Security

BFV, CKKS, LWE FHE Ciphertext Noise Budget, Relin and Bootstrapping Explainer

Run a real miniature BFV/CKKS pipeline over Z_q[x]/(xⁿ+1): exact invariant-noise budgets in bits, ciphertext multiplication with relinearization, modulus switching, SIMD slot packing and a bootstrapping refresh.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer' \
  -H 'Content-Type: application/json' \
  -d '{"scheme":"bfv-deep-multiply","ringDegree":"32","levels":2,"slotValues":"12, 34, 56, 78","multiplyDepth":4,"showBootstrap":true}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer

Parameters

Name	Type	Required	Description
scheme	select	No	—
ringDegree	select	No	—
levels	number	No	—
slotValues	text	Yes	—
multiplyDepth	number	No	—
showBootstrap

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer": {
      "name": "bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer",
      "description": "Run a real miniature BFV/CKKS pipeline over Z_q[x]/(xⁿ+1): exact invariant-noise budgets in bits, ciphertext multiplication with relinearization, modulus switching, SIMD slot packing and a bootstrapping refresh.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "bfv-ckks-lwe-fhe-ciphertext-noise-budget-relin-and-bootstrapping-explainer",
    "arguments": {
  "scheme": "bfv-deep-multiply",
  "ringDegree": "32",
  "levels": 2,
  "slotValues": "12, 34, 56, 78",
  "multiplyDepth": 4,
  "showBootstrap": true
}
  }
}

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