(,)(:PROBLEM ')( ; )( ; )( '; )( )4( ')()( )()( )3( )(mod)')(()( )(mod))(()( 21 3 11 3 2 11 2 1 1 1 1 33112 22111 3112 2111 緒 緒 緒 RLWE?
- 9. Method of concealing of a linear relationship Make (2) harder (5) )(mod)...)(mod))(mod)((...()( )(mod)...)(mod))(mod)((...()( )()()0( 3 )0( 12 )()()0( 2 )0( 11 k v k k u k pdpdpcxsxy pbpbpaxsxy )()( ￥ jppi )!2,2min(:Hardness 2)1(2 nkn
- 10. Chaos theory in cryptography Goce Jakimoski and Ljupco Kocarev, Chaos and Cryptography: Block Encryption Ciphers Based on Chaotic Maps. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 48, NO. 2, FEBRUARY 2001 Asim, M., Jeoti, V.: Efficient and simple method for designing chaotic S-boxes. ETRI Journal 30(1), 170172 (2008) Mona Dara and Kooroush Manochehri, A Novel Method for Designing S-Boxes Based on Chaotic Logistic Maps Using Cipher Key. World Applied Sciences Journal 28 (12): 2003-2009, 2013 Christopher A. Wood, Chaos-Based Symmetric Key Cryptosystems Dragan Lambi and Miodrag 貼ivkovi, COMPARISON OF RANDOM S-BOX GENERATION METHODS. PUBLICATIONS DE LINSTITUT MATHMATIQUE Nouvelle s辿rie, tome 93 (107) (2013)
- 11. Designing S-boxes with chaotic maps Good cryptographic properties Simple algorithms Random S-boxes with good cryptographic properties allow to increase a security of a white-box implementation
- 12. MDS codes and MDS matrix MDS matrix (Maximal Distance Separable matrix) is a generating matrix of an MDS code Maximal diffusion by design Is used in SPN-ciphers in diffusion layers Interesting types of matrices: Vandermonde matrix Involutory matrix (the same MDS matrix for encryption and decryption) Cauchy matrix Circulant matrix (like in Rijndael)
- 13. Cauchy matrix MDS matrix by design Simple algorithm of generation regardless of dimension The property of circularity is not principal for the white-box implementation The property of involutivity is harmful for the white-box implementation So, choose a Cauchy matrix k ijjijijiij GFayxnjmiyxyxa 2,,;0;0;0; 1 種ｏ種ｏ刻
- 14. A round of SPN-cipher Nonlinear part (S-boxes) Add round key Diffusion layer (MDS matrix + shifts)
- 15. A round of SPN cipher and T-boxes (Rijndael)
- 16. Chaotic asymmetric white-box SPN cipher S-boxes (8x8 bits) are generated randomly (using chaotic maps) for the every of the input bytes of the every of the rounds MDS matrix (16x16 bytes) is generated randomly (Cauchy matrix) for the every of the rounds A white-box implementation is based on obfuscation of the T-boxes A linear relationship between elements of the T-box is obfuscated with method of concealing of a linear relationship A set of the obfuscated T-boxes is a public key
- 17. A round of the chaotic asymmetric white-box SPN cipher iprelationshlinearaofconcealingofmethodusingnobfuscatio 2overmatrixMDStheofelementeappropriaton thetionmultiplica box-Sunique )0ifbyteinputan(orroundprevioustheofbyteoutput )6( ))((( ... ))((( ))((( ... ))((( ... ))((( ))((( ))((( ... ))((( ))((( ... )15( 8),( )( )0( 1 )15( 1 )15()15,315()15( )15( 1 )15()15,1()1( )15( 1 )15()15,0()0( )1( 1 )1()1,15()15( )1( 1 )1()1,1()1( )1( 1 )1()1,0()0( )0( 1 )0()0,15()15( )0( 1 )0()0,1()1( )0( 1 )0()0,0()0( )15( )1( )0( 緒 j kl j k j j jjjj jjjj jjjj jjjj jjjj jjjj jjjj jjjj jjjj j j j j mix )GF(t s jy ystmix ystmix ystmix ystmix ystmix ystmix ystmix ystmix ystmix y y y Y
- 18. Hiding a linear relationship between elements of the T-box )GF(hp )GF(b t valpbpbpbat valpbpbpbat valpbpbpbat valpbpbpbat valpbpbpbat aT uj i huj i n i n kn i kn i n i n i n i n i n i k i k iiiiii k i k iiiiii k i k iiiiii k i k iiiiii i nn 2overdegreewithpolinomialeirreduciblselectedrandomly 2inpolinomialselectedrandomly nobfuscatiobeforebox-Ttheofelement )7( )(mod)...)(mod))(mod)(((...( .......................................................................... )(mod)...)(mod))(mod)(((...( )(mod)...)(mod))(mod)(((...( )(mod)...)(mod))(mod)(((...( )(mod)...)(mod))(mod)(((...( ][' ),( ),( )( ),(),()1,()1,()0,()0,()( 3 ),3(),3()1,3()1,3()0,3()0,3()3( 2 ),2(),2()1,2()1,2()0,2()0,2()2( 1 ),1(),1()1,1()1,1()0,1()0,1()1( 0 ),0(),0()1,0()1,0()0,0()0,0()0( 33 22 11 00 ),(),1(),0( ... vn i v i v i ppp 刻刻
- 19. EVHEN. A chaotic asymmetric white-box cipher Is named in honor of two greatest mathematicians: Evariste Galois and Jules Henri Poincare Allows both encryption and signing of messages with a speed of a classical block cipher A size of a public key: 640 Kbytes Light requirements: 16 xors of 16-byte values per round. Only 3 operations: memory read, xor and memory write
- 21. Links EVHEN source code: https://github.com/dmschelkunov/EVHEN Authors blog: http://dschelkunov.blogspot.com Authors e-mail: d.schelkunov@gmail.com