TrustNote Cryptographic Algorithms Overview
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A quick overview of the cryptographic algorithms used by TrustNote, including hash function, signature algorithm, PoW algorithm For detailed technical information, please visit https://github.com/trustnote/document/blob/master/TrustNote-TR-2018-01.md
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Finite Field Arithmetic (1 of 2)
• In the Advanced Encryption Standard (A E S) all operations are
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Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.1 A E S Encryption Process
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.2 A E S Data Structures
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Table 6.1 A E S Parameters
Key Size (words/bytes/bits) 4/16/128 6/24/192 8/32/256
Plaintext Block Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Number of Rounds 10 12 14
Round Key Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Expanded Key Size (words/bytes) 44/176 52/208 60/240
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.3 A E S Encryption and Decryption
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
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Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
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Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.1 A E S Encryption Process
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.2 A E S Data Structures
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Table 6.1 A E S Parameters
Key Size (words/bytes/bits) 4/16/128 6/24/192 8/32/256
Plaintext Block Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Number of Rounds 10 12 14
Round Key Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Expanded Key Size (words/bytes) 44/176 52/208 60/240
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.3 A E S Encryption and Decryption
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Detailed Structure (1 of 2)
• Processes the entire data block as a single matrix during
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• The key that is provided as input is expanded into an array
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• Four different stages are used:
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Finite Field Arithmetic (1 of 2)
• In the Advanced Encryption Standard (A E S) all operations are
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• The arithmetic operations of addition, multiplication, and division
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• An example of a finite field (one with a finite number of
elements) is the set Zp consisting of all the integers {0, 1, . . . . ,
p − 1}, where p is a prime number and in which arithmetic is
carried out modulo p
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Finite Field Arithmetic (2 of 2)
• If one of the operations used in the algorithm is division, then we need
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– Division requires that each nonzero element have a multiplicative
inverse
• For convenience and for implementation efficiency we would like to
work with integers that fit exactly into a given number of bits with no
wasted bit patterns
– Integers in the range 0 through 2n – 1, which fit into an n-bit word
• The set of such integers, Z2
n, using modular arithmetic, is not a field
– For example, the integer 2 has no multiplicative inverse in Z2
n, that
is, there is no integer b, such that 2b mod 2n = 1
• A finite field containing 2n elements is referred to as G F(2n)
– Every polynomial in G F(2n) can be represented by an n-bit
number
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.1 A E S Encryption Process
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.2 A E S Data Structures
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Table 6.1 A E S Parameters
Key Size (words/bytes/bits) 4/16/128 6/24/192 8/32/256
Plaintext Block Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Number of Rounds 10 12 14
Round Key Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Expanded Key Size (words/bytes) 44/176 52/208 60/240
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.3 A E S Encryption and Decryption
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Detailed Structure (1 of 2)
• Processes the entire data block as a single matrix during
each round using substitutions and permutation
• The key that is provided as input is expanded into an array
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• Four different stages are used:
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Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Finite Field Arithmetic (1 of 2)
• In the Advanced Encryption Standard (A E S) all operations are
performed on 8-bit bytes
• The arithmetic operations of addition, multiplication, and division
are performed over the finite field G F(28)
• A field is a set in which we can do addition, subtraction,
multiplication, and division without leaving the set
• Division is defined with the following rule:
– a /b = a (b−1 )
• An example of a finite field (one with a finite number of
elements) is the set Zp consisting of all the integers {0, 1, . . . . ,
p − 1}, where p is a prime number and in which arithmetic is
carried out modulo p
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Finite Field Arithmetic (2 of 2)
• If one of the operations used in the algorithm is division, then we need
to work in arithmetic defined over a field
– Division requires that each nonzero element have a multiplicative
inverse
• For convenience and for implementation efficiency we would like to
work with integers that fit exactly into a given number of bits with no
wasted bit patterns
– Integers in the range 0 through 2n – 1, which fit into an n-bit word
• The set of such integers, Z2
n, using modular arithmetic, is not a field
– For example, the integer 2 has no multiplicative inverse in Z2
n, that
is, there is no integer b, such that 2b mod 2n = 1
• A finite field containing 2n elements is referred to as G F(2n)
– Every polynomial in G F(2n) can be represented by an n-bit
number
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.1 A E S Encryption Process
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.2 A E S Data Structures
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Table 6.1 A E S Parameters
Key Size (words/bytes/bits) 4/16/128 6/24/192 8/32/256
Plaintext Block Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Number of Rounds 10 12 14
Round Key Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128
Expanded Key Size (words/bytes) 44/176 52/208 60/240
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Figure 6.3 A E S Encryption and Decryption
Copyright © 2020 Pearson Education, Inc. All Rights Reserved.
Detailed Structure (1 of 2)
• Processes the entire data block as a single matrix during
each round using substitutions and permutation
• The key that is provided as input is expanded into an array
of forty-four 32-bit words, w[i]
• Four different stages are used:
– Substitute bytes – uses an S-box to perform a byte-by-
byte substitution of the block
– ShiftRows – a simple permutation
– MixColumns – a substitution that makes use of
arithmetic over GF(28)
– AddRoundKey – ...
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TrustNote Cryptographic Algorithms Overview
- 2. Institute of Technology TrustNote uses Blake2 as the hash function. The reasons are: 1. High hash rate 2. Reliability Hash Function
- 3. Institute of Technology 0 5 10 15 20 25 BLAKE2b BLAKE2s MD5 SHA-1 SHA-256 SHA-512 SHA3-256 SHA3-512 CyclesperbytespeedonIntelSandyBridge Hash Function Name mebibytes per second at 3.1 GHz 890 554 550 571 169 266 271 144 Blake2 comes in many flavours but the main category is Blake2b and Blake2s. The difference between b and s mostly relies on their Digest length, microcontroller/CPU structure they are optimized to support. Max Digest Length: Blake 2s = 256 bit Blake 2b = 512 bit
- 4. Institute of Technology Parameter Blocks of Blake2b Offset 0 1 2 3 0 Digest length Key length Fanout Depth 4 Leaf length 8 12 Node offset 16 Node depth Inner length RFU 20 24 28 RFU 32 … 44 Salt 48 … 60 Personalization BLAKE2b parameter block structure (offsets in bytes)
- 5. Institute of Technology Parameter Blocks of Blake2s Offset 0 1 2 3 0 Digest length Key length Fanout Depth 4 Leaf length 8 Node offset 12 Node offset (cont.) Node depth Inner length 16 20 Salt 24 28 Personalization BLAKE2s parameter block structure (offsets in bytes)
- 6. Institute of Technology C/C++ Addon Implementation of Blake2b and Blake2s: 6,605,304 hashes for Blake2b with maximum digest length 7,128,410 hashes for Blake2s with maximum digest length
- 7. Institute of Technology TrustNote uses Ed25519 as the signature algorithm. The reasons are: 1. Fast single-signature verification Reliability. 2. Very fast signing 3. Fast key generation 4. High security level 5. Collision resilience 6. Foolproof session keys 7. And so on Public-Key Cryptography Algorithm
- 9. Institute of Technology A is the public key point a is the public key H(*) is the Blake2 hash of * B is the unique point (x, 4/5) ∈ E for which x is positive M is the message l is the prime 2^252 + 27742317777372353535851937790883648493 Ed25519 Terms
- 10. Institute of Technology Ed25519 Sign / Verify Steps for signature 1. computing r = H(hb, . . . , h2b−1, M) 2. computing R = rB 3. computing S = (r + H(R, A, M)a) mod l Verification SB = R + H(R, A, M)A
- 11. Institute of Technology Ed25519 Sign
- 12. Institute of Technology Ed25519 Verify
- 13. Institute of Technology Ed25519 Fast Single Verify SB = R + H(R, A, M)A is changed to R = SB - H(R, A, M)A Saving having to decompress R
- 14. Institute of Technology Curve25519 Performance
- 15. Institute of Technology Curve25519 Performance
- 16. Institute of Technology Ed25519 Performance
- 17. Institute of Technology Ed25519 Performance
- 18. Institute of Technology C/C++ Addon Implementation of Ed25519: During 5 seconds, this package generates, signs and verifies 4,198 keys.
- 19. Institute of Technology TrustNote uses Equihash based on CPU and GPU. The reasons are: 1. ASIC resistant. 2. More fair for users. 3. More randomness. PoW Algorithms
- 20. Institute of Technology Equihash Algorithm
- 21. Institute of Technology C/C++ Implementation of Equihash with no difficulty filter N (bits) K Seed Time (ms) Difficulty Solution Size (KB) Number of solutions found 100 4 5 5,155 1 81,920 16 100 4 20 15,281 1 81,920 16 108 5 5 2,843 1 25,600 32 108 5 20 8,499 1 25,600 32 110 4 20 21,967 1 327,680 16 110 4 5 22,062 1 327,680 16 126 5 5 49,077 1 204,800 32 126 5 20 36,797 1 204,800 32
- 22. Institute of Technology Questions? Business Enquires: foundation@trustnote.org Technical Support: community@trustnote.org