• Base64 encoding converts 3 bytes (24 bits) into 4 characters
• Each Base64 character represents 6 bits
• 24 is the least common multiple of 6 (character bit width) and 8 (byte bit width)
• Without alignment, converting concatenated primitives between text and binary domains would create bit-level dependencies between adjacent primitives

Lead Bytes vs. Pad Characters

The terminology distinction is critical:

Traditional Base64 (post-padding):

• Converts raw binary to Base64
• Appends = characters to reach 4-character boundaries
• Example: 2-byte value → 3 Base64 chars + 1 = pad

CESR Approach (pre-padding with lead bytes):

• Prepends zero bytes to raw binary first
• Then converts to Base64
• No = characters needed
• Example: 2-byte value → prepend 1 zero byte → 3 bytes total → 4 Base64 chars

Calculation Formula

The number of lead bytes (ps) required is calculated as:

ps = (3 - (N mod 3)) mod 3

Where N is the size of the raw binary value in bytes.

• If N mod 3 = 0: No lead bytes needed (ps = 0)
• If N mod 3 = 1: Two lead bytes needed (ps = 2)
• If N mod 3 = 2: One lead byte needed (ps = 1)

Relationship to Derivation Codes

In CESR, the Base64 characters that result from encoding the lead bytes are replaced with derivation codes that indicate the primitive type and size. This replacement is possible because:

• Lead bytes contain no information (all zeros)
• The number of lead bytes determines how many characters can be replaced
• The derivation code length matches the number of characters produced by lead bytes

For example, a 1-byte value requires 2 lead bytes, producing 4 Base64 characters total. The first 2-3 characters (from lead bytes) can be replaced with type codes, while the remaining characters encode the actual value.

Importance for Streaming

Lead bytes enable CESR's self-framing property:

• Parsers can read the derivation code to determine primitive type and total length
• No lookahead or external delimiters needed
• Primitives can be concatenated and parsed in streams
• Conversion between text domain and binary domain preserves primitive boundaries

Related Terms

• Pre-pad: The action of prepending lead bytes
• Post-pad: Traditional trailing pad character approach
• Framing code: Type codes that replace lead byte positions
• Composability: The property that lead bytes enable
• Primitive: The cryptographic values that require lead byte alignment