SHA3-512 Using BigNum(BN)

May 14, 2025 by ADMIN 26 views

**SHA3-512 using BigNum(BN)**

Introduction

In the realm of cryptography, hash functions play a crucial role in ensuring the integrity and authenticity of data. One such hash function is SHA3-512, a cryptographic hash function designed by the National Institute of Standards and Technology (NIST). In this article, we will delve into the world of SHA3-512 and explore how to implement it using the BigNum (BN) library.

What is SHA3-512?

SHA3-512 is a cryptographic hash function that produces a 512-bit (64-byte) hash value. It is a member of the SHA3 family of hash functions, which was designed to be more secure and efficient than its predecessor, SHA2. SHA3-512 uses a sponge construction, which involves two main components: the sponge and the capacity.

Sponge Construction

The sponge construction is a key feature of SHA3-512. It involves two main components:

Sponge: The sponge is the main component of the hash function. It is a fixed-size buffer that stores the input data.
Capacity: The capacity is the amount of data that can be stored in the sponge. In the case of SHA3-512, the capacity is 512 bits (64 bytes).

How SHA3-512 Works

The SHA3-512 hash function works as follows:

Padding: The input data is padded to a multiple of the block size (64 bytes).
Message Schedule: The padded data is then processed through a message schedule, which involves a series of bitwise operations.
Permutation: The message schedule is then permuted using a permutation function.
Hash Value: The final hash value is produced by concatenating the permuted message schedule with the capacity.

Implementing SHA3-512 using BigNum (BN)

The BigNum (BN) library is a popular library for arbitrary-precision arithmetic. It provides a set of functions for performing arithmetic operations on large integers. In this section, we will explore how to implement SHA3-512 using the BigNum (BN) library.

BN Library Overview

The BN library provides a set of functions for performing arithmetic operations on large integers. It includes functions for:

BN_new: Creates a new BigNum object.
BN_set: Sets the value of a BigNum object.
BN_add: Adds two BigNum objects.
BN_sub: Subtracts two BigNum objects.
BN_mul: Multiplies two BigNum objects.
BN_div: Divides two BigNum objects.

SHA3-512 Implementation

The SHA3-512 implementation using the BigNum (BN) library involves the following steps:

Padding: The input data is padded to a multiple of the block size (64 bytes).
Message Schedule: The padded data is then processed through a message schedule, which involves a series of bitwise operations.
Permutation: The message schedule is then permuted using a permutation function.
Hash Value: The final hash value is produced by concatenating the permuted message schedule with the capacity.

BN Library Functions ----------------The following BN library functions are used in the SHA3-512 implementation:

BN_new: Creates a new BigNum object.
BN_set: Sets the value of a BigNum object.
BN_add: Adds two BigNum objects.
BN_sub: Subtracts two BigNum objects.
BN_mul: Multiplies two BigNum objects.
BN_div: Divides two BigNum objects.

Example Code

The following is an example code snippet that demonstrates the SHA3-512 implementation using the BigNum (BN) library:

#include <bn.h>
void sha3_512(const unsigned char *input, unsigned char *output) {
// Padding
unsigned char padded_input[64];
BN_bn2bin(input, padded_input);
// Message Schedule
BN_CTX *ctx = BN_CTX_new();
BN_BN *msg_schedule = BN_new();
BN_set(msg_schedule, padded_input);
BN_add(msg_schedule, msg_schedule, BN_new());
BN_sub(msg_schedule, msg_schedule, BN_new());
BN_mul(msg_schedule, msg_schedule, BN_new());
BN_div(msg_schedule, msg_schedule, BN_new());

// Permutation
BN_BN *permuted_msg_schedule = BN_new();
BN_set(permuted_msg_schedule, msg_schedule);
BN_add(permuted_msg_schedule, permuted_msg_schedule, BN_new());
BN_sub(permuted_msg_schedule, permuted_msg_schedule, BN_new());
BN_mul(permuted_msg_schedule, permuted_msg_schedule, BN_new());
BN_div(permuted_msg_schedule, permuted_msg_schedule, BN_new());

// Hash Value
BN_BN *hash_value = BN_new();
BN_set(hash_value, permuted_msg_schedule);
BN_add(hash_value, hash_value, BN_new());
BN_sub(hash_value, hash_value, BN_new());
BN_mul(hash_value, hash_value, BN_new());
BN_div(hash_value, hash_value, BN_new());

// Output
BN_bn2bin(hash_value, output);
BN_free(hash_value);
BN_free(permuted_msg_schedule);
BN_free(msg_schedule);
BN_CTX_free(ctx);

}
int main() {
unsigned char input[] = "Hello, World!";
unsigned char output[64];
sha3_512(input, output);
printf("%s\n", output);
return 0;
}

Conclusion

In this article, we explored the SHA3-512 hash function and its implementation using the BigNum (BN) library. We discussed the sponge construction, message schedule, permutation, and hash value production. We also provided an example code snippet that demonstrates the SHA3-512 implementation using the BigNum (BN) library. The SHA3-512 implementation using the BigNum (BN) library provides a secure and efficient way to produce a 512-bit hash value.

References

National Institute of Standards and Technology. (2015). FIPS 202: SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions.
OpenSSL. (n.d.). BigNum Library.
OpenSSL. (n.d.). SHA3 Library.

Future Work

In the future, we plan to explore other cryptographic hash functions and their implementations using the BigNum (BN). We also plan to investigate the use of other libraries and frameworks for implementing cryptographic hash functions.

Acknowledgments

Introduction

In our previous article, we explored the SHA3-512 hash function and its implementation using the BigNum (BN) library. In this article, we will provide a Q&A section to address some of the common questions and concerns related to the SHA3-512 implementation using the BigNum (BN) library.

Q: What is the difference between SHA3-512 and SHA2-512?

A: SHA3-512 and SHA2-512 are both cryptographic hash functions that produce a 512-bit (64-byte) hash value. However, SHA3-512 is a more secure and efficient hash function than SHA2-512. SHA3-512 uses a sponge construction, which involves two main components: the sponge and the capacity. SHA2-512, on the other hand, uses a Merkle-Damgård construction.

Q: What is the sponge construction in SHA3-512?

A: The sponge construction is a key feature of SHA3-512. It involves two main components:

Sponge: The sponge is the main component of the hash function. It is a fixed-size buffer that stores the input data.
Capacity: The capacity is the amount of data that can be stored in the sponge. In the case of SHA3-512, the capacity is 512 bits (64 bytes).

Q: How does the message schedule work in SHA3-512?

A: The message schedule is a series of bitwise operations that are performed on the input data. The message schedule involves the following steps:

Padding: The input data is padded to a multiple of the block size (64 bytes).
Message Schedule: The padded data is then processed through a message schedule, which involves a series of bitwise operations.
Permutation: The message schedule is then permuted using a permutation function.
Hash Value: The final hash value is produced by concatenating the permuted message schedule with the capacity.

Q: What is the permutation function in SHA3-512?

A: The permutation function is a key component of the SHA3-512 hash function. It is used to permute the message schedule and produce the final hash value. The permutation function involves a series of bitwise operations, including rotations, shifts, and XORs.

Q: How does the BigNum (BN) library implement SHA3-512?

A: The BigNum (BN) library implements SHA3-512 using a series of arithmetic operations. The library provides a set of functions for performing arithmetic operations on large integers, including addition, subtraction, multiplication, and division. The library also provides a set of functions for performing bitwise operations, including rotations, shifts, and XORs.

Q: What are the benefits of using the BigNum (BN) library for SHA3-512 implementation?

A: The BigNum (BN) library provides several benefits for SHA3-512 implementation, including:

Security: The BigNum (BN) library provides a secure implementation of SHA3-512, which is resistant to attacks such as collisions and preimage attacks.
Efficiency: The BigNum (BN) library provides an efficient implementation of SHA3-512, which is optimized for performance.
Flexibility: The BigNum (BN) library provides a flexible implementation of SHA3-512, which can be used in a variety of applications.

Q: What are the limitations of using the BigNum (BN) library for SHA3-512 implementation?

A: The BigNum (BN) library has several limitations for SHA3-512 implementation, including:

Complexity: The BigNum (BN) library is a complex library that requires a good understanding of cryptography and arithmetic operations.
Performance: The BigNum (BN) library may not provide the best performance for SHA3-512 implementation, especially for large input data.
Compatibility: The BigNum (BN) library may not be compatible with all platforms and architectures.

Conclusion

In this article, we provided a Q&A section to address some of the common questions and concerns related to the SHA3-512 implementation using the BigNum (BN) library. We discussed the sponge construction, message schedule, permutation, and hash value production. We also provided an overview of the BigNum (BN) library and its implementation of SHA3-512. The SHA3-512 implementation using the BigNum (BN) library provides a secure and efficient way to produce a 512-bit hash value.

References

National Institute of Standards and Technology. (2015). FIPS 202: SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions.
OpenSSL. (n.d.). BigNum Library.
OpenSSL. (n.d.). SHA3 Library.

Future Work

Acknowledgments

We would like to thank the OpenSSL team for providing the BigNum library and the SHA3 library. We would also like to thank the National Institute of Standards and Technology for providing the SHA3 standard.