Microcredit Regulatory Authority (MRA) Assistant Maintenance Engineer Exam: 2022প্রশ্ন ও সমাধান

Digital signature is a cryptographic technique that binds a signer's identity to a piece of digital data, providing authentication (proves who sent it), integrity (proves the data wasn't altered), and non-repudiation (the signer cannot later deny signing it) — the digital equivalent of a handwritten signature, but mathematically verifiable.

How it works (asymmetric cryptography + hashing):

1. Sender computes a hash (e.g. SHA-256) of the message.
2. Sender encrypts that hash with their own private key → this encrypted hash is the "signature".
3. Sender transmits the original message plus the signature.
4. Receiver decrypts the signature using the sender's public key, recovering the original hash.
5. Receiver independently computes the hash of the received message and compares it to the decrypted one.
6. A match proves the message came from the claimed sender and was not modified in transit.

sequenceDiagram
    participant S as Sender
    participant R as Receiver
    S->>S: Hash(Message) = H1
    S->>S: Encrypt H1 with Sender's Private Key = Signature
    S->>R: Message + Signature
    R->>R: Decrypt Signature with Sender's Public Key = H1'
    R->>R: Hash(received Message) = H2
    R->>R: Compare H1' with H2
    Note over R: Equal => Authentic and Unaltered

Applications: e-governance/tax filing portals, code/software signing, SSL/TLS certificates, S/MIME signed email, blockchain transactions.

Exam takeaway: digital signature = hash + encryption with the sender's private key; verification uses the sender's public key — this asymmetry is what makes it legally and technically non-repudiable, unlike a plain checksum or MAC.

Given: bandwidth B = 300 Hz, signal-to-noise ratio = 3 dB.

Step 1 — convert the SNR from dB to a plain power ratio:
SNR(dB) = 10·log10(S/N) ⟹ S/N = 10^(SNR(dB)/10)
S/N = 10^(3/10) = 10^0.3 ≈ 1.995

Step 2 — apply Shannon's channel capacity formula:
C = B · log2(1 + S/N)

Step 3 — substitute values:
C = 300 × log2(1 + 1.995)
C = 300 × log2(2.995)

Step 4 — evaluate log2(2.995):
log2(2.995) = ln(2.995) / ln(2) ≈ 1.097 / 0.693 ≈ 1.583

Step 5 — final multiplication:
C ≈ 300 × 1.583 ≈ 474.9 bps

Answer: C ≈ 475 bps (≈ 474.9 bps)

Exam takeaway: always convert a dB signal-to-noise ratio to a linear power ratio, 10^(dB/10), before substituting into Shannon's formula C = B log2(1+S/N) — plugging the raw dB figure directly into the formula is a common and serious mistake.