Cryptographic Algorithms & Attacks

Linear Congruental Generator (LCG)

• Formula: $k\cdot x+d(\mathrm{mod}8)$ (using Seed = 0).
• Characteristics: Fast, simple implementation, but predictable output distribution.

Blum Blum Shub (BBS) Mitigations

• Non-uniform distribution issues require smoothing, averaging, or taking every second output value.
• Entropy Extraction: Restrict output evaluation to specific bit positions (e.g., last 2 digits).

Square & Multiply

• Efficient algorithm used for exponentiation (e.g., $2^5$).
• Side-Channel Vulnerabilities: Execution time, power consumption, and stack movement leak state data during execution.
• Mitigation: Implement dummy multiplications (multiply by 1 when bit is 0), disable compiler optimizations, mask jumps, and complete execution loops even when remaining operations are zero.

Cryptanalytic Concepts

• Meet-in-the-Middle: Reduces time complexity bounds (comparing $n^2$ vs $2n$).
• Block Cipher Modes: Electronic Codebook (ECB) mode reveals structural patterns in identical plaintext blocks.
• Feistel Networks: Non-linear structures containing fixed points; linear functions within linear components produce linear outputs, yielding poor entropy characteristics.