List down various modes of operations of block cipher and explain anythree of them briefly.

Block ciphers can operate in several modes, each offering different security characteristics. The most common modes of operation are:

1. Electronic Codebook (ECB)
2. Cipher Block Chaining (CBC)
3. Cipher Feedback (CFB)
4. Output Feedback (OFB)
5. Counter (CTR)

Let's explain three of them:

1. Electronic Codebook (ECB): This is the simplest mode of operation. Each block of plaintext is encrypted separately with the block cipher algorithm. This means that identical plaintext blocks are encrypted into identical ciphertext blocks; thus, it does not hide data patterns well. So, its use is not recommended in most cases.

2. Cipher Block Chaining (CBC): In this mode, each block of plaintext is XORed with the previous ciphertext block before being encrypted. This way, each ciphertext block depends on all plaintext blocks processed up to that point. To make each message unique, an initialization vector must be used in the first block.

3. Counter (CTR): In CTR mode, a counter value is also used along with the plaintext to encrypt. The counter is initialized to some value and then increased by one for each subsequent block. The counter value must be different for each plaintext block that is encrypted. The encrypted counter value is then XORed with the plaintext to produce the ciphertext. This mode turns a block cipher into a stream cipher and allows for precomputation of the XOR masks, which can lead to performance improvements.

Each mode has its advantages and disadvantages, and the choice of which to use depends on the specific requirements of the cryptographic system being designed.